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Author: William A. Stein
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# UW Number Theory Seminar

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

# Winter 2012

• Thursdays 3:35 - 5:00pm in Padelford C401

 May 24 CANCELLED -- Joel Bellaiche(Brandeis University); On Hecke algebras modulo -- 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 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 for some positive integer n. In this talk, we will examine two natural questions concerning the divisors of : For a given n, how large can the coefficients of divisors of be? and How often does have a divisor of every degree between 1 and n? We will consider the latter question when is factored in both and , 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

• Thursdays 3:35 - 5:00pm in Padelford C401

 March 8, 2012 Deines-Lundell: Linearly Irregular Primes- A first report February 9, 2012 Bober: The distribution of character sums

# Fall 2011

• Thursdays 3:35 - 5:00pm in Padelford C401

 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

• Fridays 3:30 - 4:30pm in Padelford C401

 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

# 2010

• Public Calendar: XML, ICAL, HTML. If you use Google Calendar, I think you can add the number theory calendar to your calendar by pasting in the email address [email protected].

 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 December 10, 2010 Jeff Achter (Colorado State): Split reductions of simple abelian varieties

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