The Topological Field Theory Seminar is a learning seminar in Fall 2016, with the goal being to learn about topological field theories, and their applications to both representation theory, and to condensed matter physics including the classification of topological states of matter. The Topological Field Theory seminar occurs on Thursdays in A2 at 10:30AM to 12 Noon. Ron Donagi and I appear to be organising this seminar.
List of topics (being) covered/talks, together with some handwritten notes (by either S. Lee, M. Ionita or myself):
- The Cobordism Hypothesis (Talks by Seokjoo Lee), notes
- Factorization Homology (Talks by Matei Ionita), notes
- Dijkgraaf Witten Theory, Morita Categories and Line operators (Talks by B.M.), notes 1 (poor quality), notes 2
- Topological Conformal Field Theories (Talks by Seokjoo Lee), notes 1, notes 2, notes 3
- Factorization Homology of the representation category of a quantum group on surfaces (Talks by Matei Ionita), notes
- Topological Twisting (Talks by Rodrigo Barbosa)
- Betti Geometric Langlands (Talks by B.M.) notes. I hope to also add some further notes concretely describing singular support of indcoherent sheaves in simple cases.
- Extending Field Theories defined by Factorization Homology (B.M.), notes to appear.
- Invertible Field theories (Talk by Matei) notes
- TFT's from Lagranian Correspondences (Talk by SJ), notes 1, notes 2.
Condensed matter physics is probably going to be delayed until next semester.
A (incomplete) list of references used in the seminar (focusing on the mathematical idea, and applications to representation theory):
- J. Lurie, On the Classification of Topological Field Theories. (For the Cobordism Hypothesis, S1 also introduces topological field theories for a mathematical perspective)
- C. Teleman, Five Lectures on Topological Field Theory
- D. Ayala and J. Francis, Factorization homology of topological manifolds.
- G. Ginot, Notes on factorization algebras, factorization homology and applications.
- J. Lurie, Notre Dame Lectures on Finiteness and Ambidexterity in K(n)-local stable homotopy theory
- D. Freed, M. Hopkins, J. Lurie and C. Teleman, Topological Quantum Field Theories from Compact Lie Groups
- K. Costello, Topological conformal field theories and Calabi-Yau categories
- D. Ben-Zvi, A. Brochier and D. Jordan, Integrating Quantum Groups over Surfaces
- D. Ben-Zvi, A. Brochier, and D. Jordan, Quantum character varieties and braided module categories
- K. Costello, C. Scheimbauer Lectures on mathematical aspects of (twisted) supersymmetric gauge theories
- D. Ben-Zvi and D. Nadler Betti Spectral Gluing
- D. Ben-Zvi and D. Nadler, Betti Geometric Langlands
- A. Kapustin, K. Setter, K. Vyas, Surface operators in four-dimensional topological gauge theory and Langlands duality
Some references for understanding Condensed matter: