A stacky approach to crystalline (and prismatic) cohomology.

Vladimir Drinfeld
The University of Chicago; Visiting Professor, School of Mathematics
October 3, 2019

The stacky approach was originated by Bhatt and Lurie. (But the possible mistakes in my talk are mine.)

Let X be a scheme over F_p. Many years ago Grothendieck and Berthelot defined the notion of crystal on X; moreover, they defined the notion of crystalline cohomology of a crystal.

Logarithmic concavity of Schur polynomials

June Huh
Visiting Professor, School of Mathematics
October 7, 2019

Schur polynomials are the characters of finite-dimensional irreducible representations of the general linear group. We will discuss both continuous and discrete concavity property of Schur polynomials. There will be one theorem and eight conjectures. No background beyond basic representation theory will be necessary to enjoy the talk. Based on joint work with Jacob Matherne, Karola Mészáros, and Avery St. Dizier.

Bourgeois contact structures: tightness, fillability and applications.

Agustin Moreno
University of Augsburg
October 7, 2019
Starting from a contact manifold and a supporting open book decomposition, an explicit construction by Bourgeois provides a contact structure in the product of the original manifold with the two-torus. In this talk, we will discuss recent results concerning rigidity and fillability properties of these contact manifolds. For instance, it turns out that Bourgeois contact structures are, in dimension 5, always tight, independent on the rigid/flexible classification of the original contact manifold.