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Recent years have seen spectacular application of techniques from topological field theory to condensed matter physics. Topological field theory has traditionally been a topic of common interest of mathematicians and high-energy theorists. This workshop will bring together experts from the condensed matter, high-energy theory, and mathematics communities to discuss recent developments. Topics of particular interest include the classification of symmetry-protected topological phases of matter, the study of SPT phases with fermions, and the application of categorical aspects of TFT to condensed matter.
Sponsorship for this workshop has been provided by:
- Fiona Burnell, University of Minnesota
- Pavel Etingof, Massachusetts Institute of Technology
- Lukasz Fidowski, Stony Brook University
- Dan Freed, University of Texas
- Zheng-Cheng Gu, Perimeter Institute
- Theo Johnson-Freed, Northwestern University
- Anton Kapustin, California Institute of Technology
- Michael Levin, University of Chicago
- Max Metlitski, Perimeter Institute
- Shinsei Ryu, University of Illinois
- Ryan Thorngren, University of California, Berkeley
- Zhenghan Wang, Microsoft Station Q
- Ganapathy Baskaran, The Institute of Mathematical Sciences Chennai
- Lakshya Bhardwaj, Perimeter Institute
- Fiona Burnell, University of Minnesota
- Dylan Butson, Perimeter Institute
- Chun Chen, University of Minnesota
- Wongjune Choi, Perimeter Institute
- Kevin Costello, Perimeter Institute
- Pavel Etingof, Massachusetts Institute of Technology
- Lukasz Fidowski, Stony Brook University
- Dan Freed, University of Texas
- Davide Gaiotto, Perimeter Institute
- Jaume Gomis, Perimeter Institute
- Ryan Grady, Perimeter Institute
- Zheng-Cheng Gu, Perimeter Institute
- Theo Johnson-Freed, Northwestern University
- Anton Kapustin, California Institute of Technology
- Martin van Kuppeveld, Perimeter Institute
- Ho Tat Lam, Perimeter Institute
- Michael Levin, University of Chicago
- Max Metlitski, Perimeter Institute
- Seyed Faroogh Moosavian, Perimeter Institute
- Brent Perreault, University of Minnesota
- Miroslav Rapcak, Perimeter Institute
- Pratik Rath, Perimeter Instittue
- Shinsei Ryu, University of Illinois
- Nitica Sakharwade, Perimeter Institute
- Marc Schultz, University of Minnesota
- Nathan Seiberg, Institute for Advanced Study
- Ryan Thorngren, University of California, Berkeley
- Martinus van Kuppeveld, Perimeter Institute
- Chenjie Wang, Perimeter Institute
- Zhenghan Wang, Microsoft Station Q
- Xiao-Gang Wen, Perimeter Institute & Massachusetts Institute of Technology
- Brian Willet, Institute for Advanced Study
- Dominic Williamson, University of Vienna
- Phil-Sang Yoo, Northwestern University
- Guojun Zhang, Perimeter Institute
Wednesday, October 21, 2015
Time |
Event |
Location |
8:30 – 9:00am |
Registration |
Reception |
9:00 - 9:05am |
Welcome and Opening Remarks |
Bob Room |
9:05 – 10:00am |
Michael Levin, University of Chicago |
Bob Room |
10:00-11:00am |
Lukasz Fidowski, Stony Brook University |
Bob Room |
11:00 - 11:30am |
Coffee Break |
Bistro - 1^{st} Floor |
11:30 - 12:30pm |
Dan Freed, University of Texas |
Bob Room |
12:30 – 2:00pm |
Lunch |
Bistro – 2^{nd} Floor |
2:00 – 3:30pm |
Colloquium |
Theater |
3:30 – 4:00pm |
Coffee Break |
Bistro – 1^{st} Floor |
6:00pm |
Banquet |
Bistro – 2^{nd} Floor |
Thursday, October 22 2015
Time |
Event |
Location |
9:00 – 10:00am |
Xiao-Gang Wen, Perimeter Institute |
Bob Room |
10:00 – 10:30am |
Coffee Break |
Bistro – 1st Floor |
10:30 – 11:30am |
Pavel Etingof, Massachusetts Institute of Technology |
Bob Room |
11:30 – 12:00pm |
Conference Photo |
TBA |
12:00 – 1:30pm |
Lunch |
Bistro – 2^{nd} Floor |
1:30 – 2:30pm |
Anton Kapustin, California Institue of Technology |
Bob Room |
2:30 – 3:00pm |
Coffee Break |
Bistro – 1st Floor |
3:00 – 4:00pm |
Fiona Burnell, University of Minnesota |
Bob Room |
Friday, October 23, 2015
Time |
Event |
Location |
9:00 – 10:00am |
Zhenghan Wang, Microsoft Station Q |
Bob Room |
10:00 – 10:30am |
Coffee Break |
Bistro – 1st Floor |
10:30 – 11:30am |
Theo Johnson-Freyd, Northwestern University |
Bob Room |
12:00 – 1:30pm |
Lunch |
Bistro – 2^{nd} Floor |
1:30 – 2:30pm |
Ryan Thorngren, University of California, Berkeley |
Bob Room |
2:30 – 3:00pm |
Coffee Break |
Bistro – 1^{st} floor |
3:00 – 4:00pm |
Zheng-Cheng Gu, Perimeter Institute |
Bob Room |
Saturday, October 24, 2015
Time |
Event |
Location |
9:00 – 10:00am |
Shinsei Ryu, University of Illinois |
Bob Room |
10:00 – 10:30am |
Coffee Break |
Bistro – 1st Floor |
10:30 – 11:30am |
Max Melitski, Perimeter Institute |
Bob Room |
12:00pm |
Lunch |
Bistro – 1^{st} Floor |
Fiona Burnell, University of Minnesota
Time reversal invariant gapped boundaries of the double semion state
Pavel Etinghof, Massachusetts Institute of Technology
Graded fusion categories and homotopy theory
Lukasz Fidkowski, Stony Brook University
Realizing anomalous anyonic symmetries at the surfaces of 3d gauge theories
Dan Freed, University of Texas
Reflection positivity and the classification of invertible topological phases
Theo Johnson-Freyd, Northwestern University
Spin--Statistics and Categorified Galois Groups
Zheng-Cheng Gu, Perimeter Institute
Topological Quantum Field Theory approach for Bosonic Symmetry-Protected-Topological Phases with Abelian Symmetry in Three Dimensions
Symmetry protected topological(SPT) phase is a generalization of topological insulator(TI). Different from the intrinsic topological phase, e.g., the fractional quantum hall(FQH) phase, SPT phase is only distinguishable from a trivial disordered phase when certain symmetry is preserved. Indeed, SPT phase has a long history in 1D, and it has been shown that the well known Haldane phase of S=1 Heisenberg chain belongs to this class. However, in higher dimensions, most of the previous studies focus on free electron systems. Until very recently, it was realized that SPT phase also exists in interacting boson/spin systems in higher dimensions. In this talk, I will discuss the general mechanism for bosonic SPT phases and propose a corresponding topological quantum field theory(TQFT)descriptions. I will focus on examples in three (spacial) dimensions, including bosonic topological insulators(BTI).
Anton Kapustin, California Institue of Technology
Fermionic phases of matter and spin-structures
Michael Levin, University of Chicago
Bulk-boundary correspondence for 3D symmetry-protected topological phases
Max Metlitski, Perimeter Institute
S-duality of u(1) gauge theory with θ = π on non-orientable manifolds: Applications to topological insulators and superconductors
Shinsei Ryu, University of Illinois
Bulk/boundary correspondence in topological phases
Many of interesting physical (in particular topological) properties of topological phases and symmetry protected topological phases can be "inferred" from their boundary (end, edge, surface, ..) field theories. In particular, the presence of quantum anomalies in boundary field theories (or lack thereof) gives a way to diagnose bulk topological properties. I will discuss such bulk/boundary correspondence in various examples in 2d and 3d.
Ryan Thorngren, University of California, Berkeley
integrability and local formulas for spin TQFTs
Zhenghan Wang, Microsoft Station Q
Colloquium: TQFTs in Nature and Topological Quantum Computation
Topological quantum computation is based on the possibility of the realization of some TQFTs in Nature as topological phases of quantum matter. Theoretically, we would like to classify topological phases of matter, and experimentally, find non-abelian objects in Nature. We will discussion some progress for a general audience.
Zhenghan Wang, Microsoft Station Q
(3+1)-TQFTs from G-crossed braided fusion categories and their lattice realization
Unitary fusion categories are the algebraic input for the Turaev-Viro (TV) type TQFTs in (2+1)-dimensions and their Hamiltonian realization for the Levin-Wen model. We are interested in a generalization to unitary 2-fusion category for (3+1)-dimensions. Mackaay's spherical 2-categories are not general enough to include interesting examples such as the G-crossed braided fusion categories and general homotopy 2-types. We will discussion new (3+1)-TQFTs with G-crossed braided fusion categories as input, and their lattice realization based on the thesis work of Shawn X. Cui.
Xiao-Gang Wen, Perimeter Institue & Massachusetts Institute of Technology
2+1D topological orders and braided fusion category
S-duality of u(1) gauge theory with θ = π on non-orientable manifolds: Applications to topological insulators and superconductors
Bulk/boundary correspondence in topological phases
Topological Quantum Field Theory approach for Bosonic Symmetry-Protected-Topological Phases with Abelian Symmetry in Three Dimensions
Symmetry protected topological(SPT) phase is a generalization of topological insulator(TI). Different from the intrinsic topological phase, e.g., the fractional quantum hall(FQH) phase, SPT phase is only distinguishable from a trivial disordered phase when certain symmetry is preserved. Indeed, SPT phase has a long history in 1D, and it has been shown that the well known Haldane phase of S=1 Heisenberg chain belongs to this class. However, in higher dimensions, most of the previous studies focus on free electron systems.
integrability and local formulas for spin TQFTs
Spin--Statistics and Categorified Galois Groups
(3+1)-TQFTs from G-crossed braided fusion categories and their lattice realization
Unitary fusion categories are the algebraic input for the Turaev-Viro (TV) type TQFTs in (2+1)-dimensions and their Hamiltonian realization for the Levin-Wen model. We are interested in a generalization to unitary 2-fusion category for (3+1)-dimensions. Mackaay's spherical 2-categories are not general enough to include interesting examples such as the G-crossed braided fusion categories and general homotopy 2-types. We will discussion new (3+1)-TQFTs with G-crossed braided fusion categories as input, and their lattice realization based on the thesis work of Shawn X. Cui.
Time reversal invariant gapped boundaries of the double semion state
Fermionic phases of matter and spin-structures
Graded fusion categories and homotopy theory
2+1D topological orders and braided fusion category
Pages
Scientific Organizers:
- Kevin Costello, Perimeter Institute
- Davide Gaiotto, Perimeter Institute
- Xiao-Gang Wen, Perimeter Institute & Massachusetts Institute of Technology