Department of

Mathematics


Seminar Calendar
for events the day of Thursday, April 4, 2019.

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Thursday, April 4, 2019

11:00 am in 241 Altgeld Hall,Thursday, April 4, 2019

Low-lying zeros of Dirichlet L-functions

Kyle Pratt (Illinois Math)

Abstract: I will present work in progress with Sary Drappeau and Maksym Radziwill on low-lying zeros of Dirichlet L-functions. By way of motivation I will discuss some results on the spacings of zeros of the Riemann zeta function, and the conjectures of Katz and Sarnak relating the distribution of low-lying zeros of L-functions to eigenvalues of random matrices. I will then describe some ideas behind the proof of our theorem.

2:00 pm in 347 Altgeld Hall,Thursday, April 4, 2019

On the range of lattice models in high dimensions

Ed Perkins (University of British Columbia)

Abstract: We investigate the scaling limit of the {\em range} (the set of visited vertices) for a general class of critical lattice models, starting from a single initial particle at the origin. Conditions are given on the random sets and an associated ``ancestral relation" under which, conditional on longterm survival, the rescaled ranges converge weakly to the range of super-Brownian motion as random sets. These hypotheses also give precise asymptotics for the limiting behaviour of the probability of exiting a large ball, that is for the {\em extrinsic one-arm probability}. We show that these conditions are satisfied by the voter model in dimensions $d\ge2$, sufficiently spread out critical oriented percolation and critical contact processes in dimensions $d>4$, and sufficiently spread out critical lattice trees in dimensions $d>8$.