University of Michigan Student Arithmetic Seminar

Wednesday 3:10 - 4:00

3866 East Hall

If you would like to be added to the email list, give a talk, or hear a talk on a particular topic, email Craig Spencer.

Date: Speaker: Title:

9/12/07 Organizational Meeting

9/19/07 Craig Spencer Arithmetic Progressions in Finite Abelian Groups

9/26/07 Hester Graves Motzkin's Lemma! What is it good for?

10/3/07 Jonathan Bober Integer factorial ratios sequences, etc.

10/10/07 Johnson Jia Periods and L-functions

10/17/07 Wansu Kim Etale cohomology I: basic definitions and properties

10/24/07 Wansu Kim Etale cohomology II: Rationality of zeta functions via l-adic cohomology

11/7/07 Ben Weiss Mahler Measure

11/14/07 Ben Weiss Mahler Measure

11/28/07 Johnson Jia Congruences between modular forms

1/9/07 Organizational Meeting

1/23/07 Craig Spencer Diophantine Inequalities

1/30/07 Wansu Kim p-adic uniformization of an elliptic curve with multiplicative reduction

2/20/07 Craig Spencer The Circle Method

3/5/07 Jonathan Bober Bounded step functions and factorial ratio sequences

3/12/07 Johnson Jia Tate's Thesis

3/19/07 Johnson Jia Automorphic L-Functions

4/2/07 Johnson Jia TBA

4/9/07 Julian Rosen Irrationality Measure and the "Sidewalk" Function

10/3/07 Jonathan Bober Integer factorial ratios sequences, etc.

One example I will start with is (2n choose n) = (2n!)/(n!)(n!). A more complicated example is (30n)!n!/(15n)!(10n)!(6n)!, which also happens to always be an integer. These sequences can be used to give elementary estimates for the distribution of prime numbers, and they are also related to what is known as the Nyman-Beurling criterion for the Riemann Hypothesis. Much of the talk should be fairly elementary, and suitable for a wide audience.

11/7/07 Ben Weiss Mahler Measure

11/14/07

The goal of these two talks will be to introduce Mahler Measure and height from first principles, and go over some of their basic properties and motivation. We will then introduce the concept of entropy on a torus by a map (represented by a matrix), and prove the amazing result that the entropy is the Mahler Measure of the characteristic polynomial of said matrix.

University of Michigan Student Arithmetic Seminar

Wednesday 3:10 - 4:00

3866 East Hall

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Date:	Speaker:	Title:
9/12/07		Organizational Meeting
9/19/07	Craig Spencer	Arithmetic Progressions in Finite Abelian Groups
9/26/07	Hester Graves	Motzkin's Lemma! What is it good for?
10/3/07	Jonathan Bober	Integer factorial ratios sequences, etc.
10/10/07	Johnson Jia	Periods and L-functions
10/17/07	Wansu Kim	Etale cohomology I: basic definitions and properties
10/24/07	Wansu Kim	Etale cohomology II: Rationality of zeta functions via l-adic cohomology
11/7/07	Ben Weiss	Mahler Measure
11/14/07	Ben Weiss	Mahler Measure
11/28/07	Johnson Jia	Congruences between modular forms
1/9/07		Organizational Meeting
1/23/07	Craig Spencer	Diophantine Inequalities
1/30/07	Wansu Kim	p-adic uniformization of an elliptic curve with multiplicative reduction
2/20/07	Craig Spencer	The Circle Method
3/5/07	Jonathan Bober	Bounded step functions and factorial ratio sequences
3/12/07	Johnson Jia	Tate's Thesis
3/19/07	Johnson Jia	Automorphic L-Functions
4/2/07	Johnson Jia	TBA
4/9/07	Julian Rosen	Irrationality Measure and the "Sidewalk" Function