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UW Number Theory Seminar

* Organizer: William Stein ([email protected]) * Mailing List: http://groups.google.com/group/ntuw

Winter 2012

May 24

CANCELLED -- Joel Bellaiche(Brandeis University); On Hecke algebras modulo $p$ -- We will present, motivate, and discuss special cases of a conjecture on the dimension and structure of the local components of the algebra of Hecke operators acting on the space of modular forms modulo a prime $p$ of a fixed level and all weights.

May 17

David Roe: The local Langlands correspondence and character sheaves -- The local Langlands correspondence is a theorem for GL_n due to Harris, Taylor and Henniart, and recent work of Arthur makes good progress toward establishing it for all classical groups. In this talk I will describe a different approach to local Langlands, pioneered by DeBacker and Reeder, that works for arbitrary split reductive groups but imposes restrictions on the starting Galois representation. In particular, I will focus on two stories: the extension of their method to tamely ramified unitary groups, and the beginnings of an effort to geometrize the method using character sheaves (joint with Clifton Cunningham).

May 3

Lola Thompson: Products of distinct cyclotomic polynomials -- A polynomial is a product of distinct cyclotomic polynomials if and only if it is a divisor over Z[x] of $x^n-1$ for some positive integer n. In this talk, we will examine two natural questions concerning the divisors of $x^n-1$: For a given n, how large can the coefficients of divisors of $x^n-1$ be? and How often does $x^n-1$ have a divisor of every degree between 1 and n? We will consider the latter question when $x^n-1$ is factored in both $Z[x]$ and $F_p[x]$, using sieve methods and other techniques from analytic number theory in order to obtain our results.

TUESDAY April 3, 1:30-2:30 (!)

Dinesh Thakur - Diophantine approximation of algebraic quantities in finite characteristic

Winter 2012

March 8, 2012

Deines-Lundell: Linearly Irregular Primes- A first report

February 9, 2012

Bober: The distribution of character sums

Fall 2011

December 8, 2011

Deines: Ramanujan-type supercongruences

November 30, 2011

Sujatha: Deformations and non-commutative Iwasawa theory

November 17, 2011

Jon Bober: Using the explicit formula to bound ranks of elliptic curves

November 10, 2011

Ralph Greenberg: The image of Galois representations attached to elliptic curves with an isogeny

November 3, 2011

William Stein: Enumerating Elliptic Curves over Q(sqrt(5))

October 20, 2011

Ben Lundell: New Parts of Hecke Rings

October 13, 2011

William Stein: Numerical Computation of Chow-Heegner Points

October 6, 2011

Jon Bober: Computations of the Riemann zeta function

September 29, 2011

Organizational Meeting

Spring 2011

June 24, 2011

Dao Phuong Bac: On some topological properties of relative orbits of subsets

May 27, 2011

R. Greenberg: Galois representations with open image

May 20, 2011

W. Stein: Shafarevich-Tate Groups of Elliptic Curves of Rank at Least Two

May 13, 2011

A. Deines: Dembele's Algorithm for Modular Elliptic Curves Over Real Quadratic Fields

April 22, 2011

R. Greenberg: Does 37 divide the class number of Q(37-th root of 37)?

April 15, 2011

R. Balasubramanian: Additive Combinatorics

April 8, 2011

R. Greenberg: Introduction to Genus Theory 20110408abstract.pdf

March 18, 2011

Maarten Derickx from Leiden, Holland -- Torsion points on elliptic curves over number fields of small degree


October 8, 2010

Ralph Greenberg will give his ICM talk on Selmer groups and congruences

October 15, 2010

Ralph Greenberg: part 2 of above

October 22, 2010

No seminar due to ECC

October 29, 2010

William Stein: Computing Hilbert modular forms of parallel weight 2 over Q(sqrt(5))

November 5, 2010

William Stein: "Q(sqrt(5)) is the new Q"

November 12, 2010

Jennifer Balakrishnan (MIT)

November 19, 2010

Hiren Maharaj -- constructing codes using modular curves

November 26, 2010

No seminar due to Thanksgiving

December 3, 2010

Sal Baig: The Average Analytic Rank in a Family of Quadratic Twists of an Elliptic Curve over $F_q(t)$

December 10, 2010

Jeff Achter (Colorado State): Split reductions of simple abelian varieties

2013-05-11 18:34