Combinatorics/Algebra Seminar:
Fall 2004 Archive

November 29

Ling Long: From congruence to noncongruence modular forms.

Abstract: The study of modular forms for congruence subgroups of SL₂(Z) has been one of the central topics in number theory for more than a century. It has broad applications and impact in many branches of mathematics. However, despite the fact that there are far more noncongruence subgroups than congruence subgroups, the theory of modular forms for noncongruence subgroups is much less developed. In this talk, we will discuss some classical results on modular forms for congruence subgroups and some new results on modular forms for noncongruence subgroups.

November 15

Jonathan Smith: Quasigroups and approximate symmetry.

Abstract: Groups provide the mathematical language for exact symmetry. Applications in biology and other fields are now raising the problem of developing a rigorous theory of approximate symmetry. In this talk, it will be shown how approximate symmetry is determined by a quasigroup.

November 8

Ted Rice: Wythoff's Nim and Fibonacci representations.

November 1

Kristi Meyer: Quasigroups and hash functions, part II.

October 25

Kristi Meyer: Quasigroups and hash functions, part I.

October 18

Keyone Chung: Permutation binomials.

October 11

Yuri Movsisyan: A survey of hyperidentities, part II: applications in algebra.

October 4

Yuri Movsisyan: A survey of hyperidentities, part I: categorical questions.

September 27

Anna Romanowska: Duality for polytopes.

September 20

Geoffrey Mason (UC Santa Cruz): Group cohomology and binary codes.

Abstract: The low-dimensional cohomology of a group finds many applications throughout mathematics. We present some new connections with Reed-Muller binary codes and discuss some applications.

September 13

Jonathan Smith: Pascal's Triangle mod p², part II.

August 30

Jonathan Smith: Pascal's Triangle mod p², part I.

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