Harvard Mathematics Department : Undergraduate Events: Math table and Open Neighborhood Seminar

The undergraduate Mathematics Colloquium (aka Math Table) sponsored by the Mathematics Department, meets every other Wednesday night at 5:30pm PM in Science Center 507. Talks are catered with dinner starting at 6pm, and a half-hour talk starting at 6pm. Each week, students give talks on diverse topics of pure and applied mathematics. Students, irrespective of their mathematical backgrounds, are strongly encouraged to attend and/or to give talks. Unlike in years past, faculty talks aimed at students will take place in the Open Neighborhood Seminar, (here are older events), which meets on the other Wednesday nights at 4:30pm in SC 507. Please check out the

Undergraduate events page
for a calendar. Students interested in giving a talk can contact or Voula Collins. We are happy to suggest ideas for talk topics and work with you on preparing a talk!.

Voula Collins vcollins@math

Prizes

Please congratulate the recipients of the Department's undergraduate prizes and awards:

David Mumford Undergraduate Mathematics Prize: from the income of the gift in 1997 of Peter L. Falb, A.B. 1957, A.M. 1957, Ph.D. 1961 to establish the David B. Mumford Undergraduate Mathematics Prize, to be given annually to the most promising senior concentrator in mathematics, provided such concentrator is outstanding. The Mumford Prize will be shared by Peter Chen Vaughan McDonald and Filippos Sytilidis
Herb Alexander Award: from the gift of Susan Alexander, the Herb Alexander Award recognizes each year one of our outstanding undergraduates, and provides money to be used for research and travel. The Herb Alexander Award is given this year to Natalia Pacheco-Tallaj
Robert Fletcher Rogers Prizes: From the income of the gift in 1921 of the late Robert Fletcher Rogers, A.B. 1886, there have been established a first prize and second prize to be awarded annually to the College students who present the best talks before the Mathematics Table during an academic year. The Robert Fletcher Rogers Prizes are given this year to First place: Kim Nguyen Second place will be shared by Savvy Raghuvanshi and Lucy Wang
Friends Prize: Each year, two of our senior thesis writers are selected to present talks on their theses to the Friends of the Harvard Math department. The Friends prizes are given this year to Anne Carlstein and Emily Jian (runner up)
Hoopes Prize Three of our graduating seniors have been nominated for a Hoopes' Prizes for their theses this year: Anne Carlstein, Zihong Chen, Emily Jia

Last Mathtable

Lucy Wang: Though the Ultrafilter: Dictators and God

Please join us for the semester's final Math Table this Wednesday April 29th at 6pm on zoom here: https://harvard.zoom.us/j/698796794

Abstract: Ultrafilters are often studied in set theory and topology. In this talk, we'll introduce their application to two proofs that offer a more philosophical narrative: Arrow's Impossibility Theorem and G�del's ontological argument. We'll discuss how the ultrafilter construction makes a similar argument for the existence of a dictator in a voting system as it does for the existence of God. Then, we'll explore some controversial elements of these results, and whether they are as extreme as they may seem.
More ....

Spring 2020

04/29/2020	Though the Ultrafilter: Dictators and God, by Lucy Wang, Harvard undergraduate	04/15/2020	Non-University Job Panel (On ZOOM) , by Meena Boppana, Salvador Barragan-Santana, Jeffrey Molgano and Jay Gopalan, Various places
03/04/2020	Moduli spaces and their compactifications, by Dori Bejleri, Harvard University	02/26/2020	What does Math mean to you, by Beckman Myers, Harvard Undergraduate
02/19/2020	Max Dehn and the Dehn Twist., by Peter Kronheimer, Harvard University	02/12/2020	Strong law of small numbers, by Savvy Raghuvanshi, Harvard Undergraduate
02/05/2020	Negatively curved crystals, by Curtis Mc Mullen, Harvard University	01/29/2020	Hidden Markov Models as modern day map-makers, by Kim Nguyen, Harvard Undergraduate

Fall 2019

12/11/2019	Putnam Post Mortem (5:30 PM SC 507), by Noam Elkies, Harvard University	11/20/2019	Polynomials vanishing on points in the plane, by Brooke Ullery, Harvard University
11/13/2019	An Introduction to the Bernoulli Numbers, from Pythagoras to Present?, by Ellen Eischen, Oregon	10/30/2019	Fermat's little theorem and its Applications to Cryptography, by Gaurav Goel, Harvard University
10/23/2019	Why doesn't an electron fall into the nucleus?, by Marius Lemm, Harvard University	10/16/2019	Arborescences of regular covering graphs, by C.J. Dowd, Harvard Undergraduate
10/02/2019	Quantum computers and the future of cryptography, by Kate Stange, University of Colorado Boulder	10/02/2019	The Fisherman, the Graduate, and the Robot: Linear Programming for Applied Graph Theory, by Michael Kielstra, Harvard Undergraduate
09/25/2019	Mathematics for Human Flourishing, by Francis Su, Harvey Mudd University	09/18/2019	Counting Primes and Generalizing Arithmetic Progressions, by Vaughan McDonald, Harvard Undergraduate
09/11/2019	How many lines meet each of 4 given lines in 3-space, and why it matters, by Joe Harris, Harvard University	09/03/2019	A mathematical love story, by Wes Cain, Harvard University

Spring 2019

04/30/2019	Distributed Graph Coloring, by Noah Golowich , Harvard Undergraduate	04/23/2019	Snakes and Units: Algorithmic Generation of Alternating Sign Matrices, by Michael Kielstra, Harvard Undergraduate
04/16/2019	Three Consistencies, Three Theories, by Aditi Sundaram, Harvard Undergraduate	04/09/2019	Geometry of the non-Archimedean world, by Daniel Kim, Harvard Undergraduate
04/02/2019	Why is equality like a path? HoTT takes on proofs as programs., by Viinh-Kha Le, Harvard Undergraduate	03/26/2019	The Frobenius determinant theorem and the beginnings of representation theory, by Serina Hu, Harvard Undergraduate
03/12/2019	Are knots a group?, by Natalia Pacheco-Tallaj, Harvard Undergraduate	03/05/2019	The Banach-Tarski Paradox, by Hanna Mularczyk, Harvard Undergraduate
02/26/2019	The Ramanujan-Nagell equation, by Noam Elkies, Harvard University	02/19/2019	How to Not integrate: Impossibilities, by Vaughan McDonald, Harvard Undergraduate
02/12/2019	``Why Do Math" series: The Mathematics of Cooperation, by Martin Nowak, Harvard University	02/05/2019	Error Correcting Codes, by Garrett Brown, Harvard Undergraduate
01/29/2019	Euler in Action, by William Dunham, Harvard University

Fall 2018

12/06/2018	Putnam Post Mortem (3:15 PM SC 310), by Noam Elkies, Harvard University	12/04/2018	Breaking Multivariable (Abstract), by Stepan Paul, Harvard University
11/27/2018	Harmonic forms on surfaces - a visual approach (Abstract), by Bjoern Muetzel, Dartmouth College	11/13/2018	Games in New Contexts(Abstract), by Kelsey Houston-Edwards, Olin College
11/06/2018	Why Five Platonic Solids(Abstract), by Glen Whitney, Harvard University	10/30/2018	Divide and Conquer and 1-Center Clustering (Abstract), by Shyam Narayanan, Harvard Undergraduate
10/23/2018	Goldbach Comets (Abstract), by Oliver Knill, Harvard University	10/16/2018	Playing the St. Petersburg Paradox (Abstract), by Mark Kong, Harvard undergraduate
10/09/2018	Graduate School Panel (Abstract), by Various Panelists, Harvard University	10/02/2018	Eliminating Aperiodicity in Tilings (Abstract), by Daniel Kim, Harvard University
09/25/2018	Math Department Round Table Abstract), by Various Harvard Students, Harvard University	09/18/2018	Hypercomputation (Abstract), by Sebastien Vasey, Harvard University
09/11/2018	Quiver representations (Abstract), by Davis Lazowski, Harvard Undergraduate	09/04/2018	Fall 2018 Tutorial in Mathematics: Infinite Combinatorics and `The mysteries of 4 dimensions` by Cliff Taubes (Abstract)., by Gabe Goldberg, Harvard University

Spring 2018

05/01/2018	Summer Tutorials 2018, by Robert Cass, Morgan Opie and Yongquan Zhang, Harvard University	04/24/2018	The Leech Lattice, by Xavier Gonzalez, Harvard Undergraduate
04/17/2018	Preventing Period Doubling, by Wes Cain, Harvard University	04/10/2018	Cycles in Tournaments, by John Mackey, Carnegie Mellon
04/03/2018	Penrose Tilings, by Philip Engel, Harvard University	03/27/2018	The transfinite subway: counting to infinity and beyond, by Sebastien Vasey, Harvard University
03/20/2018	What Information Do You Need to Recover the Homotopy Type of a Space?, by Brabeeba Mien Wang, Harvard Undergraduate	03/06/2018	How to integrate in pi+i dimensions, by Davis Lazowski, Harvard Undergraduate
02/27/2018	The Hopf Invariant, by Reuben Stern , Harvard Undergraduate	02/20/2018	Surgery with Poincaré manifold as an application, by Frid Fu, Harvard Undergraduate
02/06/2018	Polishing Euler's Gem, by Oliver Knill, Harvard University	01/30/2018	The Geometry of Thales Contours, by Stepan Paul, Harvard University
01/23/2018	Spring 2018 Tutorials:(I) Curves on Algebraic Surfaces, and (II) Forcing , by Ziquan Yang and Gabriel Goldberg, Harvard University

Please congratulate the recipients of the Department's undergraduate prizes and awards:

David Mumford Undergraduate Mathematics Prize: from the income of the gift in 1997 of Peter L. Falb, A.B. 1957, A.M. 1957, Ph.D. 1961 to establish the David B. Mumford Undergraduate Mathematics Prize, to be given annually to the most promising senior concentrator in mathematics, provided such concentrator is outstanding. The Mumford Prize in 2018 has been awarded to James Tao.
Herb Alexander Award: from the gift of Susan Alexander, the Herb Alexander Award recognizes each year one of our outstanding undergraduates, and provides money to be used for research and travel. The Herb Alexander Award is given this year to James Hotchkiss.
Robert Fletcher Rogers Prizes: From the income of the gift in 1921 of the late Robert Fletcher Rogers, A.B. 1886, there have been established a first prize and second prize to be awarded annually to the College students who present the best talks before the Mathematics Table during an academic year. The Robert Fletcher Rogers Prizes are given this year to Cameron Krulewski for "Vector Bundles and K-Theory" and Rohil Prasad for "Introduction to Morse Theory". Honorable mentions go to both Frid Fu for "Surgery with Poincaré manifold as an application" and Xavier Gonzalez for "The Leech Lattice".
Friends Prize: Each year, two of our senior thesis writers are selected to present talks on their theses to the Friends of the Harvard Math department. The Friends prizes are given this year to to Nihal Gowravaram and Jennifer Hu
Finally, the winners of this year's Hoopes Prizes are Nihal Gowravaram, for his thesis entitled "Zero Knowledge Proofs and Applications to Financial Regulation". Jennifer Hu, for her thesis entitled "The Mathematics of Meaning: A Bayesian Approach to Comparing the Pragmatics of English and Chinese". Ravi Jagadeesan, for his thesis entitled "Crepant resolutions of Q-factorial threefolds with compound Du Val singularities" and Rohil Prasad, for his thesis entitled "The Seiberg-Witten invariant of a Homology S1 x S3".

Fall 2017

12/05/2017	Putnam Postmortem, by Noam Elkies, Harvard University	11/28/2017	Moonshine for All, by Neekon Vafa and Xavier Gonzalez Harvard Undergraduates, Harvard Undergraduates
11/14/2017	Knots and the Spirit World, by Sander Kupers, Harvard University	11/07/2017	Introduction to Morse Theory, by Rohil Prasad, Harvard Undergraduate
10/31/2017	The Monster group and scary character tables, by Brian Warner, Harvard Undergraduate	10/24/2017	Cayley Graphs and the Grothendieck Construction, by David Spivak , MIT
10/17/2017	6561101970383!, by Noam Elkies, Harvard University	10/10/2017	How to Compute a Cobordism Group, by Carlos Albors-Riera, Harvard Undergraduate
10/03/2017	Poincare-Birkhoff: an island of stability within chaos, by Davis Lazowski, Harvard Undergraduate	09/26/2017	Graduate School Panel, by Dennis Tseng, Robert Cass and Isabel Vogt, Harvard University and MIT
09/19/2017	Vector Bundles and K-Theory, by Cameron Krulewski, Harvard Undergraduate	09/12/2017	Adapting to a Chaotic World, by Rosalie Belanger-Rioux, Harvard University
09/05/2017	The Chairman's Welcoming Address: Solving the Quintic by Iteration, by Curtis T. McMullen, Harvard University	08/29/2017	Fall 2017 Tutorial in Mathematics: Arithmetic of elliptic curves, by Zijian Yao, Harvard University

Spring 2017

05/01/2017	Representation Theory and Quantum mechanics, Binary Quadratic Forms and Class Field Theory , by Justin Campbell and Zijian Yao, Harvard Mathematics Department	04/25/2017	Two (En)-Lightening Talks, by Adam Atanas and Justin Cavitt, Harvard Undergraduates
04/18/2017	Say What?!: Proving the Non-Context-Freeness of Natural Language, by Jennifer Hu, Harvard Undergraduate	04/11/2017	The Ramanujan-Nagell Equation, by Xavier Gonzalez, Harvard Undergraduate
04/04/2017	Shift Registers in Cryptography, by George Torres, Harvard Undergraduate	03/28/2017	Algebraic Functions and the Representability Zoo, by Julian Salazar, Harvard Undergraduate
03/21/2017	Who wants to be a math concentrator?, by Shanelle Eavis, Michael Fountaine, Sophie Garrett, and Kevin Yang, Harvard Undergraduates	03/07/2017	Partial Differential Equations and Universality in Probability Theory, by Kevin Yang, Harvard Undergraduate
02/28/2017	Infinitely Many Proofs of Infinitely Many Primes, by Andrew Gordon, Harvard Undergraduate	02/21/2017	Auction Theory, by Brabeeba Wang , Harvard Undergraduate
02/07/2017	Conical Algebraic Geometry, by Rohil Prasad, Harvard Undergraduate	01/31/2017	Division by Three, by Reuben Stern, Harvard Undergraduate
01/24/2017	Spring 2017 Tutorials:Category theory, Representations and cohomology of groups, by Justin Campbell and Meng Guo, Harvard University,

Please congratulate the recipients of the Department's undergraduate prizes and awards:

The Mumford Prize in 2017 will be shared by Hannah Larson and Ashvin Swaminathan
The Herb Alexander Award is given this year to Kevin Yang
The Robert Fletcher Rogers Prizes are given to Jennifer Hu and Julian Salazar. Honorable mentions to: Johann (Hans) Gaebler and George Torres for "Shift Registers in Cryptography".
The Friends prizes are given this year to Hannah Larson and Johann Gaebler.
Congratulate the recipients of this year's Hoopes Prizes. Johann Gaebler, Benjamin Lee, Gregory Parker, and Greg Yang. Congratulations again to all of our award recipients for their excellent work.

Fall 2016

12/06/2016	Putnam Postmortem, by Noam Elkies, Harvard University	11/29/2016	Understanding Inequality: A Kinetic Model of Wealth, by Marek Johnson, Undergraduate at Tufts University
11/15/2016	A look at the Mercator Projection, by Carlos Albors-Riera, Harvard Undergraduate	11/08/2016	An Introduction to Stochastic Modeling, by Adam Al-Natsheh, Harvard Math Alumnus
11/01/2016	Graduate School Panel, by Eva Belmont, Chi-Yun Hsu, Ben Landon, Morgan Opie and Krishanu Sankar, Harvard University and MIT	10/25/16	The Ergodic Theorem and Benford's Law, by Hans Gaebler, Harvard Undergraduate
10/18/16	The Bowen-Lanford Zeta function of a graph, by Oliver Knill, Harvard University	10/11/16	Counting Stacks of Blocks, by Ben Wetherfield, Harvard Undergraduate
10/04/16	Dynamics of Toppling for the Abelian Sandpile model, by Drisana Mosaphir, Harvard Undergraduate	09/27/16	Topological Data Analysis, by Julian Salazar, Harvard Undergraduate
9/20/16	Oriented Matroids and Gale diagrams, by Greg Yang, Harvard Undergraduate	9/6/16	Combinatorial Game Theory, by Jacob Lurie, Harvard University
08/30/2016	Fall 2016 Tutorial in Mathematics: Arithmetic of elliptic curves, by Zijian Yao, Harvard University

Spring 2016

05/03/2016	Summer 2016 Tutorials in Mathematics, by Geoffrey Smith: Coding Theory, Jake Marcinek and Zijian Yao: Complex and arithmetic dynamics, Meng Guo: Category theory, Harvard University	04/26/2016	Partition Party, by Hannah Larson, Harvard Undergraduate
04/19/2016	Geometric Complexity Theory, by Sitan Chen, Harvard Undergraduate	04/12/2016	The parity problem in sieve theory, by Xiaoyu He, Harvard Undergraduate
04/05/2016	Adam the Manifold Doctor, by Adam Al-Natsheh, Harvard Undergraduate	03/29/2016	Who wants to be a math concentrator?, by Students interested in a variety of areas in and near mathematics, Harvard Undergraduates
03/22/2016	Destroying Arithmetic Progressions in Abelian Groups, by Ashvin Swaminathan, Harvard Undergraduate	03/08/2016	Wu characteristic, by Oliver Knill, Harvard University
03/01/2016	Bisection Envelopes, by Noah Fechtor-Pradines, Harvard Undergraduate	02/24/2016	Parameter spaces for polygons , by Isabel Vogt , Harvard Undergraduate
02/16/2016	Mathematics of Cell Membrane Topology and Transport, by Siddhartha Jena, Harvard Undergraduate	02/09/2016	Dr. Skolem, or: How I Learned to Stop Worrying and Love the Countable, by Johann Gaebler , Harvard Undergraduate
02/02/2016	Interpolation in Algebraic Geometry, by Aaron Landesman, Harvard Undergraduate	01/26/2016	Spring 2016 Tutorials:Morse Theory and Theory of Partitions, by Boyu Zhang and Konstantin Matveev, Harvard University

Please congratulate the recipients of the Department's undergraduate prizes and awards this year.

The Mumford Prize is awarded in 2016 to Aaron Landesman.
The Wister Prize is awarded in 2016 to Sitan Chen.
The Herb Alexander Award is given this year to Kate Donahue.
The Robert Fletcher Rogers Prizes are given this year to Hannah Larson, Nat Mayer and Ashvin Swaminathan.
The Friends prizes are given this year to Aaron Landesman and Xiaoyu He.

Congratulations again to all of our award recipients for their excellent work.

Fall 2015

12/08/2015	Putnam Postmortem, by Noam Elkies, Harvard University	12/1/2015	Applications of Topology to a Problem in Algebra, by Adam Al-Natsheh , Harvard Undergraduate
11/17/2015	The Surreal Numbers and Combinatorial Game Theory, by Roman Berens , Harvard Undergraduate	11/10/2015	The Heilbronn Triangle Problem, by Xiaoyu He, Harvard Undergraduate
11/03/2015	Graduate School Panel, by Jun Hou Fung, Akhil Mathew, Alexander Smith, Isabel Vogt, Harvard University and MIT	10/27/2015	Elliptic Curve Cryptography , by Julian Salazar, Harvard Undergraduate
10/20/2015	The Gromov Non-Squeezing Theorem, by Greg Parker, Harvard Undergraduate	10/13/2015	How small is that prime?, by Ashvin Swaminathan, Harvard Undergraduate
10/06/2015	Volume Densities of Hyperbolic Knots, by Nat Mayer , Harvard Undergraduate	9/29/2015	The Banach-Tarski Paradox, by George Torres, Harvard Undergraduate
9/22/2015	Why exp(pi 163^1/2) is almost an integer, by Hannah Larson, Harvard Undergraduate	9/15/2015	Riemann-Roching out on the Projective Line, by Aaron Landesmann, Harvard Undergraduate
9/08/2015	Rotations and the four-color theorem, by Peter Kronheimer, Harvard University	9/01/2015	Fall 2015 Tutorial in Mathematics:Category Theory, by Danny Shi, Harvard University

Please congratulate the recipients of the Department's undergraduate prizes and awards this year.

The Mumford Prize is awarded in 2015 to Evan O'Dorney.
The Wister Prize is awarded in 2015 to Arpon Raksit
The Herb Alexander Award is given this year to Lily Hu.
The Robert Fletcher Rogers Prizes are given this year to Xiaoyu He and Barry Tng.
The Friends prizes are given this year to Arpon Raksit and Barry Tng.

Congratulations again to all of our award recipients for their excellent work.

Spring 2015

5/05/2015	Summertutorials 2015, by Justin Campbell, Erick Knight, Yi Xie and Boyu Zhang, Harvard University	4/21/2015	Conspiracies among quadratic residues, by Kevin Yang, Harvard Undergraduate
4/14/2015	The Rubik's Group, by George Torres, Harvard Undergraduate	4/07/2015	Who wants to be a math concentrator?, by Students interested in a variety of areas in and near mathematics, Harvard Undergraduates
3/31/2015	Integral geometry and the size of a cookie, by Barry Tng , Harvard undergraduate	3/24/2015	The Erdos-Ginzburg-Ziv Problem, by Xiaoyu He , Harvard undergraduate
3/09/2015	Topological Field Theories, by Adam Al-Natsheh, Harvard undergraduate	3/02/2015	How large is n! = n(n-1)(n-2) ... 3.2.1?, by Benedict Gross, Harvard University
2/24/2015	Universal limits in Probability Theory, by Ben Adlam, Harvard University	2/17/2015	Accidental Algorithms, by Sitan Chen, Harvard Undergraduate
2/3/2015	Counting lattice points in triangles and the Fibonacci numbers, by Dan Cristofaro-Gardiner, Harvard University	1/28/2015	Summer Tutorial: Cyclotomic Fields and Fermat's Last Theorem, Math 157 info, by Tom Lovering and Atanas Atanasov, Harvard Math Department, 4-5:30 SC30

Fall 2014

12/09/14	Putnam Postmortem, by Noam Elkies, Harvard University	12/02/14	Peck Posets , by Aaron Landesman , Harvard Undergraduate
11/18/14	Pseudorandomness and Fourier Analysis, by Sitan Chen, Harvard Undergraduate	11/11/14	Graduate School Panel, by Sherry Gong, Igor Rapinchuk, Isabel Vogt and Fan Wei, Harvard University and MIT
11/04/14	The Riemann zeta function, prime numbers, and the explicit formula, by Carl Wang Erickson, Brandeis University	10/21/14	Large Prime Gaps , by Xiaoyu He, Harvard Undergraduate
10/14/14	Algebraic Geometry and Automated Proofs, by Julian Salazar , Harvard Undergraduate	10/7/14	Lattice theory for the working Matchmaker, by Scott Kominers, Harvard University
9/30/14	Morse Theory, by Adam Al-natsheh, Harvard Undergraduate	9/23/14	Reverse Mathematics, by Stephen Mackereth , Harvard Undergraduate
9/16/14	Arboreal Galois Representations, by Ashvin Swaminathan, Harvard Undergraduate	9/9/14	Combinatorial Game Theory, by Jacob Lurie, Harvard University
9/2/14	Fall 2014 Tutorial in Mathematics: Complex multiplication, by Rong Zhou and Yihang Zhu, Harvard University

Spring 2014

5/06/2014	Summer Tutorial: Mathematical Origami , by Erick Knight , Harvard Math Department	4/29/2014	Why it takes 7 shuffles to mix a 52 card deck, by Seth Neel , Harvard Undergraduate
4/22/2014	Galois groups, by Akhil Mathew, Harvard Undergraduate	4/15/2014	What are formal groups and what are they good for?, by Isabel Vogt, Harvard Undergraduate
4/08/2014	Who wants to be a Math concentrator?, by Levent Alpoge, Sam Horan, Scott Johnson, Seth Neel, Caitlin Stanton, Isabel Vogt, Allen Yuan, Harvard Undergraduates	04/01/2014	Ignorance is Strength, by Eric Wepsic, Harvard Undergraduate
03/23/2014	How many integral points does the average elliptic curve have?, by Levent Alpoge, Harvard Undergraduate	03/11/2014	The de Rham theorem, by Evan O'Dorney, Harvard Undergraduate
03/04/2014	Categories and Kan extensions, by Marina Lehner, Harvard Undergraduate	02/25/2014	Borsuk-Ulam and combinatorics, by Sukhada Fadnavis, Harvard University
02/18/2014	Puzzles that don't exist: Hilbert's third problem, by Omar Camarena, Harvard University	02/11/2014	Metric graphs and their Jacobians , by Nathan Pflueger , Harvard University
02/04/2014	Elliptic Curves and Hypergeometric Functions, by Keenan Monks, Harvard Undergraduate

Fall 2013

12/10/13	Putnam Postmortem, by Noam Elkies, Harvard University	12/03/13	Ideas behind an amazing recent proof of bounded gaps, by Levent Alpoge, Harvard Undergraduate
11/19/13	3472073⁷ + 4627011⁷ ≈ 4710868⁷ and other LLL tricks., by Noam Elkies, Harvard Math Department	11/12/13	Perfect Powers in Recurrence Sequences, by Isabel Vogt, Harvard Undergraduate
11/05/13	Tournament Dynamics , by Daniel Conney , Harvard Undergraduate	10/29/13	Graduate School Panel, by Sukhada Fadnavis, Ben Landon, Max Menzies, Emily Riehl, Danny Shi, Hiro Tanaka, and Fan Wei, Harvard University
10/22/13	Rational distance problems , by Anand Patel , Boston College	10/15/13	Surreal Analysis: An Analogue of Real Analysis for Surreal Numbers, by Ashvin Swaminathan, Harvard Undergraduate
10/8/13	Cool theorems proved by undergrads, by Ken Ono, Emory University	10/1/13	The Ramanujan-Nagell equation x² + 7 = 2ⁿ, by Noam Elkies, Harvard University
9/23/13	Schubert Calculus, by John Sheridan, Harvard undergraduate	9/16/13	The isoperimetric problem on surfaces, by Adam Jacob, Harvard University
9/9/13	Area-preserving maps, by Peter Kronheimer , Harvard University	9/3/13	Fall 2013 Tutorial in Mathematics: Structure, Randomness and Pseudorandomness, by Konstantin Matveev, Harvard University

Please congratulate the recipients of the Department's undergraduate prizes and awards this year.
The Mumford Prize is awarded in 2013 to Eric Larson
The Wister Prize is awarded in 2013 to Tony Feng
The Herb Alexander Award is given this year to Ben Adlam
Two of our graduating seniors won 'Hoopes' Prizes for their theses this year: please congratulate Christian Anderson and Ashok Cutkosky. The Rogers prize is award to Lucia Mocz, Akhil Mathew and Dmitri Gekhtman. The Friends prize want to Eric Larson. Tony Feng was the runner up.

Spring 2013

4/23/13	Modular Forms in String Theory, by Murad Alim , Harvard University	4/16/13	What is the Birch and Swinnerton-Dyer Conjecture?, by Lucia Mocz, Harvard Undergraduates
4/09/13	Who wants to be a Math concentrator?, by Zachary Abel,Tony Liu,Lucia Mocz,Robert Nishihara,John Sheridan,Caitlin Stanton, Harvard Alumni or Harvard Undergraduates	4/02/13	The Unique Games Conjecture and Hardness of Approximation , by Elena-Madalina Persu, Harvard Undergraduate
3/26/13	The sine integral Int(sin(x)/x,x,0,INFTY)=Pi/2 by elementary calculus, by Noam Elkies, Harvard University	3/12/13	An Elementary Proof of Ostrowski's Theorem, by Seth Neel, Harvard Undergraduate
3/05/13	Topological Field Theories, by Gijs Heuts, Harvard University	2/26/13	The Poincaré Dodecahedral Space, by Andrew Cotton-Clay, Harvard University
2/19/13	Solving Equations in the Integers is Hard, by Levent Alpoge, Harvard Undergraduate	2/12/13	Finite fields and topology, by Akhil Mathew , Harvard Undergraduate
2/05/13	The controversy around the Church-Turing Thesis, by Rachel Epstein , Harvard University	1/29/13	Spring 2013 Tutorials in Mathematics, by Konstantin Matveev and Alex Perry, Harvard University

Fall 2012

12/04/12	Putnam Postmortem , by Noam Elkies, Harvard University	11/27/12	Mathematics and Finance: How Math Can Make You Money, by Ben Conlee, '07, and Peter Green, Ph.D. '05, Ellington Management Group
11/13/12	A purely analytic proof of Quadratic Reciprocity, by Levent Alpoge, Harvard Undergraduate	11/6/12	Graduate School Panel, by Zach Abel, Sukhada Fadnavis, Adam Jacob, Eric Knight, Emily Riehl, and Krishnanu Sankar, Harvard and MIT Mathematics Departments
10/30/12	Heads or Tails? Coin tossing, fair and biased, by Emily Riel , Harvard University	10/23/12	Heads or Tails? Coin tossing, fair and biased, by Alex Bloemendal , Harvard University
10/16/12	Continued Fractions and Hyperbolic Geometry, by Krishna Dasaratha, Harvard Undergraduate	10/9/12	Braid Groups , by Allen Yuan , Harvard Undergraduate
10/2/12	Bug Dynamics on Manifolds, by Dimitry Gekhtman, Harvard Undergraduate	9/25/12	Covariance Matrices, by Ben Adlam , Harvard Undergraduate
9/18/12	Pellynomials, by Lucia Mocz, Harvard Undergraduate	9/11/12	Chairman's Welcoming Address: The ABC Conjecture and why we care, by Noam Elkies , Harvard University
9/4/12	Fall 2012 Tutorial in Mathematics: Coxeter Groups., by Jessica Fintzen, Harvard University

Spring 2012

4/24/12	Simplifying Complicated Simplicial Complexes: Discrete Morse Theory and its Applications, by Rachel Zax, Harvard Undergraduate	4/17/12	The Julia and Fatou sets of a polynomial map, by Benjamin Dozier , Harvard Undergraduate
4/10/12	Special K. What is K-theory and why do we care?, by Eva Belmont, Harvard Undergraduate	4/03/12	M,1,21,23,25,55...? Who wants to be a Math Concentrator?, by Panelists: Zachary Abel '10, Eva Belmont '12, Halimeda Glickman-Hoch '12, Katrina Evtimova '13, Tony Feng '13, and Yacoub Kureh '13., Harvard Graduates and Undergraduates
3/19/12	The Ubiquity of the Bernoulli Numbers, by Levent Alpoge , Harvard Undergraduate	2/28/12	The Grothendieck group , by Akhil Mathew , Harvard Undergraduate
2/28/12	The Euler Characteristic , by Caitlin Stanton , Harvard Undergraduate	2/21/12	What can be computed in mathematics?, by Anand Deopurkar, Harvard University
2/14/12	The space (locale) of random sequences, by Emily Riehl, Harvard University	2/7/12	Euler Integrals, and Gauss and Jacobi Sums, by Noam Elkies, Harvard University
1/31/12	Zolotarev's combinatorial proof of quadratic reciprocity, by Joseph Rabinoff , Harvard University	1/24/12	Spring 2012 Tutorials in Mathematics: Groupoids in Topology and The Figure Eight Knot: Introduction to Hyperbolid Geometry, by Omar Antolin Camarena and Stergios Antonakoudis, Harvard University

Fall 2011

12/6/11	Putnam Postmortem, by Noam Elkies, Harvard University	11/29/11	Fun with Carl and Carl, Messing Around with Gauss and Jacobi Sums, by Levent Alpoge, Harvard Undergraduate
11/15/11	Exotic spheres, by Akhil Mathew , Harvard Undergraduate	11/8/11	Orthogonal polynomials, Gaussian quadrature, and Rolle's theorem, by Noam Elkies, Harvard University
11/1/11	Graduate School Panel, by Zach Abel,George Boxer,Nathan Kaplan,Eric Riedl,Peter Smillie,Ethan Street,Meghan Anderson,Jennifer Balakrishnan, Harvard and MIT Mathematics Departments	10/11/25	How to count like Schubert, by Jack Huizenga, Harvard University
10/11/18	Why Many Published Experimental Findings Are Probably False, by Daniel Benjamin '99, Cornell and National Bureau of Economic Research	10/11/11	Bruhat-Tits Buildings of GL_n(Q_p) and SL_n(Q_p), by Lucia Mocz, Harvard Undergraduate
10/4/11	Interval exchange maps, by Vaibhav Gadre, Harvard University	9/20/11	Unfolding Polyhedra is NP-Hard, by Zach Abel `10, MIT
9/13/11	6561101970383!, by Noam Elkies, Harvard University	9/6/11	How I Learned the Fundamental Theorem of Algebra, by Peter Kronheimer, Harvard University
8/30/11	Fall 2011 Tutorial:Category Theory, by Atanas Atanasov, Harvard University

Spring 2011

5/3/11	Summer Tutorials 2011, by Aliakbar Daemi, Nathan Kaplan, Sam Raskin: Symplectic Geometry, Coding theory, Representation Theory, Harvard University	4/26/11	Irreducibility of M_g,, by Francois Greer, Harvard Undergraduate
4/19/11	Scaling Dimensions with Fractal Curves, by Adrian Sanborn, Harvard Undergraduate	4/12/11	Interactive Proofs, by Akhil Mathew , Harvard Undergraduate
4/05/11	M,1,21,23,25,55...? Who wants to be a Math Concentrator?, by Panelists: Zachary Abel '10, Tiffany Cai '12, Eva Belmont '12, Francois Greer '11, Dmitri Vaintrob '11, Harvard	3/29/11	Quaternions in everyday life, by Joe Rabinoff, Harvard University
3/22/11	Three faces of the Rado graph: What other multi-visaged structures are out there?, by Rehana Patel,	3/8/11	Crossing numbers of graphs: origins and recent progress, by John Mackey, Carnegie Mellon
3/1/11	pi proofs that pi² smaller 10, by Noam Elkies, Harvard University	2/15/11	Solving an MC Escher Mystery With Mathematics, by Juliana Belding, Harvard University
2/8/11	Continued fractions and interval exchange maps, by Vaibhav Gadre, Harvard University	1/25/11	Spring Tutorial 2011, by Stergios Antonakoudis. "Operators on Hilbert spaces: analysis and application", Harvard University

Please congratulate the recipients of the Department's undergraduate prizes and awards this year.
David Mumford Undergraduate Mathematics Prize	From the income of the gift in 1997 of Peter L. Falb, A.B. 1957, A.M. 1957, Ph.D. 1961 to establish the David B. Mumford Undergraduate Mathematics Prize, to be given annually to the most promising senior concentrator in mathematics, provided such concentrator is outstanding. The David Mumford Undergraduate Mathematics Prize is awarded in 2011 to Arnav Tripathy.
Winster Prize	From the gift of Susan Alexander, the Herb Alexander Award recognizes each year one of our outstanding undergraduates, and provides money to be used for research and travel The Wister Prize is awarded in 2011 to Sherry Gong.
Herb Alexander Award	From the gift of Susan Alexander, the Herb Alexander Award recognizes each year one of our outstanding undergraduates, and provides money to be used for research and travel. The Herb Alexander Award is given this year to Jonathan Wang.
Robert Fletcher Rogers Prizes	From the income of the gift in 1921 of the late Robert Fletcher Rogers, A.B. 1886, there have been established a first prize and second prize to be awarded annually to the College students who present the best talks before the Mathematics Table during an academic year. The Rogers Prizes are awarded this year as follows: First prize: Adrian Sanborn, for his talk Scaling Dimensions with Fractal Curves Second prize: to be divided equally between Eric Larson for his talk "An Inequality Involving the Perimeter and Curvature of Plane Curve", and Akhil Mathew for his talk "Translation-Invariant Binary Representations".
Hoopes Prize	Michael Viscardi has been awarded the Hoopes' Prize this year, for his senior thesis "Alternative compactifications of the moduli space of genus on maps." Hoopes' Prizes were also won by two of our joint concentrators: Andrei Cristea (Economics and Math), and Chrisopher Lim (Music and Math).
Congratulations to all! Peter Kronheimer, Director of Undergraduate Studies, Department of Mathematics

Fall 2010

12/7/10	Putnam Postmortem, by Noam Elkies, Harvard University	11/30/10	Determinacy, by Joel Specter, Visiting Harvard Undergraduate
11/23/10	Stably Surrounding Sphere with Smallest String Size, by Zach Abel ('10), MIT graduate student	11/16/10	Large Games IV: A New Hope, by Scott Kominers ('09), Economics graduate student at HBS
11/9/10	Graduate School Panel, by Zach Abel, Nathan Kaplan, Erich Riedl, Ethan Street, Charmaine Sia and Sarah Koch, Harvard and MIT Mathematics Departments	11/2/10	Inversive Geometry, by Noam Elkies, Harvard Mathematics Department
10/26/10	Translation-Invariant Binary Representations, by Akhil Mathews , Harvard Undergraduate	10/19/10	On a conjecture of Lubin, by Joel Specter, Visiting Harvard Undergraduate
10/12/10	Tannakian Duality for Finite Groups, by Eric Larson , Harvard Undergraduate	10/5/10	Block Monoids and Factorizations of Algebraic Integers, by Scott Chapman, Sam Houston State University (Huntsville, Texas)
9/28/10	Fourier Series and Elliptic Regularity, by Akhil Mathew , Harvard Undergraduate	9/21/10	Limits, measures and democracy , by Gabor Lippner, Harvard University
9/14/10	An Inequality Involving the Perimeter and Curvature of Plane Curves, by Eric Larson , Harvard Undergraduate	9/7/10	Chairman's Welcoming Address: The maximum principle, by Shing-Tung Yau , Harvard University
8/31/10	Fall 2010 Tutorial:Ricci Flow on Surfaces , by Yi Li, Harvard University



Photos of the mathtable of September 7, 2010. Shing-Tung Yau gives a talk on the maximum principle. [See larger panorama photo].

Please congratulate the recipients of the Department's undergraduate prizes and awards this year.
David Mumford Undergraduate Mathematics Prize	From the income of the gift in 1997 of Peter L. Falb, A.B. 1957, A.M. 1957, Ph.D. 1961 to establish the David B. Mumford Undergraduate Mathematics Prize, to be given annually to the most promising senior concentrator in mathematics, provided such concentrator is outstanding. The Mumford Prize is awarded to Michael Viscardi.
Herb Alexander Award	From the gift of Susan Alexander, the Herb Alexander Award recognizes each year one of our outstanding undergraduates, and provides money to be used for research and travel. The Herb Alexander Award is given this year to Zachary Abel.
Robert Fletcher Rogers Prizes	From the income of the gift in 1921 of the late Robert Fletcher Rogers, A.B. 1886, there have been established a first prize and second prize to be awarded annually to the College students who present the best talks before the Mathematics Table during an academic year. The two prizes are awarded equally this year to: Zhou Fan, for his talk "Random Matrices, Catalan Numbers, and Wigner's Semicircle Law;" Dmitri Vaintrob, for his talk "1+2+3+ ... = -1/12: Values of the Zeta Function at Negative Integers."
Hoopes Prize	Michael Viscardi has been awarded the Hoopes' Prize this year, for his senior thesis "Alternative compactifications of the moduli space of genus on maps." Hoopes' Prizes were also won by two of our joint concentrators: Andrei Cristea (Economics and Math), and Chrisopher Lim (Music and Math).
Congratulations to all! Peter Kronheimer, Director of Undergraduate Studies, Department of Mathematics

Spring 2010

4/27/10	Summertutorials 2010, by Ronen Mukamel: Teichmüller Theory and Thurston's Classification of Mapping Classes, Ryan Reich: Linear Algebraic Groups, Jack Thorne: p-adic Arithmetic and p-adic Analysis., Harvard University	4/20/10	Empirical Knot Theory, by Zachary Abel, Harvard undergraduate
4/13/10	M,1,21,23,25,55...? Who wants to be a Math Concentrator?, by Junior and senior math concentrators, Harvard undergraduate	4/6/10	Newton Polygons, by Elena-Madalina Persu, Harvard undergraduate
3/30/10	The Spirit of Moonshine, by Jeremy Booher, Harvard undergraduate	3/23/10	Representation by quadratic forms, by Christian Zamora Jaen, Harvard undergraduate
3/9/10	A Slice of Pi, by Luke Anderson, Harvard Administration and founder of TeachPi.org	3/2/10	The outer automorphism of S₆, by Noam Elkies, Harvard University
2/23/10	Spaces that Don't Quite Fit in R³, by Laura Starkston, Harvard Undergraduate	2/16/10	On Oranges and the Sun, by Nir Avni , Harvard University
2/9/10	Supersymmetric nonlinear sigma model, by Youngsub Yoon, Harvard Unvergraduate	2/8/10	Low dimensional topology for fun and profit (Monday, SciC 232, 4 PM), by Clifford Stoll, Teacher and Entrepreneur
2/2/10	1 + 2 + 3 + ... = -1/12. Values of the zeta function at negative integers., by Dmitry Vaintrob, Harvard Undergraduate	1/26/10	Spring Tutorial: Combinatorial and geometric group theory and symmetric functions in algebraic combinatorics, by Thomas Koberda and Greta Panova, Harvard Math Department

Fall 2009

12/8/09	Putnam Postmortem, by Noam Elkies, Harvard University	12/1/09	Random Matrices, Catalan Numbers, and Wigner's Semicircle Law, by Zhou Fan, Harvard Undergraduate
11/24/09	The McKay Correspondence, by Yi Sun, Harvard Undergraduate	11/17/09	Extremal functions of forbidden double permutation matrices, by Jesse Geneson, Harvard Undergraduate
11/10/09	The Partial Assignment Problem, by Olga Zverovich, Harvard Undergraduate	11/3/09	Graduate School Panel, by Ronen Mukamel, Ethan Street, Wei Ho and Joe Rabinoff, Harvard University
10/27/09	Calculus on Non-Standard Domains, by Harrison Pugh, Harvard Undergraduate	10/20/09	Matings of Polynomials, by Sarah Koch , Harvard University
10/13/09	What Is the LLL Algorithm?, by Zachary Abel, Harvard Undergraduate	10/6/09	The real and p-adic lives of n!, by Benedict Gross, Harvard Math Department
9/29/09	Thin Lehman Matrices and Their Graphs, by Johnathan Wang, Harvard Undergraduate	9/15/09	3472073⁷ + 4627011⁷ ~=~ 4710868⁷ and other LLL tricks., by Noam Elkies, Harvard Math Department
9/8/09	Welcoming Address: Knots and Complexity, by Peter Kronheimer, Head Tutor in Mathematics, Harvard University	9/1/09	Fall 2009 Tutorial: Dynamics of analytic maps: small divisor problems Abstract., by Giulio Tiozzo, Harvard University

Please congratulate the recipients of the Department's undergraduate prizes and awards this year.
David Mumford Undergraduate Mathematics Prize	From the income of the gift in 1997 of Peter L. Falb, A.B. 1957, A.M. 1957, Ph.D. 1961 to establish the David B. Mumford Undergraduate Mathematics Prize, to be given annually to the most promising senior concentrator in mathematics, provided such concentrator is outstanding. The Mumford Prize is awarded in 2009 jointly to John Lesieutre and Shrenik Shah.
Wister Prize	From a bequest of Charles J. Wister, a prize is awarded in alternate years to the Senior concentrating in Mathematics or Music who has the highest record in his/her field of concentration. In 2008-09 the prize is open to concentrators in Mathematics, in 2009-10 to concentrators in Music. The Wister Prize is awarded to Samuel Lichtenstein.
Herb Alexander Award	From the gift of Susan Alexander, the Herb Alexander Award recognizes each year one of our outstanding undergraduates, and provides money to be used for research and travel. The Herb Alexander Award is given this year to Nike Sun.
Robert Fletcher Rogers Prizes	From the income of the gift in 1921 of the late Robert Fletcher Rogers, A.B. 1886, there have been established a first prize and second prize to be awarded annually to the College students who present the best talks before the Mathematics Table during an academic year. First Prize: Zachary Abel for his talk "Hinged dissections exist". Second Prize: Laura Starkston, for her talk "Khovanov homology". Hoopes Prize Scott Kominers for his submission "Weighted Generating Functions and Configuration Results for Type II Lattices and Codes". Shrenik Shah for his submission "Framed Deformation and Modularity". Nils Wernerfelt for his submission "The Evolution of Cooperation on Dynamic Graphs". Congratulations again to all Peter Kronheimer, Director of Undergraduate Studies, Department of Mathematics

Spring 2009

5/12/09	Summertutorials 2009, by Ivana Bozic: Stochastic Models in Biology, Tanya Kobylyatskaya and Ethan Street: Knot Theory Le Anh Vinh: Additive Combinatorics, Harvard University	5/5/09	The Rap Battle of the Millennium, by Zachary Abel and Scott Kominers , Harvard undergraduates
4/28/09	Phylogenetic tropical geometry, by Kelley Harris , Harvard undergraduate	4/21/09	New Application of the Inclusion-Exclusion Principle to Graph Coloring, by Olga Zverovich , Harvard undergraduate
4/14/09	Koch's Condition on Type II Codes of Length 24, by Scott Kominers, Harvard undergraduate	4/7/09	The Curry-Howard Correspondence, by Grant Dasher , Harvard undergraduate
3/31/09	Khovanov Homology , by Laura Starkston , Harvard undergraduate	3/17/09	Who wants to be a Math Concentrator?, by Junior and senior math concentrators, Harvard undergraduates
3/10/09	A Slice of Pi , by Luke Anderson, Harvard Administration and founder of TeachPi.org	3/3/09	Computation at a Distance, by Lawren Smithline, Center for Communications Research at Princeton
2/24/09	Treasure Hunting Perfect Euler Bricks, by Oliver Knill, Harvard University	2/17/09	Pairings on Elliptic Curves in Cryptography: Friend or Foe, by Juliana Belding, Harvard University
2/10/09	The secret lives of class numbers, by David Hansen, Brown University Undergraduate	2/03/09	Why stop at bilinear forms?, by Noam Elkies, Harvard Math Department
1/27/09	Spring Tutorial: Morse Theory , by Chen-Yu Chi , Harvard Math Department

Fall 2008

12/9/08	Putnam Postmortem, by Noam D. Elkies, Harvard Math Department	12/02/08	Analyzing Complex Semisimple Lie Algebras, by Christian Zamora Jaen , Harvard Undergraduate
11/25/08	Many Proofs of Quadratic Reciprocity, by Jeremy Booher, Harvard Undergraduate	11/18/08	The Math Graduate School Discussion Panel, by recent Ph.D.'s and graduate students , from Berkeley, Cambridge, MIT, Harvard, Princeton etc.
11/11/08	Matchmaker, matchmaker, clear out my house., by Scott Kominers, Harvard Undergraduate	11/4/08	Hinged dissections exist, by Zachary Abel, Harvard Undergraduate
10/28/08	Dynkin diagrams, or what to tell the aliens, by John Duncan, Harvard University	10/21/08	Knots, Spirals, and Superinvariants, by Laura Starkston , Harvard Undergraduate
10/14/08	Mathtable joins Clay Math public lecture. "A Tribute to Euler", by William Dunham, Harvard University	10/7/08	The gap between the first two eigenvalues of the Schroedinger operator and methods from geometry, by Sing-Tung Yau, Harvard University
9/23/08	The Weil representation, by Noam Elkies, Harvard University	9/16/08	Fall 2008 Tutorials: Tropical Geometry and Algebraic Graph Theory, by Ryan Reich and LeAnh Vinh, Harvard University

Please join me in congratulating the recipients of the Department's undergraduate prizes and awards this year.
David Mumford Undergraduate Mathematics Prize	The Mumford prize is awarded to Dustin Clausen. From the income of the gift in 1997 of Peter L. Falb, A.B. 1957, A.M. 1957, Ph.D. 1961 to establish the David B. Mumford Undergraduate Mathematics Prize, to be given annually to the most promising senior concentrator in mathematics, provided such concentrator is outstanding.
The Herb Alexander Award	The Herb Alexander Award is given this year to Elena Yudovina. From the gift of Susan Alexander, the Herb Alexander Award recognizes each year one of our outstanding undergraduates, and provides money to be used for research and travel to mathematics conferences.
The Robert Fletcher Rogers Prizes:	First Prize: Scott Kominers, for his talk "C=15". Second Prize: Christian Zamora Jaen, for his talk "Fermat's Last Theorem". From the income of the gift in 1921 of the late Robert Fletcher Rogers, A.B. 1886, there have been established a first prize and second prize to be awarded annually to the College students who present the best talks before the Mathematics Table during an academic year.
Hoopes Prizes	Dustin Clausen and Alison Miller were recipients of the Hoopes Prizes this year, for their outstanding senior theses. Congratulations again to all! Peter Kronheimer, Director of Undergraduate Studies, Department of Mathematics

Spring 2008

5/06/08	Division Algebras over R, by Jeremy Booher, Harvard Undergraduate	4/29/08	Self-Reference and Provability, by Jesse Geneson , Harvard Undergraduate
4/22/08	General Relativity and the Mathematics of the Universe, by Lydia Bieri, Harvard University	4/15/08	Mono-monostatic bodies: the story of the Gomboc, by Gabor Domokos and Peter Varkonyi, Budapest University of Technology and Economics.
4/8/08	Beyond Batting Averages, by Rohit Acharya and Alex D'Amour, Harvard Undergraduates	4/1/08	Fermat's Last Theorem, by Christian Zamora Jaen, Harvard Undergraduate
3/18/08	The Fraisse Construction and its Descendants, by Rehana Patel, Harvard University	3/14/08	Pi-day 2008, by Pi, Mathematical constant
3/4/08	Color by Numbers, by Daniel Litt, Harvard Undergraduate	2/26/08	Probabilistic Group Theory, by Bret Benesh, Harvard University
2/5/08	Curves, Cryptography and Primes of the Form x² + D y², by Juliana Belding , University of Maryland

Gabor Domokos visits Harvard on April 15'th 2008 and demonstrates the gomboc. His mathtable talk was a big success.	The Gomboc was created by Gabor Domokos and Peter Varkonyi, Budapest University of Technology and Economics. The 'Gomboc' became very popular. The website attracts hundreds of thousand of visitors (mostly non-mathematicians) from over hundred countries. References: Domokos, G., Ruina, A., Papadopoulos, J.: Static equilibria of rigid bodies: is there anything new? J. Elasticity, 36 (1994), 59-66. Varkonyi, P., Domokos G.: Static equilibria of rigid bodies: dice, pebbles and the Poincare-Hopf Theorem. J. Nonlinear Science 16 (2006), 255-281.	A better movie.
Abstract: The weeble (also called the 'Comeback Kid') is the favorite of many children: whenever knocked over, it always returns to the same (stable) equilibrium position. This toy is, of course, not homogenous, spontaneous self-righting is guaranteed by the weight at the bottom. We may also observe that most weebles have only one unstable balance point, at the top. When we look at homogeneous objects, the problem becomes less trivial. In two dimensions, it is relatively easy to prove that each homogeneous, convex slab has at least two stable (S=2) and two unstable (U=2) equilibria when rolling under gravity on a horizontal surface, i.e. homogeneous 2D weebles do not exist. One can imagine several three dimensional generalizations to this statement: a) S>1 b) U>1 c) S+U>2 While a) and b) can be shown to be false, c) posed a considerable puzzle for many years. Finally, in 1995, V.I. Arnold conjectured that c) is NOT true either, in other words, convex, homogeneous solids with just one stable and one unstable point of equilibrium (also called mono- monostatic) may exist. These are 'special weebles' which share the number and type of equilibria of the toy, however, no weight is added. Not only did his conjecture turn out to be true, the newly discovered objects show various interesting features. Our goal is to give an overview of these findings with emphasis on a qualitative approach based on dynamical systems theory, as well as to present some new results. We will point out that mono-monostatic bodies are neither flat, nor thin, they are not similar to typical objects with more equilibria and they are hard to approximate by polyhedra. Despite these "negative" traits, there seems to be strong indication that these forms appear in Nature due to their special mechanical properties. These new forms, called 'Gomboc' became very popular on the internet, the website attracting hundreds of thousand of visitors (mostly non-mathematicians) from over hundred countries.

Fall 2007

12/11/07	Integers and Sequences, by Tanya Khovanova, Lead Analyst at BAE Systems	12/4/07	Putnam Postmortem, by Noam D. Elkies, Harvard Math Department
11/27/07	"Binary Quadratic Forms and Ideal Class Groups", by Christian Zamora Jaen, Harvard Undergraduate	11/20/07	"Playing Modulor: Combination and the Golden Ratio in the Work of Le Corbusier", by Julia Shlozman, Harvard Undergraduate
11/06/07	"Relativistic Electromagnetism", by Arnav Tripathy, Harvard Undergraduate	10/30/07	"C=15", by Scott Kominers, Harvard Undergraduate
10/23/07	"Firefly Self-Synchronization models and their applications", by Pablo Azar , Harvard Undergraduate	10/16/07	"The Mathematics of fixed income Markets", by Andrew Lesniewski, Managing Director Ellington Management Group
10/09/07	"Mathematics used at Google", by A Representative from the Company, Google	10/02/07	"The Icosahedral Group", by Bret Benesh, Harvard University
9/25/07	Knots, and how to unknot them , by Peter Kronheimer , Head Tutor in Mathematics Harvard Math Department.	9/18/07	Introductions, Announcements, and Problem Solving, by Bret Benesh, Harvard University

mathtable panorama photo of September 25 2007

Photos of the mathtable of September 25, 2007. Peter Kronheimer gives a talk on knots. [See larger panorama photo].

Spring 2007

4/24/07	A Queuing Model for Use of Laundry Machines in Student Dormitories, by Serena Rezny, Harvard Undergraduate	4/17/07	Presentations for 3 Summer Tutorials: Ramsey Theory, Enumerative Geometry, Elliptic Curves, by Thomas Barnet-Lamb, Dawei Chen, David Geraghty and Jeechul Woo, Harvard University
4/3/07	Quantum Computation and Shor's Algorithm, by Shrenik Shah, Harvard Undergraduate	3/13/07	Abelian extensions and analytic functions, by Kaloyan Slavov, Harvard Undergraduate
2/27/07	How many irreducibles?, by Noam Elkies, Harvard University	2/20/07	How many primes?, by Zachary Abel, Harvard Undergraduate
2/13/07	Young tableaux and permutations, by Thomas Lam, Harvard University	1/30/07	Spring 2007 Tutorials: Elliptic functions, Geometry in Real and Complex Projective Space, by Chung Pang Mok, Rina Anno, Harvard University

Please join me in congratulating the recipients of the Department's undergraduate prizes and awards this year.
David Mumford Undergraduate Mathematics Prize	The Mumford prize is awarded to Kaloyan Slavov. From the income of the gift in 1997 of Peter L. Falb, A.B. 1957, A.M. 1957, Ph.D. 1961 to establish the David B. Mumford Undergraduate Mathematics Prize, to be given annually to the most promising senior concentrator in mathematics, provided such concentrator is outstanding.
The Wister Prize	The Wister Prize is awarded to Anatoly Preygel. From a bequest of Charles J. Wister, a prize is awarded in alternate years to the Senior concentrating in Mathematics or Music who has the highest record in his/her field of concentration. In 2006-07 the prize is open to concentrators in Mathematics, in 2007-08 to concentrators in Music.
The Herb Alexander Award	The Herb Alexander Award is given this year to Igor Rapinchuk. From the gift of Susan Alexander, the Herb Alexander Award recognizes each year one of our outstanding undergraduates, and provides money to be used for research and travel to mathematics conferences.
The Robert Fletcher Rogers Prizes:	First Prize: Robin Walters, for his talk "Generalizations of the Hexagonal Honeycomb Theorem". Second Prize: Gerardo Con Diaz, for his talk "Cutting and Pasting Doughnuts: Three Ways of Constructing Lens Spaces". Honorable Mention: Alison Miller, for her talk "Exp(pi*Sqrt(163)) and Friends". From the income of the gift in 1921 of the late Robert Fletcher Rogers, A.B. 1886, there have been established a first prize and second prize to be awarded annually to the College students who present the best talks before the Mathematics Table during an academic year.
Hoopes Prizes	Mark Lipson and Kaloyan Slavov were recipients of the Hoopes Prizes this year, for their outstanding senior theses. The Hoopes Prize committee awarded Goutham Seshadri an honorable mention. Congratulations again to all! Peter Kronheimer, Director of Undergraduate Studies, Department of Mathematics

Mathtable Icontable

As of January 1, 2007, there were 184 mathtable talks in our database. Click on the icon mosaic, to see a table of all icons.

Some large icons.

Fall 2006

12/11/06	Exp(piSqrt(163)) and Friends, by Alison Miller*, Harvard Undergraduate	12/5/06	Putnam Postmortem , by Noam D. Elkies, Harvard Math Department
11/28/06	Dunking Donuts: Morse theory and the Poincare-Hopf theorem, by Alexander Ellis, Harvard Undergraduate	11/21/06	Opetopia, by Scott Kominers, Harvard Undergraduate
11/14/06	SO(4)/{1,-1} = SO(3) x SO(3) , by Noam Elkies, Harvard Math Department	10/31/06	Inversive Geometry , by Noam Elkies, Harvard Mathematics Department
10/24/06	Generalizations of the Hexagonal Honeycomb Theorem , by Robin Walters, Harvard Undergraduate	10/17/06	Cutting and Pasting Doughnuts: Three Ways of Constructing Lens Spaces, by Gerardo Con Diaz, Harvard Undergraduate
10/11/06	Mathematics and financial modeling , by Andrew Lesniewski, Managing Director, Ellington Management Group	10/3/06	Rubik's Hyperhexahedra , by Stewart Wilcox, Harvard Mathematics Department
9/26/06	Spectral flow , by Clifford Taubes, William Petschek Professor of Mathematics and Chair of the Harvard Mathematics Department	9/19/06	Tutorials "Enumerative Geometry", "Morse Theory" "Geometry and Physics" , by Dawei Chen, Chen-Yu Chi, Aleksandar Subotic, Harvard Math Department

This year, the Mumford Prize will be split between Stefan Patrikis, and Nikita Rozenblyum. "From the income of the gift in 1997 of Peter L. Falb, A.B. 1957, A.M. 1957, Ph.D. 1961 to establish the David B. Mumford Undergraduate Mathematics Prize, to be given annually to the most promising senior concentrator in mathematics, provided such concentrator is outstanding."	The Herb Alexander Award is given this year to Sheel Ganatra. "From the gift of Susan Alexander, the Herb Alexander Award recognizes each year one of our outstanding undergraduates, and provides money to be used for research and travel to mathematics conferences."	The Robert Fletcher Rogers Prizes are split equally between: Gerardo Con Diaz, Igor Rapinchuk and Inna Zakharevich. "From the income of the gift in 1921 of the late Robert Fletcher Rogers, A.B. 1886, there have been established a first prize and second prize to be awarded annually to the College students who present the best talks before the Mathematics Table during an academic year."	In addition Stefan Patrikis and Gregory Valliant were recipients of Hoopes Prizes this year, for their outstanding senior theses.
Congratulations to all!	Peter Kronheimer, Director of Undergraduate Studies, Department of Mathematics	(Winners of the Department's prizes and awards should contact Ruby in the main office.)

Spring 2006

5/2/06	The 30 Minute Introduction to Algebraic Geometry, by Corina Tarnita Patrascu, Harvard Undergraduate	4/25/06	Homotopy and Simplicial Sets, by Inna Zakharevich, Harvard Undergraduate
4/18/06	The Summer tutorials: Category theory", "Group cohomology", "Modular forms", "Morse Theory, by Thomas Barnet-Lamb, John Francis, Mike Hill, Andrew Lobb, Harvard Math Department	4/11/06	The maximal abelian extension of Q_p, by Emily Riehl, Harvard Undergraduate
4/4/06	The inefficiency of selfishness, by Greg Valiant, Harvard Undergraduate	3/21/06	Dirichlet's Prime Number Theorem: Algebraic and Analytic Aspects , by Igor Rapinchuk, Harvard Math Department
3/14/06	Why Pi = 2.2222 ..., by Paul Bamberg, Harvard Math Department	2/28/06	The outer automorphism of S₆, by Noam Elkies, Harvard Math Department
2/21/06	Metric-Preserving Functions, by Scott Kominers, Harvard Undergraduate	2/14/06	Zero-Knowledge Proofs, by Joshua Kroll, Harvard Undergraduate
2/1/06	Spring 2006 Tutorials 'Height Functions in Diophantine Geometry', 'Sphere Packing', 'Geometry and Physics', by Sonal Jain, Abhinav Kumar, Aleksandar Subotic, Harvard Math Department

Photos of the mathtable of November 22, 2005. Also present is John Tate, who had attended some Math table talks here at Harvard as an undergraduate 60 years ago.

Fall 2005

12/13/05	The Mathematics Contest in Modeling: A Better QuickPass System for Amusement Parks, by Ivan Corwin, Sheel Ganatra, and Nik Rozenblyum, Harvard Undergraduates	12/6/05	Putnam Post Mortem, by Noam Elkies, Harvard Math Department
11/29/05	Measurable dynamics of the p-adic shift and its relatives, by Alex Levin and Anatoly Preygel, Harvard Undergraduates	11/22/05	3472073⁷ + 4627011⁷ ~=~ 4710868⁷ and other LLL tricks., by Noam Elkies, Harvard Math Department
11/15/05	Bugs, blobs, and rotor-routers: an introduction to quasirandomness, by Jim Propp, University of Wisconsin at Madison	11/8/05	Quadratic extensions of Q_p, by Emily Riehl, Harvard Undergraduate
11/1/05	Trefoils on your Shoes,Knots, Surfaces and Matrices, by Gerardo Con Diaz, Harvard Undergraduate	10/25/05	Elliptic Curves and Mordell's Theorem, by Igor Rapinchuk, Harvard Undergraduate
10/18/05	Modeling Financial Risk, by Michael Vranos and Andrew Lesniewski, CEO, Ellington Management Group, rsp. Director of Quantitative Research	10/11/05	What do the integers from 1 to 10 know about the Cantor set?, by Benedict Gross, Leverett Professor of Mathematics and Dean of Harvard College.
9/27/05	Knaster's conjecture, and level landing sites for lunar modules., by Peter Kronheimer, Head Tutor in Mathematics Harvard Math Department.	9/20/05	Tutorials 'Binary quadratic forms', 'Holomorphic vector bundles', by Chung Pang Mok, Sabin Cautis, Harvard Math Department

Image credit: Doug Dunham, based on pictures of the Dutch artist M. C. Escher.

Congratulations to the winners of the prizes for undergraduates 2004-2005:

1. DAVID MUMFORD PRIZE will go to Gabriel Carroll and Ian Le

DAVID B. MUMFORD UNDEGRADUATE MATHEMATICS PRIZE From the income of the gift in 1997 of Peter L. Falb, A.B. 1957, A.M. 1957, Ph.D. 1961 to establish the David B. Mumford Undergraduate Mathematics Prize, to be given annually to the most promising senior concentrator in mathematics, provided such concentrator is outstanding.

2. ROBERT FLETCHER ROGERS PRIZES for 2004-2005: First prize: Ronen Mukamel for his talk on "Four Things You Can Do in the Hyperbolic Plane that Your Parents Couldn't in the Euclidean" Two Second Prizes will go to: Mike Hamburg for his talk on "Compass and Straightedge Constructions for Projectile and Orbital Motion" Adam Levine for his talk on "Word-Hyperbolic Coxeter Groups"

ROBERT FLETCHER ROGERS PRIZE. From the income of the gift in 1921 of the late Robert Fletcher Rogers, A.B. 1886, there have been established a first prize and second prize to be awarded annually to the College students who present the best talks before the Mathematics Table during an academic year. In making the awards, emphasis will be laid primarily on the excellence of the oral presentation. It is not essential that the material presented be original, but mastery of the subject and adaptation of the presentation will be regarded as important. The prizes will be awarded by the Department of Mathematics on the recommendation of the Mathematics Table. For further information, please contact the Mathematics Department.

3. The WISTER PRIZE will go to Andrei Jorza

WISTER PRIZE. From a bequest of Charles J. Wister, a prize is awarded in alternate years to the senior concentrating in Mathematics or Music who has the highest record in his/her field of concentration. In 2004-05 the prize is open to concentrators in Mathematics, in 2005-06 to concentrators in Music.

Spring 2005

5/10/05	Four things you can do in the Hyperbolic plane that your parents couldn't in the Euclidean, by Ronen Mukamel, Harvard Undergraduate	5/3/05	A Modular Proof of the Class Number One Problem, by Tseno Tselkov, Harvard Undergraduate
4/26/05	The Riemann-Weierstrass Function, by Ian Le, Harvard Undergraduate	4/19/05	World-Hyperbolic Coxeter Groups, by Adam Levine, Harvard Undergraduate
4/12/05	Tropical Geometry, by Ilia Zharkov, Harvard Math Department	4/5/05	Summertutorials 'Bilinear forms in algebra', 'topology and arithmetic', 'Knot theory', 'Spectral sequences, How to talk to physicists, Groups, symmetry and topology', by John Francis, Andrew Lobb, Mike Hill, Daniel Larson, Harvard Math Department
3/22/05	Math and Logic Puzzles: Base 3 Representations, Modular Arithmetic and other fun techniques, by Daniel Gardiner, Harvard Undergraduate	3/15/05	Your Answer May Vary: Probability Enigmas Beyond Monty Hall, by Eric Wepsic, D.E. Shaw \& Co
3/8/05	Are we living in 10 dimensional space-time?, by René Reinbacher, Harvard Math Department	3/1/05	The curious power series, by Noam Elkies, Harvard Math Department
2/22/05	The busy Laplacian, by Mark Reeder, Boston College	2/15/05	Solving equations using unique factorization, by Robert Pollack, Boston University
2/8/05	An introduction to Geometric Knot Theory, by Elizabeth Denne, Harvard Math Department	2/1/05	Tutorials: Complex Multiplication and Sheaves in Logic and Geometry, by Sug Woo Shin and Teru Yoshida, Jay Pottharst and Cameron Freer, Harvard Math Department

Fall 2004

12/7/04	Putnam Post Mortem, by Noam Elkies, Harvard Math Department	11/30/04	A Sharp Bound for the Degree of Proper Monomial Mappings Between Balls: a combinatorial approach, by Emily Riehl, Harvard Undergraduate
11/23/04	Compass and straightedge constructions for projectile and orbital motion, by Mike Hamburg, Harvard Undergraduate	11/16/04	Math for America, by Irwin Kra, Math for America
11/9/04	The Math Graduate School Discussion Panel, by recent Ph.D.'s and current graduate students, from Harvard, MIT, Princeton, Berkeley, Chicago, etc	11/2/04	Cryptography and Electronic Elections" , by Alex Levin, Harvard Undergraduate
10/19/04	cos(2 Pi/17), by Matt Leingang, Mathematics Department	10/12/04	Mathematical Topics in Quantum Physics, by Robbie Martinez, Division of Engeneering and Applied Sciences
10/5/04	Wavelets, Uniform and Otherwise, by Derek Bruff, Mathematics Department	9/28/04	Welcoming Address: "The Evolution of Plane Curves , by Joe Harris , Chair of the Mathematics Department
9/21/04	Tutorials, by Additive Number Theory and Algebraic Surfaces and Complex Manifolds of Higher Dimension, Michael Schein and Sabin Cautis

Congratulations to the winners of the Math Prizes 2003-2004: 

1. DAVID MUMFORD PRIZE goes to Dimitar Jetchev

2. ROBERT FLETCHER ROGERS PRIZES for 2003-2004:

Corina Patrascu - the First Prize for a talk on
"Computing order statistics in the Farey sequence"

Jonathan Bloom - the Second Prize for a talk on
"The Local Structure of Smooth Maps of Manifolds"

Spring 2004

4/27/04	The Local Structure of Smooth Maps of Manifolds, by Jonathan Bloom, Harvard Undergraduate	4/20/04	Number Theory in Function Fields: Dirichlet's Theorem about Primes in Arithmetic Progressions, by Athanasios Papaioannou, Harvard Undergraduate
4/13/04	Summer Tutorials Riemann Surfaces, Spinors, Differential Geometry with a view toward Physics and Ramsey Theory, by Deepee Khosla, John Francis, Aaron Tievsky and Alexander Pekker, Harvard University	4/6/04	Computing order statistics in the Farey sequence, by Corina Patrascu, Harvard Undergraduate
3/23/04	Automatic Groups, by Kazem Mahdavi, SUNY Potsdam and Harvard Math Department	3/16/04	On Quaternions and Octonions, by Andrew Ostergaard, Harvard Undergraduate
3/2/04	The Incredible Shrinking Data, by Derek Bruff, Harvard Math Department	2/24/04	Applications of Subharmonic Functions, by Oliver Knill, Harvard Math Department
2/17/04	The Ising model in Statistical Mechanics, by Alberto DeSole, Harvard Math Department

Fall 2003

12/9/03	This years Putnam Exam, by Noam Elkies, Harvard Math Department	11/25/03	Infinite-dimensional Lie algebras and the Virasoro algebra, by Alberto DeSole, Harvard Math Department
11/18/03	A proof of a theorem of Euclid, by Richard Rivero, Harvard Undergraduate	11/11/03	Lost in 3-Space: Electric Circuits and Polya's Theorem on Random Walks, by Phil Zeyliger, Harvard Undergraduate
11/4/03	The Graduate School Discussion Panel , by recent Ph.D.'s and current graduate students, from Harvard, MIT, Princeton, Berkeley, Chicago, Stanford	10/28/03	Perfect Matchings and the Octahedron Recurrence, by Gabriel Carroll, Harvard Undergraduate
10/21/03	Three Dimensional Manifolds and Surgery, by Tom Coates, Harvard Math Department	10/14/03	Testing for Mersenne Primes" by, by Benedict H. Gross, Dean of Harvard College
10/6/03	The Cayley-Menger Determinant and You, by Matt Leingang, Harvard Math Department	9/30/03	Mathematics as a Cultural System, by Colin Kelly, Harvard Undergraduate
9/23/03	Quantum Gravity, by Cliff Taubes, Harvard Math Department	9/16/03	Tutorials: 'Geometric Topology' 'Morse Theory' , by Curt McMullen and Erick Matsen and Ciprian Manolescu, Harvard Math Department

Math Prizes 2002-2003:
1. DAVID MUMFORD PRIZE goes to Andrew Cotton
2. WISTER PRIZE goes to James Fowler
3. ROBERT FLETCHER ROGERS PRIZES: Andrew Cotton and James Fowler

Spring 2003

5/13/03	An Introduction to the Word Problem in Finitely Presented Groups, by Jordanna Schutz , Harvard Undergraduate	5/6/03	Holomorphic curves and minimal surfaces, by Andy Cotton , Harvard Undergraduate
4/29/03	SL₂(Q₂) and the Homogeneous Tree of Degree 3, by Joe Rabinoff , Harvard Undergraduate	4/22/03	Singular Moduli, by Tony Varilly , Harvard Undergraduate
4/15/03	Julia Sets, by Dustin Cartwright , Harvard Undergraduate	4/8/03	Summer Tutorials 'Symplectic and Contact Geometry', Real and Complex Manifolds' Topics in Group Theory Geometry and General Relativity, by Ciprian Manolescu, Deepee Khosla, Abhinav Kumar, Vivek Mohta, Mathematics Department
3/18/03	Primes in Arithmetic Sequences" , by Gordon Savin, University of Utah	3/11/03	The Banach-Tarski Paradox" , by Matt Bainbridge, Harvard Graduate Student
3/4/03	How to Triangulate a Polytope" , by Laura Matusevich , Harvard Math Department	2/25/03	Multiple Zeta Values" , by Richard Cudney , Harvard Undergraduate
2/18/03	The m-step, same-step and any-step competition graphs" , by Wei Ho , Harvard Undergraduate	2/11/03	Approximation by Polynomials with Integral Coefficients" , by Laurent Berger, Harvard Math Department
2/4/03	Surreal games" , by Jim Fouler, Harvard Undergraduate	1/28/03	Tutorials: K-Theory and its Applications ,Quantum Mechanics for the Masses and the Mass-less , by Nick Ramsey, Greg Grigorov, Spiro Karigiannis , Harvard Math Department

Fall 2002

12/10/02	The 2002 Putnam exam , by Noam Elkies , Harvard Math Department	12/3/02	Graduate Discussion Panel , by Recent Ph.D's and current Grad students , Harvard/MIT/Berkeley,Chicago,Columbia
11/26/02	Domains of Holomorphy and the Levi Problem, by Andreea Nicoara , Harvard Math Department	11/19/02	Mortgages Mathematics, by Michael Vranos and John Geanakoplos , CEO and Managing Partner Ellington Management Group rsp. Professor of Economics, Yale University
11/12/02	Geometric Group Theory, by Kathy Paur, Harvard Math Department	11/5/02	Reachability of Points in Phase Space, by Michael Brian McElroy, Graduate Student at DEAS, Harvard Math Department
10/29/02	Foundations of Decision Theory, by Howard Raiffa, Frank P. Ramsey Professor of Managerial Economics Emeritus, Harvard Math Department	10/22/02	Kronecker's Theorem on the Density of Cyclic Subgroups of (R/Z)^k, by Peter Green , Harvard Math Department
10/15/02	Loves Me, Loves Me Not: what you shouldn't do after you dissect a Square into Identical Triangles, by Jim Fowler , Harvard Undergraduate	10/8/02	The Singular Value Decomposition and Image Storage, by Thomas Judson , Harvard Math Department
10/1/02	Computer Generation of the Maskit Slice, by Zak Stone , Harvard Undergraduate	9/24/02	Are Cubics Rational? (Welcoming Address), by Joe Harris, Chair of the Mathematics Department
9/17/02	Math Tutorials: A Plethora of Polynomials, Bundles of Bundles, by Matt Bainbridge, Alina Marian , Harvard Math Department

Math Prizes: 2001-2002: Lionel Levine, for his talk on "Clifford Algebras and Vector Fields on Spheres" and Alex Healy, for his talk on "Zero Knowledge Proofs"

Spring 2002

5/14/02	Soliton Cellular Automata, by Richard Cudney , Harvard undergraduate	5/7/02	Steenrod Powers, the Serre Spectral Sequence and the Computation of Homotopy Groups of Spheres Using Cohomology, by Mike Hill, Harvard undergraduate
4/30/02	The generalized Poincaré Conjecture, Exotic Spheres and the Surgery Theoretic Classification of High-Dimensional Manifolds, by Jonathan Kelner, Harvard undergraduate	4/23/02	Three Proofs of Quadratic Reciprocity in 33 Minutes, by Noah Snyder, Harvard undergraduate
4/16/02	Do Math, Have Fun, Get Paid: R.E.A.C.H.-ing new results in Combinatorics, by Jim Propp , Harvard Math Department	4/9/02	Cleverly Painted Mules: Epistemic Closure, Logic, and Evidence, by Haiwen Chu , Harvard Undergraduate
4/2/02	Summer Tutorials!, by Ciprian Manolescu, David Dumas, Noah Snyder and Peter Green , Harvard Math Department	3/19/02	The 7-Color Theorem, by Stephen DeBacker , Harvard Math Department
3/12/02	Is there a cube-tiling of dimension 7 in which no pair of cubes share a complete 6-dimensional face?, by John Mackey , Harvard Math Department	3/5/02	How Many Equilibria Are There? An Introduction to Morse Theory, by Robin Forman, Rice University (Harvard Ph.D. '85)
2/26/02	Clifford Algebras and Vector Fields on Spheres, by Lionel Levine , Harvard Undergraduate	2/19/02	Finite Projective Planes: A Mathematical Definition of 'Nice', by Gregg Musiker , Harvard Undergraduate
2/12/02	Zero Knowledge Proofs, by Alex Healy, Harvard Undergraduate	2/5/02	Predicting Gene Function, by Steve Altschulter , Center for Genomics Research
1/29/02	Math Tutorials: Statistics and Applications to Biology, Milnor's Seven Spheres - Algebraic and Differential Topology, by Stan Sawyer, Jake Rasmussen, Harvard Math Department

Photos from the event on Wednesday, September 19. 2001, Cliff Taubes gave the welcoming talk on the impact of path integrals in Mathematics.

Fall 2001

12/12/01	The COMAP Mathematical Modelling Competition, The Putnam Exam for Applied Mathematics, by Michael Brenner, Harvard Math Department (DEAS)	12/5/01	Noam Elkies, by Problems from this years Putnam exam, Harvard Math Department
11/27/01	1+1 \<1, by Richard Cudney, Harvard Undergraduate	11/20/01	q-series Identities and a New Result on the Representation of Integers as Sums of Triangular Numbers, by Jayce Getz, Harvard Undergraduate
11/13/01	Graduate Discussion Panel, by Recent Ph.D's and current grad students, Harvard Math Department/MIT/Berkeley,Chicago,Columbia	11/6/01	Geometric Evolution, by Albert Chau, Harvard Math Department
10/30/01	Well-covered graphs and the roller coaster conjecture, by Phil Matchett, Harvard Undergraduate	10/23/01	Groups of Loops, Bounding the Volume of Hyperbolic 3-manifolds, by Jim Fowler, Harvard Undergraduate
10/16/01	Tony Varilly, by Harvard Undergraduate , Primes mod 4 and Dirichlets Theorem on Arithmetic Progressions	10/09/01	The Volume and Area of the n-Sphere, by Youngsub Yoon, Harvard Undergraduate
10/02/01	Cause we living in an Euclidean world, 'Proofs' of the Parallel Postulate, by Ari Schwayder, Harvard Undergraduate	9/25/01	Kant and the Axiom of Abstraction, by Sarah Moss , Harvard Undergraduate
9/16/01	The impact of path integrals in Mathematics (Photos), by Cliff Taubes , Harvard Math Department	9/11/01	The REACH Program and Exciting Math Tutorials, by Jim Propp, Eddy Lee and Marty Weissman, Harvard Math Department

Food and chat before the talk.

Spring 2001

5/8/01	Rearrangeable Oompaloompas: Recent Open Questions in Graph Theory, by Sarah Moss, Harvard Undergraduate	5/1/01	Lifting the p-th Power Map to Characteristic 0, by Anna Medvedovsky, Harvard Undergraduate
4/24/01	Fun with p-Orderings, by Davesh Maulik, Harvard Undegraduate	4/17/01	Mandelbrot's Conjecture and Critical Exponents for Brownian Motion, by Nick Roussanov, Harvard Undergraduate
4/3/01	All Functions Are Continuous, by Richard Cudney, Harvard Undergraduate	3/20/01	Doing Gauss one better: Construction of the regular 257-gon using Mathematica , by Qian (Pinky) Zhang, Harvard Undergraduate
2/20/01	Accounting for Variability: Algebra, Statistics, and Measure Theory, by Rick Cleary, Associate Dean at Cornell	2/13/01	Finite Geometries, by Lionel Levine, Harvard Undergraduate
2/6/01	Richard Cudney, by y x = q x y, Harvard Undergraduate	1/30/01	Tutorials: Codes and Algebraic Curves, Symmetric Groups, Fourier Analysis , by Greg Warrington, Russ Mann, Andy Engelward and John Boller , Harvard Math Department


The speaker Cliff Taubes on "4 dimensions" 26. September 2000

Fall 2000

12/12/00	Really Big Numbers, by Jim Fowler, Harvard Undergraduate	12/5/00	Ramsey Theory, or Why Are There So Many People Who Don't Know Each Other at my Party, by Andrew Ostergaard, Harvard Undergraduate
11/28/00	The Symplectic Camel and other animals, by Dusa McDuff, SUNY Stony Brook	11/21/00	The Graduate School Discussion Panel, by recent Ph.D.'s and current graduate students , Harvard, MIT, etc
11/14/00	Voter Distances, by Ken Fan, Harvard University	11/7/00	Wild Topology in 2 and 3 Dimensions, by Danny Calegari, Harvard Math Department
10/31/00	Why exp(pi 163^1/2) is almost an integer... or April Fools, Elliptic Curves and Complex Multiplication, by Matthew Baker, Harvard Math Department	10/24/00	Dennis Clark, by Harvard Undergraduate , Lattices on Parabolic Trees
10/17/00	An Intriguing Open Problem in Chaos Theory, by Oliver Knill, Harvard Math Department	10/10/00	Permutations, reduced decompositions, and Young tableaux, by Richard Stanley, MIT and Harvard Math Departments
10/3/00	Keller's Cube Tiling Conjecture, by John Mackey, Harvard Math Department	9/26/00	Four Dimensions, by Cliff Taubes, Harvard Math Department
9/19/00	Tutorials: Making Waves: Fourier Analysis and Applications Computational Algebraic Geometryg , by Russ Mann and Hal Schenck, Harvard Math Department

Spring 2000

5/14/00	Seniors' Thesis Reflections , by Various speakers, Harvard Undergraduates	5/9/00:	Efficient Methods for Almost Proving Things , by Lauren Williams, Harvard Undergraduate
5/2/00	Breakfast on the Beach: Tiling Beach Balls and Bagels , by Lisa Powell, Harvard Undergraduate	4/25/00	Spinors in Mathematics , by Dan Lee, Harvard Undergraduate
4/18/00	A "new" proof that the square root of 2 is irrational , by Max Lieblich, Harvard Undergraduate	4/11/00	Spacetime Geometry, Graph Theory , by Spiro Karigiannis, Ian Dowker, Harvard Math Department
4/4/00:	Coloring Links in the Plane , by Travis Schedler, Harvard Undergraduate	3/21/00	Quantum Factorization , by Richard Cudney, Harvard Undergraduate
3/14/00	Contrary to Popular Belief, Rⁿ is not the same as R^m, by Mike Hill, Harvard Undergraduate	3/7/00:	Zeta(3) is irrational , by Stephen Miller, Yale University
2/29/00	Iterates of a Spiky Function , by Lionel Levine, Harvard Undergraduate	2/22/00	Lie Groups and Geometry , by Megan Kerr, Wellesley College
2/15/00	Knots and Knotted Graphs , by Daniel Allcock, Harvard Math Department	2/8/00:	The Ham Sandwich Theorem , by Tara Holm, MIT Grad student

DAVID B. MUMFORD UNDERGRADUATE MATHEMATICS PRIZE From the income of the gift in 1997 of Peter L. Falb, A.B. 1957, A.M. 1957, Ph.D. 1961 to establish the David B. Mumford Undergraduate Mathematics Prize, to be given annually to the most promising senior concentrator in mathematics, provided such concentrator is outstanding.)
WISTER PRIZE From a bequest of Charles J. Wister, a prize is awarded in alternate years to the Senior concentrating in Mathematics or Music who has the highest record in his/her field of concentration. In 2001-2002 the prize is open to concentrators in Music, in 2002-03 to concentrators in Mathematics. Further information may be obtained from the Departments of Mathematics and Music.)
ROBERT FLETCHER ROGERS PRIZE From the income of the gift in 1921 of the late Robert Fletcher Rogers, A.B. 1886, there have been established a first prize and second prize to be awarded annually to the College students who present the best talks before the Mathematics Table during an academic year. In making the awards, emphasis will be laid primarily on the excellence of the oral presentation. It is not essential that the material presented be original, but mastery of the subject and adaptation of the presentation will be regarded as important. The prizes will be awarded by the Department of Mathematics on the recommendation of the Mathematics Table.

Fall 1999

12/7/99	Pondering Putnam Problems , by Noam Elkies, Harvard Math Department	11/30/99	Making Money with Math , by Eric Wepsic, Harvard Alumnus
11/23/99	Hyperspheres, symmetries and Diophantine equations , by Damien Wisniewski, Harvard Undergrduate	11/16/99	Panel Discussion on Graduate Schools , by Recent Ph.D.'s and current graduate students, from Harvard, MIT, Princeton, Berkeley, Chicago, etc
11/2/99	All triangles are isosceles and other strange p-adic facts , by John Boller, Harvard Math Department	10/26/99	Polytopes in four dimensions , by Eric Sommers, Harvard Math Department
10/19/99	Polytopes and their fans , by Kalle Karu, Harvard Math Department	10/12/99	Inverse Galois theory , by Tammy Lefcourt, Harvard Math Department
10/5/99	The geometric structure of a 1-point space , by Brian Conrad, Harvard Math Department	9/28/99	Lattices in Euclidean Space , by Benedict Gross, Harvard Math Department

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