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), 11 am

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

Insung Park (Stony Brook)

TBA

TBA

August 5 (Tue), 11 am

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

Ryoo, Seung-Yeon (Caltech)

TBA

TBA