Department of Mathematics FAS Harvard University One Oxford Street Cambridge MA 02138 USA Tel: (617) 495-2171 Fax: (617) 495-5132

Latest Mathtable

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

Fall 2008

12/9/08 Noam D. Elkies Putnam Postmortem, by Noam D. Elkies, Harvard Math Department 12/02/08 Christian Zamora Jaen Analyzing Complex Semisimple Lie Algebras, by Christian Zamora Jaen , Harvard Undergraduate
11/25/08 Jeremy Booher Many Proofs of Quadratic Reciprocity, by Jeremy Booher, Harvard Undergraduate 11/18/08 recent Ph.D.'s and graduate students The Math Graduate School Discussion Panel, by recent Ph.D.'s and graduate students , from Berkeley, Cambridge, MIT, Harvard, Princeton etc.
11/11/08 Scott Kominers Matchmaker, matchmaker, clear out my house., by Scott Kominers, Harvard Undergraduate 11/4/08 Zachary Abel Hinged dissections exist, by Zachary Abel, Harvard Undergraduate
10/28/08 John Duncan Dynkin diagrams, or what to tell the aliens, by John Duncan, Harvard University 10/21/08 Laura Starkston Knots, Spirals, and Superinvariants, by Laura Starkston , Harvard Undergraduate
10/14/08 William Dunham Mathtable joins Clay Math public lecture. "A Tribute to Euler", by William Dunham, Harvard University 10/7/08 Sing-Tung Yau The gap between the first two eigenvalues of the Schroedinger operator and methods from geometry, by Sing-Tung Yau, Harvard University
9/23/08 Noam Elkies The Weil representation, by Noam Elkies, Harvard University 9/16/08 Ryan Reich and LeAnh Vinh 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 Jeremy Booher Division Algebras over R, by Jeremy Booher, Harvard Undergraduate 4/29/08 Jesse Geneson Self-Reference and Provability, by Jesse Geneson , Harvard Undergraduate
4/22/08 Lydia Bieri General Relativity and the Mathematics of the Universe, by Lydia Bieri, Harvard University 4/15/08 Gabor Domokos and Peter Varkonyi Mono-monostatic bodies: the story of the Gomboc, by Gabor Domokos and Peter Varkonyi, Budapest University of Technology and Economics.
4/8/08 Rohit Acharya and Alex D'Amour Beyond Batting Averages, by Rohit Acharya and Alex D'Amour, Harvard Undergraduates 4/1/08 Christian Zamora Jaen Fermat's Last Theorem, by Christian Zamora Jaen, Harvard Undergraduate
3/18/08 Rehana Patel The Fraisse Construction and its Descendants, by Rehana Patel, Harvard University 3/14/08 Pi Pi-day 2008, by Pi, Mathematical constant
3/4/08 Daniel Litt Color by Numbers, by Daniel Litt, Harvard Undergraduate 2/26/08 Bret Benesh Probabilistic Group Theory, by Bret Benesh, Harvard University
2/5/08 Juliana Belding Curves, Cryptography and Primes of the Form x2 + D y2, by Juliana Belding , University of Maryland
Gabor Domokos
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:
  1. Domokos, G., Ruina, A., Papadopoulos, J.: Static equilibria of rigid bodies: is there anything new? J. Elasticity, 36 (1994), 59-66.
  2. 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 Tanya Khovanova Integers and Sequences, by Tanya Khovanova, Lead Analyst at BAE Systems 12/4/07 Noam D. Elkies Putnam Postmortem, by Noam D. Elkies, Harvard Math Department
11/27/07 Christian Zamora Jaen "Binary Quadratic Forms and Ideal Class Groups", by Christian Zamora Jaen, Harvard Undergraduate 11/20/07 Julia Shlozman "Playing Modulor: Combination and the Golden Ratio in the Work of Le Corbusier", by Julia Shlozman, Harvard Undergraduate
11/06/07 Arnav Tripathy "Relativistic Electromagnetism", by Arnav Tripathy, Harvard Undergraduate 10/30/07 Scott Kominers "C=15", by Scott Kominers, Harvard Undergraduate
10/23/07 Pablo Azar "Firefly Self-Synchronization models and their applications", by Pablo Azar , Harvard Undergraduate 10/16/07 Andrew Lesniewski "The Mathematics of fixed income Markets", by Andrew Lesniewski, Managing Director Ellington Management Group
10/09/07 A Representative from the Company "Mathematics used at Google", by A Representative from the Company, Google 10/02/07 Bret Benesh "The Icosahedral Group", by Bret Benesh, Harvard University
9/25/07 Peter Kronheimer Knots, and how to unknot them , by Peter Kronheimer , Head Tutor in Mathematics Harvard Math Department. 9/18/07 Bret Benesh Introductions, Announcements, and Problem Solving, by Bret Benesh, Harvard University
 
mathtable photo of September 25 2007
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 Serena Rezny A Queuing Model for Use of Laundry Machines in Student Dormitories, by Serena Rezny, Harvard Undergraduate 4/17/07 Thomas Barnet-Lamb, Dawei Chen, David Geraghty and Jeechul Woo 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 Shrenik Shah Quantum Computation and Shor's Algorithm, by Shrenik Shah, Harvard Undergraduate 3/13/07 Kaloyan Slavov Abelian extensions and analytic functions, by Kaloyan Slavov, Harvard Undergraduate
2/27/07 Noam Elkies How many irreducibles?, by Noam Elkies, Harvard University 2/20/07 Zachary Abel How many primes?, by Zachary Abel, Harvard Undergraduate
2/13/07 Thomas Lam Young tableaux and permutations, by Thomas Lam, Harvard University 1/30/07 Chung Pang Mok, Rina Anno 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

icons 		As of January 1, 2007, there are 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 Alison Miller Exp(pi*Sqrt(163)) and Friends, by Alison Miller, Harvard Undergraduate 12/5/06 Noam D. Elkies Putnam Postmortem , by Noam D. Elkies, Harvard Math Department
11/28/06 Alexander Ellis Dunking Donuts: Morse theory and the Poincare-Hopf theorem, by Alexander Ellis, Harvard Undergraduate 11/21/06 Scott Kominers Opetopia, by Scott Kominers, Harvard Undergraduate
11/14/06 Noam Elkies SO(4)/{1,-1} = SO(3) x SO(3) , by Noam Elkies, Harvard Math Department 10/31/06 Noam Elkies Inversive Geometry , by Noam Elkies, Harvard Mathematics Department
10/24/06 Robin Walters Generalizations of the Hexagonal Honeycomb Theorem , by Robin Walters, Harvard Undergraduate 10/17/06 Gerardo Con Diaz Cutting and Pasting Doughnuts: Three Ways of Constructing Lens Spaces, by Gerardo Con Diaz, Harvard Undergraduate
10/11/06 Andrew Lesniewski Mathematics and financial modeling , by Andrew Lesniewski, Managing Director, Ellington Management Group 10/3/06 Stewart Wilcox Rubik's Hyperhexahedra , by Stewart Wilcox, Harvard Mathematics Department
9/26/06 Clifford Taubes Spectral flow , by Clifford Taubes, William Petschek Professor of Mathematics and Chair of the Harvard Mathematics Department 9/19/06 Dawei Chen, Chen-Yu Chi, Aleksandar Subotic 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 Corina Tarnita Patrascu The 30 Minute Introduction to Algebraic Geometry, by Corina Tarnita Patrascu, Harvard Undergraduate 4/25/06 Inna Zakharevich Homotopy and Simplicial Sets, by Inna Zakharevich, Harvard Undergraduate
4/18/06 Thomas Barnet-Lamb, John Francis, Mike Hill, Andrew Lobb 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 Emily Riehl The maximal abelian extension of Qp, by Emily Riehl, Harvard Undergraduate
4/4/06 Greg Valiant The inefficiency of selfishness, by Greg Valiant, Harvard Undergraduate 3/21/06 Igor Rapinchuk Dirichlet's Prime Number Theorem: Algebraic and Analytic Aspects , by Igor Rapinchuk, Harvard Math Department
3/14/06 Paul Bamberg Why Pi = 2.2222 ..., by Paul Bamberg, Harvard Math Department 2/28/06 Noam Elkies The outer automorphism of S6, by Noam Elkies, Harvard Math Department
2/21/06 Scott Kominers Metric-Preserving Functions, by Scott Kominers, Harvard Undergraduate 2/14/06 Joshua Kroll Zero-Knowledge Proofs, by Joshua Kroll, Harvard Undergraduate
2/1/06 Sonal Jain, Abhinav Kumar, Aleksandar Subotic Spring 2006 Tutorials 'Height Functions in Diophantine Geometry', 'Sphere Packing', 'Geometry and Physics', by Sonal Jain, Abhinav Kumar, Aleksandar Subotic, Harvard Math Department
mathtable photo of november 22 2005
mathtable photo of november 22 2005
mathtable photo of november 22 2005
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 Ivan Corwin, Sheel Ganatra, and Nik Rozenblyum 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 Noam Elkies Putnam Post Mortem, by Noam Elkies, Harvard Math Department
11/29/05 Alex Levin and Anatoly Preygel Measurable dynamics of the p-adic shift and its relatives, by Alex Levin and Anatoly Preygel, Harvard Undergraduates 11/22/05 Noam Elkies 34720737 + 46270117 ~=~ 47108687 and other LLL tricks., by Noam Elkies, Harvard Math Department
11/15/05 Jim Propp Bugs, blobs, and rotor-routers: an introduction to quasirandomness, by Jim Propp, University of Wisconsin at Madison 11/8/05 Emily Riehl Quadratic extensions of Qp, by Emily Riehl, Harvard Undergraduate
11/1/05 Gerardo Con Diaz Trefoils on your Shoes,Knots, Surfaces and Matrices, by Gerardo Con Diaz, Harvard Undergraduate 10/25/05 Igor Rapinchuk Elliptic Curves and Mordell's Theorem, by Igor Rapinchuk, Harvard Undergraduate
10/18/05 Michael Vranos and Andrew Lesniewski Modeling Financial Risk, by Michael Vranos and Andrew Lesniewski, CEO, Ellington Management Group, rsp. Director of Quantitative Research 10/11/05 Benedict Gross 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 Peter Kronheimer Knaster's conjecture, and level landing sites for lunar modules., by Peter Kronheimer, Head Tutor in Mathematics Harvard Math Department. 9/20/05 Chung Pang Mok, Sabin Cautis Tutorials 'Binary quadratic forms', 'Holomorphic vector bundles', by Chung Pang Mok, Sabin Cautis, Harvard Math Department
 


illustration by Doug Dunham based on Escher
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 Ronen Mukamel 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 Tseno Tselkov A Modular Proof of the Class Number One Problem, by Tseno Tselkov, Harvard Undergraduate
4/26/05 Ian Le The Riemann-Weierstrass Function, by Ian Le, Harvard Undergraduate 4/19/05 Adam Levine World-Hyperbolic Coxeter Groups, by Adam Levine, Harvard Undergraduate
4/12/05 Ilia Zharkov Tropical Geometry, by Ilia Zharkov, Harvard Math Department 4/5/05 John Francis, Andrew Lobb, Mike Hill, Daniel Larson 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 Daniel Gardiner Math and Logic Puzzles: Base 3 Representations, Modular Arithmetic and other fun techniques, by Daniel Gardiner, Harvard Undergraduate 3/15/05 Eric Wepsic Your Answer May Vary: Probability Enigmas Beyond Monty Hall, by Eric Wepsic, D.E. Shaw \& Co
3/8/05 René Reinbacher Are we living in 10 dimensional space-time?, by René Reinbacher, Harvard Math Department 3/1/05 Noam Elkies The curious power series, by Noam Elkies, Harvard Math Department
2/22/05 Mark Reeder The busy Laplacian, by Mark Reeder, Boston College 2/15/05 Robert Pollack Solving equations using unique factorization, by Robert Pollack, Boston University
2/8/05 Elizabeth Denne An introduction to Geometric Knot Theory, by Elizabeth Denne, Harvard Math Department 2/1/05 Sug Woo Shin and Teru Yoshida, Jay Pottharst and Cameron Freer 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 Noam Elkies Putnam Post Mortem, by Noam Elkies, Harvard Math Department 11/30/04 Emily Riehl A Sharp Bound for the Degree of Proper Monomial Mappings Between Balls: a combinatorial approach, by Emily Riehl, Harvard Undergraduate
11/23/04 Mike Hamburg Compass and straightedge constructions for projectile and orbital motion, by Mike Hamburg, Harvard Undergraduate 11/16/04 Irwin Kra Math for America, by Irwin Kra, Math for America
11/9/04 recent Ph.D.'s and current graduate students 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 Alex Levin Cryptography and Electronic Elections" , by Alex Levin, Harvard Undergraduate
10/19/04 Matt Leingang cos(2 Pi/17), by Matt Leingang, Mathematics Department 10/12/04 Robbie Martinez Mathematical Topics in Quantum Physics, by Robbie Martinez, Division of Engeneering and Applied Sciences
10/5/04 Derek Bruff Wavelets, Uniform and Otherwise, by Derek Bruff, Mathematics Department 9/28/04 Joe Harris Welcoming Address: "The Evolution of Plane Curves , by Joe Harris , Chair of the Mathematics Department
9/21/04 Additive Number Theory and Algebraic Surfaces and Complex Manifolds of Higher Dimension 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 Jonathan Bloom The Local Structure of Smooth Maps of Manifolds, by Jonathan Bloom, Harvard Undergraduate 4/20/04 Athanasios Papaioannou Number Theory in Function Fields: Dirichlet's Theorem about Primes in Arithmetic Progressions, by Athanasios Papaioannou, Harvard Undergraduate
4/13/04 Deepee Khosla, John Francis, Aaron Tievsky and Alexander Pekker 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 Corina Patrascu Computing order statistics in the Farey sequence, by Corina Patrascu, Harvard Undergraduate
3/23/04 Kazem Mahdavi Automatic Groups, by Kazem Mahdavi, SUNY Potsdam and Harvard Math Department 3/16/04 Andrew Ostergaard On Quaternions and Octonions, by Andrew Ostergaard, Harvard Undergraduate
3/2/04 Derek Bruff The Incredible Shrinking Data, by Derek Bruff, Harvard Math Department 2/24/04 Oliver Knill Applications of Subharmonic Functions, by Oliver Knill, Harvard Math Department
2/17/04 Alberto DeSole The Ising model in Statistical Mechanics, by Alberto DeSole, Harvard Math Department

Fall 2003

12/9/03 Noam Elkies This years Putnam Exam, by Noam Elkies, Harvard Math Department 11/25/03 Alberto DeSole Infinite-dimensional Lie algebras and the Virasoro algebra, by Alberto DeSole, Harvard Math Department
11/18/03 Richard Rivero A proof of a theorem of Euclid, by Richard Rivero, Harvard Undergraduate 11/11/03 Phil Zeyliger Lost in 3-Space: Electric Circuits and Polya's Theorem on Random Walks, by Phil Zeyliger, Harvard Undergraduate
11/4/03 recent Ph.D.'s and current graduate students The Graduate School Discussion Panel , by recent Ph.D.'s and current graduate students, from Harvard, MIT, Princeton, Berkeley, Chicago, Stanford 10/28/03 Gabriel Carroll Perfect Matchings and the Octahedron Recurrence, by Gabriel Carroll, Harvard Undergraduate
10/21/03 Tom Coates Three Dimensional Manifolds and Surgery, by Tom Coates, Harvard Math Department 10/14/03 Benedict H. Gross Testing for Mersenne Primes" by, by Benedict H. Gross, Dean of Harvard College
10/6/03 Matt Leingang The Cayley-Menger Determinant and You, by Matt Leingang, Harvard Math Department 9/30/03 Colin Kelly Mathematics as a Cultural System, by Colin Kelly, Harvard Undergraduate
9/23/03 Cliff Taubes Quantum Gravity, by Cliff Taubes, Harvard Math Department 9/16/03 Curt McMullen and Erick Matsen and Ciprian Manolescu 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 Jordanna Schutz An Introduction to the Word Problem in Finitely Presented Groups, by Jordanna Schutz , Harvard Undergraduate 5/6/03 Andy Cotton Holomorphic curves and minimal surfaces, by Andy Cotton , Harvard Undergraduate
4/29/03 Joe Rabinoff SL2(Q2) and the Homogeneous Tree of Degree 3, by Joe Rabinoff , Harvard Undergraduate 4/22/03 Tony Varilly Singular Moduli, by Tony Varilly , Harvard Undergraduate
4/15/03 Dustin Cartwright Julia Sets, by Dustin Cartwright , Harvard Undergraduate 4/8/03 Ciprian Manolescu, Deepee Khosla, Abhinav Kumar, Vivek Mohta 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 Gordon Savin Primes in Arithmetic Sequences" , by Gordon Savin, University of Utah 3/11/03 Matt Bainbridge The Banach-Tarski Paradox" , by Matt Bainbridge, Harvard Graduate Student
3/4/03 Laura Matusevich How to Triangulate a Polytope" , by Laura Matusevich , Harvard Math Department 2/25/03 Richard Cudney Multiple Zeta Values" , by Richard Cudney , Harvard Undergraduate
2/18/03 Wei Ho The m-step, same-step and any-step competition graphs" , by Wei Ho , Harvard Undergraduate 2/11/03 Laurent Berger Approximation by Polynomials with Integral Coefficients" , by Laurent Berger, Harvard Math Department
2/4/03 Jim Fouler Surreal games" , by Jim Fouler, Harvard Undergraduate 1/28/03 Nick Ramsey, Greg Grigorov, Spiro Karigiannis 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 Noam Elkies The 2002 Putnam exam , by Noam Elkies , Harvard Math Department 12/3/02 Recent Ph.D's and current Grad students Graduate Discussion Panel , by Recent Ph.D's and current Grad students , Harvard/MIT/Berkeley,Chicago,Columbia
11/26/02 Andreea Nicoara Domains of Holomorphy and the Levi Problem, by Andreea Nicoara , Harvard Math Department 11/19/02 Michael Vranos and John Geanakoplos Mortgages Mathematics, by Michael Vranos and John Geanakoplos , CEO and Managing Partner Ellington Management Group rsp. Professor of Economics, Yale University
11/12/02 Kathy Paur Geometric Group Theory, by Kathy Paur, Harvard Math Department 11/5/02 Michael Brian McElroy Reachability of Points in Phase Space, by Michael Brian McElroy, Graduate Student at DEAS, Harvard Math Department
10/29/02 Howard Raiffa Foundations of Decision Theory, by Howard Raiffa, Frank P. Ramsey Professor of Managerial Economics Emeritus, Harvard Math Department 10/22/02 Peter Green Kronecker's Theorem on the Density of Cyclic Subgroups of (R/Z)k, by Peter Green , Harvard Math Department
10/15/02 Jim Fowler 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 Thomas Judson The Singular Value Decomposition and Image Storage, by Thomas Judson , Harvard Math Department
10/1/02 Zak Stone Computer Generation of the Maskit Slice, by Zak Stone , Harvard Undergraduate 9/24/02 Joe Harris Are Cubics Rational? (Welcoming Address), by Joe Harris, Chair of the Mathematics Department
9/17/02 Matt Bainbridge, Alina Marian 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 Richard Cudney Soliton Cellular Automata, by Richard Cudney , Harvard undergraduate 5/7/02 Mike Hill Steenrod Powers, the Serre Spectral Sequence and the Computation of Homotopy Groups of Spheres Using Cohomology, by Mike Hill, Harvard undergraduate
4/30/02 Jonathan Kelner The generalized Poincaré Conjecture, Exotic Spheres and the Surgery Theoretic Classification of High-Dimensional Manifolds, by Jonathan Kelner, Harvard undergraduate 4/23/02 Noah Snyder Three Proofs of Quadratic Reciprocity in 33 Minutes, by Noah Snyder, Harvard undergraduate
4/16/02 Jim Propp 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 Haiwen Chu Cleverly Painted Mules: Epistemic Closure, Logic, and Evidence, by Haiwen Chu , Harvard Undergraduate
4/2/02 Ciprian Manolescu, David Dumas, Noah Snyder and Peter Green Summer Tutorials!, by Ciprian Manolescu, David Dumas, Noah Snyder and Peter Green , Harvard Math Department 3/19/02 Stephen DeBacker The 7-Color Theorem, by Stephen DeBacker , Harvard Math Department
3/12/02 John Mackey 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 Robin Forman How Many Equilibria Are There? An Introduction to Morse Theory, by Robin Forman, Rice University (Harvard Ph.D. '85)
2/26/02 Lionel Levine Clifford Algebras and Vector Fields on Spheres, by Lionel Levine , Harvard Undergraduate 2/19/02 Gregg Musiker Finite Projective Planes: A Mathematical Definition of 'Nice', by Gregg Musiker , Harvard Undergraduate
2/12/02 Alex Healy Zero Knowledge Proofs, by Alex Healy, Harvard Undergraduate 2/5/02 Steve Altschulter Predicting Gene Function, by Steve Altschulter , Center for Genomics Research
1/29/02 Stan Sawyer, Jake Rasmussen 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.
table
 

Fall 2001

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

Spring 2001

5/8/01 Sarah Moss Rearrangeable Oompaloompas: Recent Open Questions in Graph Theory, by Sarah Moss, Harvard Undergraduate 5/1/01 Anna Medvedovsky Lifting the p-th Power Map to Characteristic 0, by Anna Medvedovsky, Harvard Undergraduate
4/24/01 Davesh Maulik Fun with p-Orderings, by Davesh Maulik, Harvard Undegraduate 4/17/01 Nick Roussanov Mandelbrot's Conjecture and Critical Exponents for Brownian Motion, by Nick Roussanov, Harvard Undergraduate
4/3/01 Richard Cudney All Functions Are Continuous, by Richard Cudney, Harvard Undergraduate 3/20/01 Qian (Pinky) Zhang Doing Gauss one better: Construction of the regular 257-gon using Mathematica , by Qian (Pinky) Zhang, Harvard Undergraduate
2/20/01 Rick Cleary Accounting for Variability: Algebra, Statistics, and Measure Theory, by Rick Cleary, Associate Dean at Cornell 2/13/01 Lionel Levine Finite Geometries, by Lionel Levine, Harvard Undergraduate
2/6/01 y x = q x y Richard Cudney, by y x = q x y, Harvard Undergraduate 1/30/01 Greg Warrington, Russ Mann, Andy Engelward and John Boller Tutorials: Codes and Algebraic Curves, Symmetric Groups, Fourier Analysis , by Greg Warrington, Russ Mann, Andy Engelward and John Boller , Harvard Math Department
 
Cliff Taubes Mathtable Talk mathtable talk
The speaker Cliff Taubes on "4 dimensions" 26. September 2000
 

Fall 2000

12/12/00 Jim Fowler Really Big Numbers, by Jim Fowler, Harvard Undergraduate 12/5/00 Andrew Ostergaard 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 Dusa McDuff The Symplectic Camel and other animals, by Dusa McDuff, SUNY Stony Brook 11/21/00 recent Ph.D.'s and current graduate students The Graduate School Discussion Panel, by recent Ph.D.'s and current graduate students , Harvard, MIT, etc
11/14/00 Ken Fan Voter Distances, by Ken Fan, Harvard University 11/7/00 Danny Calegari Wild Topology in 2 and 3 Dimensions, by Danny Calegari, Harvard Math Department
10/31/00 Matthew Baker Why exp(pi 1631/2) is almost an integer... or April Fools, Elliptic Curves and Complex Multiplication, by Matthew Baker, Harvard Math Department 10/24/00 Harvard Undergraduate Dennis Clark, by Harvard Undergraduate , Lattices on Parabolic Trees
10/17/00 Oliver Knill An Intriguing Open Problem in Chaos Theory, by Oliver Knill, Harvard Math Department 10/10/00 Richard Stanley Permutations, reduced decompositions, and Young tableaux, by Richard Stanley, MIT and Harvard Math Departments
10/3/00 John Mackey Keller's Cube Tiling Conjecture, by John Mackey, Harvard Math Department 9/26/00 Cliff Taubes Four Dimensions, by Cliff Taubes, Harvard Math Department
9/19/00 Russ Mann and Hal Schenck Tutorials: Making Waves: Fourier Analysis and Applications Computational Algebraic Geometryg , by Russ Mann and Hal Schenck, Harvard Math Department

Spring 2000

5/14/00 Various speakers Seniors' Thesis Reflections , by Various speakers, Harvard Undergraduates 5/9/00: Lauren Williams Efficient Methods for Almost Proving Things , by Lauren Williams, Harvard Undergraduate
5/2/00 Lisa Powell Breakfast on the Beach: Tiling Beach Balls and Bagels , by Lisa Powell, Harvard Undergraduate 4/25/00 Dan Lee Spinors in Mathematics , by Dan Lee, Harvard Undergraduate
4/18/00 Max Lieblich A "new" proof that the square root of 2 is irrational , by Max Lieblich, Harvard Undergraduate 4/11/00 Spiro Karigiannis, Ian Dowker Spacetime Geometry, Graph Theory , by Spiro Karigiannis, Ian Dowker, Harvard Math Department
4/4/00: Travis Schedler Coloring Links in the Plane , by Travis Schedler, Harvard Undergraduate 3/21/00 Richard Cudney Quantum Factorization , by Richard Cudney, Harvard Undergraduate
3/14/00 Mike Hill Contrary to Popular Belief, Rn is not the same as Rm, by Mike Hill, Harvard Undergraduate 3/7/00: Stephen Miller Zeta(3) is irrational , by Stephen Miller, Yale University
2/29/00 Lionel Levine Iterates of a Spiky Function , by Lionel Levine, Harvard Undergraduate 2/22/00 Megan Kerr Lie Groups and Geometry , by Megan Kerr, Wellesley College
2/15/00 Daniel Allcock Knots and Knotted Graphs , by Daniel Allcock, Harvard Math Department 2/8/00: Tara Holm 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 Noam Elkies Pondering Putnam Problems , by Noam Elkies, Harvard Math Department 11/30/99 Eric Wepsic Making Money with Math , by Eric Wepsic, Harvard Alumnus
11/23/99 Damien Wisniewski Hyperspheres, symmetries and Diophantine equations , by Damien Wisniewski, Harvard Undergrduate 11/16/99 Recent Ph.D.'s and current graduate students Panel Discussion on Graduate Schools , by Recent Ph.D.'s and current graduate students, from Harvard, MIT, Princeton, Berkeley, Chicago, etc
11/2/99 John Boller All triangles are isosceles and other strange p-adic facts , by John Boller, Harvard Math Department 10/26/99 Eric Sommers Polytopes in four dimensions , by Eric Sommers, Harvard Math Department
10/19/99 Kalle Karu Polytopes and their fans , by Kalle Karu, Harvard Math Department 10/12/99 Tammy Lefcourt Inverse Galois theory , by Tammy Lefcourt, Harvard Math Department
10/5/99 Brian Conrad The geometric structure of a 1-point space , by Brian Conrad, Harvard Math Department 9/28/99 Benedict Gross Lattices in Euclidean Space , by Benedict Gross, Harvard Math Department
 
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