Department of

Mathematics


Seminar Calendar
for events the day of Thursday, November 14, 2019.

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Thursday, November 14, 2019

11:00 am in 241 Altgeld Hall,Thursday, November 14, 2019

Bounds on $S(t)$

Ghaith Hiary (Ohio State University)

Abstract: I survey some upper and lower bounds in the theory of the Riemann zeta function, in particular lower bounds on $S(t)$, the fluctuating part of the zeros counting function for the Riemann zeta function. I outline a new unconditional lower bound on $S(t)$, which is work in progress.

12:00 pm in 243 Altgeld Hall,Thursday, November 14, 2019

From curves to currents

Didac Martinez-Granado (Indiana University)

Abstract: Geodesic currents are measures introduced by Bonahon in 1986 that realize a suitable closure of the space of closed curves on a surface. Bonahon proved that intersection number and hyperbolic length for curves extend to geodesic currents. Since then, many other functions defined on the space of curves have been extended to currents, such as negatively curved lengths, lengths from singular flat structures or stable lengths for surface groups. In this talk, we explain how a function defined on the space of curves satisfying some simple conditions can be extended continuously to geodesic currents. The most important of these conditions is that the function decreases under smoothing of essential crossings. Our theorem subsumes previous extension results. Furthermore, it gives new extensions such as extremal length. This is joint work with Dylan Thurston.

2:00 pm in 347 Altgeld Hall,Thursday, November 14, 2019

Probabilistic solutions for fluid systems and stochastic Noether-Kelvin theorem

Jianyu Hu (UIUC Math)

Abstract: In this talk, we will study a probabilistic representations for the fluid systems based on stochastic Lagrangian paths. Unlike the Feynman-Kac formula, this theorem is a representation for nonlinear equations. When the systems have some noise, we will study the stochastic Noether-Kelvin theorem for a class of stochastic fluid equations. In general, the solutions of these systems do not preserve energy conservation, but rather than circulation conservation.