Five College Number Theory Seminar -- 2000-2001

Five College Number Theory Seminar, 2000-2001

Unless noted otherwise, all talks take place at 4:00 p.m. in room Seeley-Mudd 207, Amherst College. Refreshments are served at 3:30 p.m. in Seeley-Mudd 208.

Driving Direction to Amherst College

Campus maps for Hampshire, Mt. Holyoke, Smith, and UMass

Here's a list of the regular participants:

Amherst College
  • David Cox , Gregory Call
  • Mount Holyoke College
  • Giuliana P. Davidoff , Margaret Robinson
  • Smith College
  • Leanne Robertson
  • UMass Amherst
  • Assaf Goldberger , David Hayes , Siman Wong , Michael Reid

  • Schedule for Spring 2001




    Feb 13


    Organization meeting

    Feb 20

    David Hayes (UMass)

    Aligning Brumer-Stark elements into a Hecke character, I

    Feb 27

    David Hayes (UMass)

    Aligning Brumer-Stark elements into a Hecke character, II

    March 6 (cancelled due to weather)

    Avner Ash (Boston College)

    An analogue for GL(n) of Serre's conjecture on mod p Galois representations (rescheduled)

    March 13

    no talk

    no talk

    March 20

    Spring Break

    Spring Break

    March 27

    no talk

    no talk

    April 3

    Larry Washington (University of Maryland)

    Visibility in class groups and Shafarevich-Tate groups

    April 4

    Larry Washington (University of Maryland)

    Diophantus and Fermat (Smith UCVC)


    April 10

    Dinesh Thakur (University of Arizona)

    Diophantine approximation and function fields

    April 18 (Wed)

    Ken Ono (U Wisconsin)

    Number Theory and Partitions: The legacy of Dyson and Ramanujan (UMass UCVC)


    April 19 (Thur)

    Ken Ono (U Wisconsin)

    Arithmetic of the Values of Modular functions and the divisors of modular form (UMass Colloquium)

    April 24

    Noam Elkies (Harvard)

    Nonlinear algebro-geometric codes

    May 1

    Benji Fisher (Boston College)

    Double Dirichlet series over function fields

    May 8



    Larry Washington (Univ. Maryland)

    Abstract. Can you find a right triangle with integer sides such that the hypotenuse and the sum of the legs are perfect squares? Fermat solved this in 1643. The smallest answer involves 13-digit numbers. How did he find them? The talk will start with Diophantus and show how his ideas led to Fermat's work, and beyond. Along the way, several historical issues will arise. For example, what happened in 1453, and why is it relevant?

    Ken Ono (Univ. Wisconsin)

    Abstract. We will discuss the mathematics of partition theory. In particular, we will discuss the story of Ramanujan, the legendary Indian number theorist, and some of his most famous discoveries. In addition, I will describe some conjectures of Freeman Dyson, the celebrated British physicist, which were inspired by Ramanujan's work. I will conclude the lecture with a brief overview of some of the advances that have been made in the last few years.

    Schedule for Fall 2000




    Sept 12


    Organization meeting

    Sept 19

    Michael Reid, UMass

    On Stark's conjectures

    Sept 26

    Greg Call, Amherst College

    An ideal class pairing on elliptic curves

    Oct 3

    Cristina Ballantine, Dartmouth

    Hypergraphs and Automorphic Forms

    Oct 10



    Oct 18 (Wednesday)

    Charlie Toll, NSA

    Pseudo-random binary sequences.

    Undergraduate Connecticut Valley Colloquium

    Oct 24

    Paul Gunnells, Rutgers University

    Dedekind sums, special values of partial zeta functions, and the Eisenstein cocycle

    Oct 31

    Robert Sczech, Rutgers University

    Derivatives at s=0 of zeta functions associated to real quadratic fields (abstract)

    Nov 7



    Nov 14

    Gary Walsh, University of Ottawa

    Algorithms for solving classes of Diophantine Equations (abstract)

    Nov 21



    Nov 28

    Leanne Robertson

    Power Bases for 2-Power Cyclotomic Fields

    Dec 5

    Dan Lieman (Univ. Georgia & NTRU Corp.)

    The security of the Diffie-Hellman Key exchange protocol (or: an improved bound on the number of zeros of a sparse polynomial)

    Dec 12



    Home pages for the 96/97 , 97/98 , 98/99 and 99/00 Five College Number Theory Seminars.

    This page is maintained by Siman Wong.

    Robert Sczech (Rutgers), Derivatives at s=0 of zeta functions associated to real quadratic fields

    Abstract. According to the well known conjectures of Stark, certain derivatives at s=0 of partial zeta functions associated to an algebraic number field are regulators (volumes) of unit groups. The most interesting case is the case of the first order derivative where the regulator can be written as the logarithm of the absolute value of a unit. In my talk, I will present a formula (involving a new generalization of classical Dedekind sums) for calculating this first order derivative over real quadratic fields.

    Gary Walsh (Univ.~Ottawa)

    Abstract. The study of Diophantine equations has a long history in Mathematics. In recent years the use of computational devices has led to the development of methods to solve Diophantine problems by way of such techniques as linear forms in logarithms combined with lattice basis reduction, along with their variations. We discuss these techniques, but also methods which allow the complete solution to families of Diophantine equations, such as parametric families of Thue equations, parametric families of elliptic curves, and related problems.
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