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9/30/14 Adam Al-natsheh Morse Theory, by Adam Al-natsheh, Harvard Undergraduate
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Abstract:

Raoul Bott supposedly said, "Every mathematician has a secret weapon; mine is Morse theory." Indeed Morse theory is a powerful tool for studying the topology of manifolds via certain real-valued functions on them. We begin by introducing some topological notions such as homotopy (of functions), homotopy equivalence, and deformation retract. In particular, we discuss CW complexes and why they are so important topology. We then build up some of the basic theory, leading towards the Morse lemma and three important theorems. With these results, we can recover the CW structure of a manifold by choosing a 'suitable' function f: M -> R. This structure, which would otherwise be very difficult to obtain, allows us to compute certain topological invariants of a manifold, such as homology. Finally, we conclude with an application to the classification of compact manifolds. The emphasis for the talk will be on developing intuition for how to choose functions and apply the results, rather than on the exact details of the proofs. Much of this information is contained in the first chapter of the classic text Morse Theory by J. Milnor.

Fall 2014

9/30/14 Adam Al-natsheh Morse Theory, by Adam Al-natsheh, Harvard Undergraduate 9/23/14 Stephen Mackereth Reverse Mathematics, by Stephen Mackereth , Harvard Undergraduate
9/16/14 Ashvin Swaminathan Arboreal Galois Representations, by Ashvin Swaminathan, Harvard Undergraduate 9/9/14 Jacob Lurie Combinatorial Game Theory, by Jacob Lurie, Harvard University
9/2/14 Rong Zhou and Yihang Zhu Fall 2014 Tutorial in Mathematics: Complex multiplication, by Rong Zhou and Yihang Zhu, Harvard University

Spring 2014

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

Fall 2013

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

Spring 2013

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

Fall 2012

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

Spring 2012

4/24/12 Rachel Zax Simplifying Complicated Simplicial Complexes: Discrete Morse Theory and its Applications, by Rachel Zax, Harvard Undergraduate 4/17/12 Benjamin Dozier The Julia and Fatou sets of a polynomial map, by Benjamin Dozier , Harvard Undergraduate
4/10/12 Eva Belmont Special K. What is K-theory and why do we care?, by Eva Belmont, Harvard Undergraduate 4/03/12 Panelists: Zachary Abel '10, Eva Belmont '12, Halimeda Glickman-Hoch '12, Katrina Evtimova '13, Tony Feng '13, and Yacoub Kureh '13. 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 Levent Alpoge The Ubiquity of the Bernoulli Numbers, by Levent Alpoge , Harvard Undergraduate 2/28/12 Akhil Mathew   The Grothendieck group , by Akhil Mathew , Harvard Undergraduate
2/28/12 Caitlin Stanton The Euler Characteristic , by Caitlin Stanton , Harvard Undergraduate 2/21/12 Anand Deopurkar What can be computed in mathematics?, by Anand Deopurkar, Harvard University
2/14/12 Emily Riehl The space (locale) of random sequences, by Emily Riehl, Harvard University 2/7/12 Noam Elkies Euler Integrals, and Gauss and Jacobi Sums, by Noam Elkies, Harvard University
1/31/12 Joseph Rabinoff                                   Zolotarev's combinatorial proof of quadratic reciprocity, by Joseph Rabinoff , Harvard University 1/24/12 Omar Antolin Camarena and Stergios Antonakoudis 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 Noam Elkies Putnam Postmortem, by Noam Elkies, Harvard University 11/29/11 Levent Alpoge Fun with Carl and Carl, Messing Around with Gauss and Jacobi Sums, by Levent Alpoge, Harvard Undergraduate
11/15/11 Akhil Mathew Exotic spheres, by Akhil Mathew , Harvard Undergraduate 11/8/11 Noam Elkies Orthogonal polynomials, Gaussian quadrature, and Rolle's theorem, by Noam Elkies, Harvard University
11/1/11 Zach Abel,George Boxer,Nathan Kaplan,Eric Riedl,Peter Smillie,Ethan Street,Meghan Anderson,Jennifer Balakrishnan 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 Jack Huizenga How to count like Schubert, by Jack Huizenga, Harvard University
10/11/18 Daniel Benjamin '99 Why Many Published Experimental Findings Are Probably False, by Daniel Benjamin '99, Cornell and National Bureau of Economic Research 10/11/11 Lucia Mocz Bruhat-Tits Buildings of GLn(Qp) and SLn(Qp), by Lucia Mocz, Harvard Undergraduate
10/4/11 Vaibhav Gadre Interval exchange maps, by Vaibhav Gadre, Harvard University 9/20/11 Zach Abel `10 Unfolding Polyhedra is NP-Hard, by Zach Abel `10, MIT
9/13/11 Noam Elkies 6561101970383!, by Noam Elkies, Harvard University 9/6/11 Peter Kronheimer How I Learned the Fundamental Theorem of Algebra, by Peter Kronheimer, Harvard University
8/30/11 Atanas Atanasov Fall 2011 Tutorial:Category Theory, by Atanas Atanasov, Harvard University

Spring 2011

5/3/11 Aliakbar Daemi, Nathan Kaplan, Sam Raskin: Symplectic Geometry, Coding theory, Representation Theory Summer Tutorials 2011, by Aliakbar Daemi, Nathan Kaplan, Sam Raskin: Symplectic Geometry, Coding theory, Representation Theory, Harvard University 4/26/11 Francois Greer Irreducibility of Mg,, by Francois Greer, Harvard Undergraduate
4/19/11 Adrian Sanborn Scaling Dimensions with Fractal Curves, by Adrian Sanborn, Harvard Undergraduate 4/12/11 Akhil Mathew Interactive Proofs, by Akhil Mathew , Harvard Undergraduate
4/05/11 Panelists: Zachary Abel '10, Tiffany Cai '12, Eva Belmont '12, Francois Greer '11, Dmitri Vaintrob '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 Joe Rabinoff Quaternions in everyday life, by Joe Rabinoff, Harvard University
3/22/11 Rehana Patel Three faces of the Rado graph: What other multi-visaged structures are out there?, by Rehana Patel, 3/8/11 John Mackey Crossing numbers of graphs: origins and recent progress, by John Mackey, Carnegie Mellon
3/1/11 Noam Elkies pi proofs that pi2 smaller 10, by Noam Elkies, Harvard University 2/15/11 Juliana Belding Solving an MC Escher Mystery With Mathematics, by Juliana Belding, Harvard University
2/8/11 Vaibhav Gadre Continued fractions and interval exchange maps, by Vaibhav Gadre, Harvard University 1/25/11 Stergios Antonakoudis. 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 Noam Elkies Putnam Postmortem, by Noam Elkies, Harvard University 11/30/10 Joel Specter Determinacy, by Joel Specter, Visiting Harvard Undergraduate
    11/23/10 Zach Abel ('10) Stably Surrounding Sphere with Smallest String Size, by Zach Abel ('10), MIT graduate student 11/16/10 Scott Kominers ('09) Large Games IV: A New Hope, by Scott Kominers ('09), Economics graduate student at HBS
    11/9/10 Zach Abel, Nathan Kaplan, Erich Riedl, Ethan Street, Charmaine Sia and Sarah Koch 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 Noam Elkies Inversive Geometry, by Noam Elkies, Harvard Mathematics Department
    10/26/10 Akhil Mathews Translation-Invariant Binary Representations, by Akhil Mathews , Harvard Undergraduate 10/19/10 Joel Specter On a conjecture of Lubin, by Joel Specter, Visiting Harvard Undergraduate
    10/12/10 Eric Larson Tannakian Duality for Finite Groups, by Eric Larson , Harvard Undergraduate 10/5/10 Scott Chapman Block Monoids and Factorizations of Algebraic Integers, by Scott Chapman, Sam Houston State University (Huntsville, Texas)
    9/28/10 Akhil Mathew Fourier Series and Elliptic Regularity, by Akhil Mathew , Harvard Undergraduate 9/21/10 Gabor Lippner Limits, measures and democracy , by Gabor Lippner, Harvard University
    9/14/10 Eric Larson    An Inequality Involving the Perimeter and Curvature of Plane Curves, by Eric Larson , Harvard Undergraduate 9/7/10 Shing-Tung Yau Chairman's Welcoming Address: The maximum principle, by Shing-Tung Yau , Harvard University
    8/31/10 Yi Li Fall 2010 Tutorial:Ricci Flow on Surfaces , by Yi Li, Harvard University
    mathtable photo of September 7, 2010
    mathtable photo of September 7, 2010 mathtable photo of September 7, 2010
    Photos of the mathtable of September 7, 2010. Shing-Tung Yau gives a talk on the maximum principle. [See larger panorama photo].


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

    David Mumford Undergraduate Mathematics Prize

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

    Herb Alexander Award

    From the gift of Susan Alexander, the Herb Alexander Award recognizes each year one of our outstanding undergraduates, and provides money to be used for research and travel.
    The Herb Alexander Award is given this year to Zachary Abel.

    Robert Fletcher Rogers Prizes

    From the income of the gift in 1921 of the late Robert Fletcher Rogers, A.B. 1886, there have been established a first prize and second prize to be awarded annually to the College students who present the best talks before the Mathematics Table during an academic year.
    The two prizes are awarded equally this year to:
    • Zhou Fan, for his talk "Random Matrices, Catalan Numbers, and Wigner's Semicircle Law;"
    • Dmitri Vaintrob, for his talk "1+2+3+ ... = -1/12: Values of the Zeta Function at Negative Integers."

    Hoopes Prize

    Michael Viscardi has been awarded the Hoopes' Prize this year, for his senior thesis "Alternative compactifications of the moduli space of genus on maps." Hoopes' Prizes were also won by two of our joint concentrators: Andrei Cristea (Economics and Math), and Chrisopher Lim (Music and Math).
    Congratulations to all!

    Peter Kronheimer, Director of Undergraduate Studies, Department of Mathematics
     

    Spring 2010

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

    Fall 2009

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

    David Mumford Undergraduate Mathematics Prize

    From the income of the gift in 1997 of Peter L. Falb, A.B. 1957, A.M. 1957, Ph.D. 1961 to establish the David B. Mumford Undergraduate Mathematics Prize, to be given annually to the most promising senior concentrator in mathematics, provided such concentrator is outstanding. The Mumford Prize is awarded in 2009 jointly to John Lesieutre and Shrenik Shah.

    Wister Prize

    From a bequest of Charles J. Wister, a prize is awarded in alternate years to the Senior concentrating in Mathematics or Music who has the highest record in his/her field of concentration. In 2008-09 the prize is open to concentrators in Mathematics, in 2009-10 to concentrators in Music. The Wister Prize is awarded to Samuel Lichtenstein.

    Herb Alexander Award

    From the gift of Susan Alexander, the Herb Alexander Award recognizes each year one of our outstanding undergraduates, and provides money to be used for research and travel. The Herb Alexander Award is given this year to Nike Sun.

    Robert Fletcher Rogers Prizes

    From the income of the gift in 1921 of the late Robert Fletcher Rogers, A.B. 1886, there have been established a first prize and second prize to be awarded annually to the College students who present the best talks before the Mathematics Table during an academic year. First Prize: Zachary Abel for his talk "Hinged dissections exist". Second Prize: Laura Starkston, for her talk "Khovanov homology".

    Hoopes Prize

    • Scott Kominers for his submission "Weighted Generating Functions and Configuration Results for Type II Lattices and Codes".
    • Shrenik Shah for his submission "Framed Deformation and Modularity".
    • Nils Wernerfelt for his submission "The Evolution of Cooperation on Dynamic Graphs".
    Congratulations again to all

    Peter Kronheimer, Director of Undergraduate Studies, Department of Mathematics
     

    Spring 2009

    5/12/09 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 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 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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