Department of Mathematics

University of Mississippi

Algebra and Number Theory Seminar

Thursday, December 4, 2014, 4:00-4:50 PM, Hume 331.

Steve Lester
Tel Aviv University

Zeros of modular forms and quantum unique ergodicity (pdf)

Friday, May 30, 2014.

Emanuel Carneiro
IMPA, Rio de Janeiro

Hilbert spaces and the pair correlation of zeros of the Riemann zeta-function
This talk lies on the interface of analysis and analytic number theory. I will show how to construct a special reproducing kernel Hilbert space related to the Riemann zeta-function and how one can use this space to obtain bounds for the pair correlation of zeros of the zeta-function, extending classical work of P. X. Gallagher (1985). This is a joint work with V. Chandee, M. Milinovich and F. Littmann.

Monday, April 28, 2014.

Tristan Freiberg
University of Missouri

Limit points of the sequence of normalized prime gaps
Let p_n denote the n-th smallest prime number, and let L denote the set of limit points of the sequence of normalized differences between consecutive primes. We show that for k = 50 and for any sequence of k nonnegative real numbers beta_1 < beta_2 < … < beta_k, at least one of the numbers beta_j – beta_i
belongs to L. It follows that more than 2% of all nonnegative real numbers belong to L.

Thursday, April 24, 2014.

Ryan Daleida
Trinity University

Making imprimitive Dirichlet characters behave primitively
Given a Dirichlet character \chi mod q, it is traditional to extend \chi to all of Z/qZ by declaring that \chi(n) = 0 when (n,q) \neq 1. When \chi is primitive (i.e. not induced by a Dirichlet character mod d for some proper divisor d of q), this extension endows the associated Gauss sum and L-function with properties that are lost when \chi is imprimitve. In this talk we will introduce a modification to the traditional extension of imprimitive characters which causes them to behave primitively, in the sense that the relevant properties of the Gauss sum and L-function take on the form usually only associated to primitive characters.

Tuesday, Jan. 28, Thursday, Feb. 6, and Thursday, Feb. 13, 2014.

Nathan Jones
University of Mississippi

Probability and elliptic curves (I, II and III)
This expository lecture will be the (first/second/third) of a short series surveying work of Lang and Trotter from the 1970s. For an elliptic curve y^2 = x^3 + ax + b (with a and b integers) and a prime number p, one may consider the elliptic curve modulo p, i.e. one may consider the equation y^2 congruent to x^3 + ax + b modulo p. In particular, it is of wide interest to understand the number N_p of solutions (x,y) modulo p to this congruence, and how this number N_p varies as the prime p varies. In these lectures, we will use probabilistic notions to make very precise conjectures about some aspects of the variation of N_p with p. This talk will be accessible to graduate students.

Friday, October 11, 2013.

Jim Coykendall
Clemson University

An Overview of Factorization: Algebraic and Graphical
Since about 1990, there has been a large amount of effort devoted to the study of factorization in integral domains (as well as in other structures). Much of this study can be interpreted as an attempt to understand how the multiplicative structure of an integral domain “works” when we do not have unique factorization. A classical example is the class group, the size and complexity of which may be interpreted as a measure of “how far” a (Krull) domain is from being a Unique Factorization Domain.

The aim of this talk will be to give an overview of recent factorization theory. We will highlight some basic definitions, examples, and results. We will also highlight some more recent results that lend themselves to visualizations and have interesting connections to graph theory.

Thursday, November 11, 2010, 3:00-3:50pm, Hume 331.

Tsz Ho Chan
University of Memphis

A Look at the Modular Hyperbola (pdf)

Tuesday, April 6, 2010, 1:30-2:20pm, Hume 321.

David Farmer
American Institute of Mathematics

Finding and calculating L-functions (pdf)

Wednesday, March 24, 2010, 3:00-3:50pm, Hume 331.

Stephan Baier
University of Bristol

Subconvexity bounds for L-functions (pdf)

Wednesday, November 18, 2009, 3:00-3:50pm, Hume 331.

Micah Milinovich
University of Mississippi

The Riemann Hypothesis… (pdf)

Thursday, November 5, 2009, 4:00-4:50pm, Hume 331.

Tsz Ho Chan
University of Memphis

Sums of two Squares and Almost Squares (pdf)

Wednesday, October 21, 2009, 3:00-3:50pm, Hume 331.

Ryan Daileda
Trinity University

Maximal Class Numbers of CM Number Fields (pdf)

Friday, April 3, 2009, 1:00-1:50pm, Hume 331.

Andrew Odlyzko
University of Minnesota

Zeros of the Riemann zeta function: computations and implications (pdf)

Wednesday, March 25, 2009, 2:00-2:50pm, Hume 321.

Hung Manh Bui
Oxford University

Gaps between consecutive zeros of the Riemann zeta-function (pdf)

Thursday, February 26, 2009, 2:00-2:50pm, Hume 321.

Zhu Cao
University of Mississippi

Integer Matrix Exact Covering Systems and Product Identities for Theta Functions (pdf)

Monday, February 23, 2009, 2:00-2:50pm, Hume 331.

Neil Epstein
University of Michigan

Closure Operations on Ideals in Commutative Rings (pdf)

Friday, November 7, 2008, 3:00-3:50pm, Hume 331.

Zhu Cao
University of Mississippi

A new proof of Winquist’s Identity (pdf)

Friday, October 24, 2008, 3:00-3:50pm, Hume 331.

Zhu Cao
University of Mississippi

A Proof of Lagrange’s Four-Square Theorem (pdf)

Friday, October 3, 2008, 2:30-3:20pm, Hume 331.

Micah Milinovich
University of Mississippi

Distribution of the Prime Numbers (pdf)