Analysis Day

SCHEDULE

11:00-12:00 Tomasz Kaczynski (Sherbrooke University)
Homological approach to detection of interesting dynamics

Abstract: I will give an overview of methods based on Conley and fixed point indices for proving interesting features of dynamical systems such as the existence of invariant sets or the existence of periodic orbits of specific periods in specific neighborhoods. As many mathematical statements, the ones we discuss contain hypotheses that are not easily verified in practice. I will describe a homology calculus that enables a computer-assisted rigorous verification of empirically based hypotheses.

12:00-13:30 Lunch break

13:30-14:20 Alexey Kokotov (Concordia University)
Some extremal problems for curves of genus 0, 1 and 2

Abstract: Osgood, Phillips and Sarnak proved that the (normalized) determinant of laplacian on elliptic surface is less or equal to $\sqrt{3}/2|\eta(1/2+i\sqrt{3}/2)|^4$, where $\eta$ is Dedekind's eta-function. We shall discuss some analogs of this result in genera 0 and 2.

14:30-15:30 Fedor Nazarov (Michigan State University)
On the minimum of one fancy functional

Abstract: Let $\mu$ be a symmetric positive measure on $[-1,1]$ of total mass $1$. We shall find the minimal value of $\int_R |t|\cdot|\widehat\mu(t)|\,dt$.

For additional information please contact Dmitry Jakobson at:

jakobson@math.mcgill.ca