Guest lectures and seminars - Page 123

Seckin Adali (UiO), gives the Seminar in Algebra and Algebraic Geometry:

Singularities of Restriction Varieties in OG(k,n)

In the nineties, Deninger gave a detailed description of a conjectural cohomological interpretation of the (completed) Hasse-Weil zeta function of a regular scheme proper over the ring of rational integers. He envisioned the cohomology theory to take values in countably infinite dimensional complex vector spaces and the zeta function to emerge as the regularized determinant of the infinitesimal generator of a Frobenius flow. In this talk, I will explain that for a scheme smooth and proper over a finite field, the desired cohomology theory naturally appears from the Tate cohomology of the action by the circle group on the topological Hochschild homology of the scheme in question.  

Abstract: Exploring connections between subfactors and conformal field theories, Vaughan Jones recently observed that planar algebras give rise to unitary representations of the Thompson group F, and more generally,  to unitary representations of the group of fractions of certain categories. Remarkably, this procedure applies to oriented link invariants. In particular, a suitably normalized HOMFLYPT polynomial is a positive definite function on the oriented Thompson group. (Based on joint work with V. Aiello and V. Jones.)

The motivic Adams spectral sequence is a general tool for calculating homotopy groups of a motivic spectrum X. We will investigate the construction of the motivic Adams spectral sequence, determine the second page of the spectral sequence, and identify what it converges to in good cases. If time permits, we will show how to use the motivic Adams spectral sequence to obtain explicit calculations of the motivic homotopy groups of spheres and other spectra.