2025

July 1 (Tue), 10 am (note the time!)

KIAS 8101 & Zoom https://kimsh.kr/vz

Insung Park (Stony Brook)

Zelditch’s Trace Formula and Effective Equidistribution of Closed Geodesics on Hyperbolic Surfaces

In the early 1990s, Zelditch modified the Selberg trace formula to establish an effective version of Bowen’s equidistribution result for closed geodesics on hyperbolic surfaces. Expanding on his framework, and in joint work with Junehyuk Jung and Peter Zenz, we have refined this method to obtain the optimal error bound in the equidistribution of closed geodesics on compact hyperbolic surfaces. This talk will begin with an introduction to the fundamentals of trace formulas and then highlight new advancements. No prior background knowledge of trace formulas is assumed.

July 4 (Fri), 11 am

KIAS 8101 & Zoom https://kimsh.kr/vz

Alexander Stoimenow (Dongguk University)

Strong quasipositivity, Thurston-Bennequin invariants, and arc index

This talk gives a survey of recent work with several collaborators (mostly G.T.Jin and H.J.Lee, but also V.Singh) on establishing connections between the concepts in the title. Specifically, we relate to Rudolph's result about strong quasipositivity of annuli, the Livingston-Naik inequalities for jump numbers of slice-torus invariants, the Bennequin sharpness problem for Whitehead doubles, the Ohyama braid index inequality, and a recent result of Diao-Morton about the braid indices of reverse parallels of alternating knots. We introduce an alternative approach towards estimating Thurston-Bennequin invariants and arc index of knots from link polynomials, with special discussion of torus knots.

August 5 (Tue), 11 am

KIAS 1423 & Zoom https://kimsh.kr/vz

Ryoo, Seung-Yeon (Caltech)

TBA

TBA

August 8 (Fri), 11 am

KIAS 1423 & Zoom https://kimsh.kr/vz

Jang, Seung-Uk (Rennes)

Dynamics of the Sturmian Trace Skew Product

In this talk, we focus on the spectrum of the discrete Schrödinger equation with a quasi-periodic potential called Sturmian potential. Eigenvector problem with a Sturmian potential is associated to a dynamics of the Markov surface, together with a control variable of "rotation angle," leading us to a study of a skew product system.

Our understanding is that this skew product system exhibits a sort of hyperbolicity. As a first step to establish it, we have shown that there exists a cone field on the Markov surface that contracts by the dynamics, which is independently defined by the angle variable. The discovery is more or less elementary, initiated by some geometric observations of the Markov dynamics. After sketching the tricks, we will announce some prospective after having a cone field, including the "holonomy" between Sturmian spectra.

This talk is based on a joint work with Anton Gorodetski and Victor Kleptsyn.