June 2 (Mon), 11 am

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

Alexis Marchand (Kyoto)

Sharp spectral gaps for scl from negative curvature

Stable commutator length is a measure of homological complexity of group elements, with connections to many topics in geometric topology, including quasimorphisms, bounded cohomology, and simplicial volume. The goal of this talk is to shed light on some of its relations with negative curvature. We will present a new geometric proof of a theorem of Heuer on sharp lower bounds for scl in right-angled Artin groups. Our proof relates letter-quasimorphisms (which are analogues of real-valued quasimorphisms with image in free groups) to negatively curved angle structures for surfaces estimating scl.

June 18 (Wed), 10 am

Online only. Zoom https://kimsh.kr/vz

Aidan Backus (University of Toronto)

The canonical lamination calibrated by a cohomology class

Let \rho be a unit cohomology class of degree d - 1, on a closed oriented Riemannian manifold of degree d. We construct a lamination \lambda_\rho whose leaves are exactly the minimal hypersurfaces calibrated by every calibration in \rho. The geometry of \lambda_\rho is closely related to the geometry of the unit ball of H_{d - 1}(M, \mathbb R) when it is equipped with Gromov's stable norm, so our main theorem constrains the shape of the stable unit ball in terms of the topology of M. These results establish a close analogy between the stable norm and Thurston's earthquake norm on the tangent space to Teichmueller space.

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.

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.