Texas Tech Summer Seminar

Time and place: Thursday at 2 p.m., MATH 11. Online streaming via Zoom is available, contact the organizer for credentials.

Organizer: Dmitri Pavlov

Summer 2021

Handwritten notes by Rachel Harris are hyperlinked in the titles.

May 18
Dmitri Pavlov. Functor of points and derived geometry: new directions and open problems.
May 27
Dmitri Pavlov. Derived differentiable stacks. Abstract: We will look at a simplified definition of derived differentiable stacks (using derived cartesian spaces). Just like the last time, several easy-to-write open problems will be communicated.
June 3
Dmitri Pavlov. Algebraic structures on derived critical loci. Abstract: We will examine a simplified definition of differential forms in the setting of derived differentiable stacks. We will then relate it to the usual definition by Ben Zvi and Nadler. Finally, we will apply these ideas to define algebraic structures on derived critical loci, such as the shifted symplectic structures of Pantev–Toën–Vaquié–Vezzosi. I will in part follow a recent paper by Vezzosi “Basic structures on derived critical loci”, except that our basic setup is differential geometry, not algebraic geometry.
June 17
Rachel Harris. Shifted symplectic structures.
July 1
James Francese. Maurer-Cartan stacks for exceptional generalized geometry, Part I. Abstract: In this talk we lay down the groundwork for studying geometric structures on Leibniz algebroids which generalize known integrability conditions of the classical twisted Courant bracket, the setting for Dirac structures. We explain 11-dimensional supergravity as a Leibniz algebroid constructed solely out of natural operations on a generalized tangent bundle, with a bracket twisted by de Rham cohomology classes defined by auxiliary fields satisfying Bianchi-type identities. This is the type of geometric structure we care to study in a derived context by means of Maurer-Cartan stacks controlling higher derived brackets twisted by arbitrary natural operations on a generalized tangent complex.

List of papers

(More) derived geometry

The first four papers are surveys:

Higher Lie theory

A worthy goal would be to understand the work of Pridham and Lurie on the connection between deformation theory and differential graded Lie algebras.

Another worthy goal would be to understand the papers on higher Lie integration of Henriques, Zhu, and others.

Synthetic differential geometry, tangent categories, and Goodwillie calculus

We studied SDG in the Winter Seminar, we could study it more and establish some connections to Goodwillie calculus.

A worthy goal would be to understand the recent remarkable paper by Bauer, Burke, Ching (see below), which makes rigorous the connection between differential calculus and Goodwillie calculus.

Summer 2020

Time and place: typically Tuesday or Thursday 1–5 p.m., somewhere in Lubbock, Texas.

May 19
May 28
June 2
June 9
June 16
June 23
July 3
July 16
July 24
July 28
August 4
August 13
August 20