# Events for 01/18/2019 from all calendars

## Probability Seminar

**Time:** 11:00AM - 12:00PM

**Location:** BLOC 628

**Speaker:** SHAMGAR GUREVITCH, U Wisconsin-Madison

**Title:** *Harmonic Analysis on GLn over finite fields, and Random Walks*

**Abstract:** There are many formulas that express interesting properties of a group G in terms of sums over its characters. For evaluating or estimating these sums, one of the most salient quantities to understand is the {\it character ratio}: $$trace (\rho(g))/dim (\rho),$$ for an irreducible representation $\rho$ of G and an element g of G. For example, Diaconis and Shahshahani stated a formula of this type for analyzing G-biinvariant random walks on G. It turns out that, for classical groups G over finite fields (which provide most examples of finite simple groups), there is a natural invariant of representations that provides strong information on the character ratio. We call this invariant {\it rank}. This talk will discuss the notion of rank for GLn over finite fields, and apply the results to random walks. This is joint work with Roger Howe (TAMU).

## Colloquium - Daniel Hernandez

**Time:** 4:00PM - 5:00PM

**Location:** BLOC 220

**Speaker:** Daniel Hernandez, University of Kansas

**Description:**

**Title:** Applications of Frobenius to characteristic zero

**Abstract:** For nearly forty years, mathematicians have used the Frobenius morphism, or p-th power map, to investigate phenomena in algebraic geometry, representation theory, number theory, and commutative algebra. Remarkably, though Frobenius only makes sense in prime characteristic, some of its most interesting applications occur in the context of characteristic zero! In this talk, we will discuss some of these applications, with an eye towards classical singularity theory , and birational algebraic geometry, both over the complex numbers.