# Next Week's Events

## Seminars

Click on seminar heading to go to seminar page.

• ### Algebra Seminar

Monday September 24, 2018 at 13:30, Wachman 617
Dynamics of Belyi maps

Valentijn Karemaker, University of Pennsylvania

A (genus 0) Belyi map is a finite map from the projective line to itself, branched exactly at 0, 1, and infinity. Such maps can be described combinatorially by their generating systems. Assuming further that 0, 1, and infinity are both fixed points and the unique ramification points above 0, 1, and infinity respectively yields dynamical Belyi maps, since the resulting maps can be iterated and will therefore exhibit dynamical behaviour. In this talk, we will discuss several results on the dynamics, reductions, and monodromy of dynamical Belyi maps, and the interplay between these. (This is joint work with J. Anderson, I. Bouw, O. Ejder, N. Girgin, and M. Manes.)

• ### Probability Seminar

Tuesday September 25, 2018 at 15:00, Penn (DRL 4C8)
Zeros of polynomials, the distribution of coefficients, and a problem of J.E. Littlewood

Julian Sahasrabudhe, Cambridge University

While it is an old and fundamental fact that every (nice enough) even function $f : [-\pi,\pi] \rightarrow \mathbb{C}$ may be uniquely expressed as a cosine series $f(\theta) = \sum_{r \geq 0 } C_r\cos(r\theta),$ the relationship between the sequence of coefficients $(C_r)_{r \geq 0 }$ and the behavior of the function $f$ remains mysterious in many aspects. We mention two variations on this theme. First a more probabilistic setting: what can be said about a random variable if we constrain the roots of the probability generating function? We then settle on our main topic; a solution to a problem of J.E. Littlewood about the behavior of the zeros of cosine polynomials with coefficients $C_r \in \{0,1\}$.

• ### Applied Mathematics and Scientific Computing Seminar

Wednesday September 26, 2018 at 16:00, 617 Wachman Hall

Andreas Stathopoulos, College of Wiliam and Mary

• ### Global Analysis Seminar

Friday September 28, 2018 at 11:20, Rutgers-Camden (specific location to be determined)

Vladimir Matveev, Friedrich Schiller University, Jena, Germany

With the help of a generalization of the Fermat principle in general relativity, we show that chains in CR geometry are geodesics of a certain Kropina metric constructed from the CR structure. We study the projective equivalence of Kropina metrics and show that if the kernel distributions of the corresponding 1-forms are non-integrable then two projectively equivalent metrics are trivially projectively equivalent. As an application, we show that sufficiently many chains determine the CR structure up to conjugacy, generalizing and reproving the main result of [J.-H. Cheng, 1988]. The talk is based on a joint paper with J.-H. Cheng, T. Marugame and R. Montgomery.