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.

- 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

- 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.