Texas Tech Quantum Homotopy Seminar

Time and place: Wednesday 2–4 p.m. in MATH 111.

Official mailing list: math.geometry (add ttu edu at the end).

Organizer: Dmitri Pavlov

MATH 5101.006, CRN 52236. Departmental seminar website.

Spring 2020 Schedule

January 15
Daniel Grady. Smooth stacks and Čech cocycles 1. Abstract: This talk will provide an introduction to smooth stacks. The talk will begin with some motivation and continue with several explicit examples of cocycle data which can be obtained via descent. The talk will conclude with an outlook of the general theory.
January 22
Daniel Grady. Smooth stacks and Čech cocycles 2. Abstract: This talk is a continuation of the first. The talk will begin with a discussion on model structures and Bousfield localization and continue with presentations for the infinity category of smooth stacks. We will use Dugger’s characterization of cofibrant objects to unpackage cocycle data explicitly in several examples.
January 29
Dmitri Pavlov. Lie groupoids and simplicial presheaves.
February 5
No seminar (snow storm).
February 12
February 19
James Francese. Précis on Homotopy Type Theory. Abstract: I will review the Curry-Howard-Lambek correspondence, the notion of internal language, the framework of intensional dependent type theory, then Hofmann-Streicher's discovery that identity types have groupoidal structure and Lumsdaine's confirmation that they are actually ∞-groupoids, which via the homotopy hypothesis are identified as topological spaces. I will then describe how HoTT makes this particular idea a theorem, by serving as a synthetic theory of ∞-groupoids which is also apparently “foundational” for mathematics. So mostly a conceptual talk, but I will throw in a range of technical tidbits.
February 26
Introduction to Fibrational Semantics.
March 4
Categorical Tripos Constructions: Typed and Un(i)typed Models of Mathematics.
March 11
Models of Type Theory: Univalence, Realizability.
March 25
Homotopy Theory and Opetopic Constructions with Applications in Categorical Logic.
April 1
April 8
April 15
April 22
April 29

Fall 2019 Schedule

August 26
Dmitri Pavlov. What is quantum homotopy?
September 2
No seminar
September 9
Stephen Peña: Introduction to quantum field theory 1. Mechanics on manifolds and classical field theory.
September 16
Stephen Peña: Introduction to quantum field theory 2. Quantum mechanics I.
September 23
Stephen Peña: Introduction to quantum field theory 3. Quantum mechanics II.
September 30
Stephen Peña: Introduction to quantum field theory 4. Quantum mechanics III.
October 7
Stephen Peña: Introduction to quantum field theory 5. Gauge theory I.
October 14
Stephen Peña: Introduction to quantum field theory 6. Gauge theory II.
October 21
Stephen Peña: Introduction to quantum field theory 7. Functorial field theory and algebraic quantum field theory.
October 28
James Francese: Introduction to Lie Theory and Natural Operations.
November 4
James Francese: On the Uniqueness of Lie Theory.
November 11
James Francese: Introduction to Leibniz Algebras.
November 18
James Francese: Generalizations of Lie Theory: Smooth Mal'cev Theories, Formal Group Laws, Fat Points.
November 25
James Francese: Internal Logic of Fat Points.
December 2
James Francese: Internal Logic of Fat Points II: Models for a Leibniz Theory.