UIUC Dept. of Mathematics Seminar Calendar

    February 2012            March 2012             April 2012     
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           1  2  3  4                1  2  3    1  2  3  4  5  6  7
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Tuesday, March 27, 2012

Ergodic Theory
11:00 am in 347 Altgeld Hall, Tuesday, March 27, 2012

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Submitted by jathreya.

Anish Ghosh (University of East Anglia)
Measure Rigidity for torus actions
Abstract: Recent years have seen major developments in the theory of measure rigidity for group actions on homogeneous spaces. I will explain some of these developments and present a few recent advances.

Number Theory Seminar
11:00 am in 241 Altgeld Hall, Tuesday, March 27, 2012

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Submitted by ford.

Vorrapan Chandee (CRM, University of Montreal)
Bounding S(t) via extremal functions
Abstract: Assuming the Riemann hypothesis we consider the argument function of the Riemann zeta function, $S(t)$. We will prove that for large $t$, $$|S(t)| \leq ( 1/4 + o(1) ) \log t /\log \log t,$$ which is an improvement of the previous work of Goldston and Gonek by a factor of 2. The result may reasonably be thought of as having attained the limit of existing methods of bounding $S(t)$ under RH. Two different approaches to improve a bound for $S(t)$ will be presented in the talk. Both methods rely on the solution of the Beurling-Selberg extremal problem from recent works by Carneiro, Littmann and Vaaler.

Probability Seminar
2:00 pm in Altgeld Hall, Tuesday, March 27, 2012

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Submitted by kkirkpat.

Philip Matchett Wood (U Wisconsin-Madison)
Survey of the Circular Law
Abstract: What do the eigenvalues of a random matrix look like? This talk will focus on large square matrices where the entries are independent, identically distributed random variables. In the most basic case, the distribution of the eigenvalues in the complex plane (suitably scaled) approaches the uniform distribution on the unit disk, which is called the circular law. We will discuss some of the methods that have been used to prove the circular law, including recent work that has extended the circular law to the most general situation, and we will also discuss generalizations to situations where the eigenvalue distributions are stable, but non-circular.

Graph Theory and Combinatorics
3:00 pm in 241 Altgeld Hall, Tuesday, March 27, 2012

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Cory Palmer (UIUC Math)
Turan numbers for forests
Abstract: The Turán number of a graph $H$, written $ex(n,H)$, is the maximum number of edges in a graph on $n$ vertices that does not contain $H$ as a subgraph. The Erdős-Stone-Simonovits Theorem computes $ex(n,H)$ asymptotically for graphs of chromatic number at least 3. For bipartite graphs much is still unknown. Of particular interest is the Turán number for trees (this is the Erdős-Sós conjecture). We will concentrate our attention on the Turán number of forests. Bushaw and Kettle determined the Turán number of a forest made up of copies of a path of a fixed length. We generalize their result by finding the Turán number for a forest composed of arbitrary length paths. We also determine the Turán number for a forest made up of arbitrary size stars. In both cases we characterize the extremal graphs. (Joint work with Hong Liu and Bernard Lidicky.)