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

### Latest Mathtable

The undergraduate Mathematics Colloquium meets most Tuesday nights at 5:30 PM in Mather House Private Dining Rooms A & B.
 05/01/2018 Summer Tutorials 2018, by Robert Cass, Morgan Opie and Yongquan Zhang, Harvard University
 Click on the large icon to see all mini posters. Sign up deadline for Summer tutorials: May 11, 2018 Yongquan Zhang Title: Hyperbolic 3-manifolds and Kleinian groups Abstract: Hyperbolic geometry in dimension three connects many topics in mathematics, including three-dimensional topology, Kleinian groups, Teichumuller theory, circle packings and many more. This tutorial focuses on the connection between three dimensional hyperbolic geometry and conformal dynamics on the extended complex plane, via Kleinian groups. The conformal action of Kleinian groups on the extended complex plane provides a visual guide to our study, and we will look at (and try to make!) many fascinating pictures throughout the tutorial. In the end, we will try to venture into the more theoretic side, and depending on the interest and background of the participants, we can talk about structure of cusps, geometric finiteness, arithmetic hyperbolic manifolds, reflection groups and many more. Morgan Opie Tutorial topic: Category Theory Since Eilenberg and Mac Lane introduced category theory in the 1940s, the subject has developed rapidly and become a fundamental part of modern mathematics. Category theory provides a framework to study mathematical structures and constructions, and makes precise analogies between different areas. This tutorial will introduce the tools of category theory, focusing on examples tailored to participants' backgrounds. Fundamental concepts such as categories, functors, natural transformations, representability, limits and colimits, and adjunctions will be covered in detail. We'll also venture into more advanced topics, which, depending on the interests of participants, might include monoidal categories, abelian categories and derived categories, model categories, or infinity categories. In my Math Table talk, I'll give a sense of what category theory is all about and explain why a categorical perspective is useful with a few illustrative examples. Robert Cass Title: Elliptic Curves and Drinfeld Modules Abstract: Elliptic curves are central objects of study in number theory. Elliptic curves can be defined algebraically as the set of solutions to a polynomial equation, but this definition hides one of their fundamental properties: the set of points on an elliptic curve forms a group. In the first half of this tutorial we will establish the basic properties of elliptic curves and explore their connection with Galois theory over the rational numbers. One can also consider elliptic curves over fields of positive characteristic. However, another type of object called a Drinfeld module often contains more interesting arithmetic information. In the second half of this tutorial we will develop the theory of Drinfeld modules while emphasizing their analogies with elliptic curves.

### 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

### Spring 2017

 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

 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

 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.

### 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

### 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

### 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 GLn(Qp) and SLn(Qp), 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 Mg,, 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:
1. First prize: Adrian Sanborn, for his talk Scaling Dimensions with Fractal Curves
2. 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

### Fall 2009

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
 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(pi*Sqrt(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 Qp, 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

 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 1631/2) 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