# 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