Fall 2016 GRASP Seminar: TQFT and related topics
GRASP Seminar meets Friday afternoons 3-4pm in 939 Evans.
Topics to be covered
The semester is divided into approximately 3 parts: the first part of the semester is the "Qiaochu zone," where we focus on categorical formalisms and the cobordism hypothesis; the second part is the Chern-Simons zone, where we discuss some aspects of Chern-Simons theory; the third part is for additional topics, which are yet to be decided. Depending on people's interests, additional topics may include, inter alia, anomaly theories (à la [FHLT]); Betti Langlands (especially [BBJ]); complex Chern-Simons; what Chern-Simons assigns to a point; topological twisting; cohomological and open-closed field theories; factorization homology.
Agenda
Feel free to email me or Qiaochu if you have any questions about the talk you are giving, or about anything else related to this seminar.
Qiaochu zone
24 August: A survey of TQFTs (Ryan T.)
26 August: String diagrams (Qiaochu Y.)
2 September: Cobordisms [F2][T] (Kevin D.)
9 September: Classification of 2D topological field theories [A][K] (Calvin M.-S.)
16 September: Cobordism hypothesis, part I [At][F][L] (Qiaochu Y.)
23 September: Dijkgraaf-Witten theory (especially 3D) [DW][F] (Tao S.)
30 September: Cobordism hypothesis, part II [L] (Qiaochu Y.)
Chern-Simons zone
7 October: Reshetikhin-Turaev [RT][*][BHMV] (Eugene R.)
14 October: Turaev-Viro and relation to Reshetikhin-Turaev [TV][BK][DSPS] (Aran K.)
21 October: Classification of spin Chern-Simons theories [BM] (Jon A.)
28 October: 3D TFT and rational 2D CFT [K][FRS][KS2] (Alex T.)
Additional topix
4 November: Perturbative Chern-Simons theory (Jeff H.)
11 November No seminar. (Armistice Day.)
18 November No seminar. (Berkeley-Tokyo Autumn School.)
25 November: No seminar. (Thanksgiving.)
2 December: Cohomological field theories (Pelle S.)
References
[A] Abrams, Two-dimensional topological quantum field theories and Frobenius algebras.
[At] Atiyah, Topological quantum field theory.
[BK] Balsam and Kirillov Jr., Turaev-Viro Invariants as an Extended TQFT.
[BM] Belov and Moore, Classification of abelian spin Chern-Simons theories.
[BHMV] Blanchet, Habegger, Masbaum, Vogel, Topological quantum field theories derived from the Kaufmann bracket.
[CG] Costello and Gwilliam, Factorization algebras in quantum field theory.
[DSPS] Douglas, Schommer-Pries, and Snyder, Dualizable tensor categories.
[DW] Dijkgraaf and Witten, Topological gauge theories and group cohomology.
[F] Freed, Quantum Groups from Path Integrals.
[F2] Freed, The Cobordism Hypothesis.
[FRS] Fuchs, Runkel, and Schweigert, TFT construction of RCFT correlators.
[FSV1] Bicategories for boundary conditions and for surface defects in 3-d TFT.
[FSV2] A geometric approach to boundaries and surface defects in Dijkgraaf-Witten theories.
[Ka] Kapustin, Topological Field Theory, Higher Categories, and Their Applications.
[KS1] Kapustin and Saulina, Topological boundary conditions in abelian Chern-Simons theory.
[KS2] Kapustin and Saulina, Surface operators in 3d Topological Field Theory and 2d Rational Conformal Field Theory.
[Ko] Kock, Frobenius algebras and 2D topological quantum field theories.
[K] Kontsevich, Rational conformal field theory and invariants of 3-dimensional manifolds.
[L] Lurie, On the Classification of Topological Field Theories.
[RT] Reshetikhin and Turaev, Ribbon graphs and their invariants derived from quantum groups.
[T] Quelques propriétés globales des variétés différentiables.
[TV] Turaev and Viro, State-sum invariants of 3-manifolds and quantum 6j-symbols.
[W] Walker, TQFTs.
[W] Witten, Quantum Field Theory and the Jones Polynomial.
[*] http://mathoverflow.net/questions/86120/reshetikhin-turaev-as-a-3-2-1-theory