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.
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.
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.)
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.)
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.)
[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.