Department of Mathematics
Mathematics Colloquium
Organizer Mailing list: https://groups.google.com/forum/#!forum/ccnymathcolloquium/joinThe Mathematics Department Colloquium typically meets on Thursdays from 12:30 pm to 1:20 pm in NAC 6/114. This will typically be preceded by tea and coffee at noon in the math lounge, and will be followed by lunch. To receive announcements via email, please join our google group
Upcoming talks

Thursday, March 21, 2019, 12:30PM, NAC 6/114
Yung Choi (U. Conn), TBATBA
Most recent talks

Thursday, December 06, 2018, 12:30PM, NAC 6/114
Giulio Tiozzo (University of Toronto), Trees, entropy, and the Mandelbrot setThe notion of topological entropy, arising from information theory, is a fundamental tool to understand the complexity of a dynamical system. When the dynamical system varies in a family, the natural question arises of how the entropy changes with the parameter.
In the last decade, W. Thurston introduced these ideas in the context of complex dynamics by defining the "core entropy" of a quadratic polynomials as the entropy of a certain forwardinvariant set of the Julia set (the Hubbard tree).
As we shall see, the core entropy is a purely topological / combinatorial quantity which nonetheless captures the richness of the fractal structure of the Mandelbrot set. In particular, we will relate the variation of such a function to the geometry of the Mandelbrot set. We will also prove that the core entropy on the space of polynomials of a given degree varies continuously, answering a question of Thurston.

Thursday, November 29, 2018, 12:30PM, NAC 6/114
Philippe Sosoe (Cornell U.), Applications of CLTs and homogenization for Dyson Brownian Motion to Random Matrix TheoryI will explain how two recent technical developments in Random Matrix Theory allow for a precise description of the fluctuations of single eigenvalues in the spectrum of large symmetric random matrices. No prior knowledge of random matrix theory will be assumed.
(Based on joint work with B Landon and HT Yau)

Thursday, November 15, 2018, 12:30PM, NAC 6/114
Khalid BouRabee (CCNY), On local residual finiteness of abstract commensurators of Fuchsian groupsThe abstract commensurator (aka “virtual automorphisms”) of a group encodes “hidden symmetries”, and is a natural generalization of the automorphism group. In this talk, I will give an introduction to these mysterious and classical groups and then discuss their residual finiteness. Recall that residual finiteness is a property enjoyed by linear groups (by A. I. Malcev), mapping class groups of closed oriented surfaces (by EK Grossman), and branch groups (by definition!). Moreover, by work of Armand Borel, Gregory Margulis, G. D. Mostow, and Gopal Prasad, the abstract commensurator of any irreducible lattice in any “nice enough” semisimple Lie group is locally residually finite (a property is termed “local” if it is satisfied by every finitely generated subgroup of the group). “Nice enough” is sufficiently broad that the only remaining unknown case is PSL2(R). Are abstract commensurators of lattices in PSL2(R) locally residually finite? Lattices here are commensurable with either a free group of rank 2 or the fundamental group of an oriented surface of genus 2. I will present a complete answer to this decades old question with a proof that is computerassisted. Our answer and methods open up new questions and research directions, so graduate students are especially encouraged to attend. This talk covers joint work with Daniel Studenmund.