Condensed Matter Physics and Topological Field Theory

Conference Date: 
Wednesday, October 21, 2015 (All day) to Saturday, October 24, 2015 (All day)
Scientific Areas: 
Condensed Matter
Mathematical Physics

 

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
Bulk-boundary correspondence for 3D symmetry-protected topological phases

Bob Room

10:00-11:00am

Lukasz Fidowski, Stony Brook University
Realizing anomalous anyonic symmetries at the surfaces of 3d gauge theories

Bob Room

11:00 - 11:30am

Coffee Break

Bistro - 1st Floor

11:30 - 12:30pm

Dan Freed, University of Texas
Reflection positivity and the classification of invertible
topological phases

Bob Room

12:30 – 2:00pm

Lunch

Bistro – 2nd Floor

2:00 – 3:30pm

Colloquium
Zhenghan Wang, Microsoft Station Q
TQFTs in Nature and Topological Quantum Computation

Theater

3:30 – 4:00pm

Coffee Break

Bistro – 1st Floor

6:00pm

Banquet

Bistro – 2nd Floor

 

Thursday, October 22 2015

Time

Event

Location

9:00 – 10:00am

Xiao-Gang Wen, Perimeter Institute
2+1D topological orders and braided fusion category

Bob Room

10:00 – 10:30am

Coffee Break

Bistro – 1st Floor

10:30 – 11:30am

Pavel Etingof, Massachusetts Institute of Technology
Graded fusion categories and homotopy theory

Bob Room

11:30 – 12:00pm

Conference Photo

TBA

12:00 – 1:30pm

Lunch

Bistro – 2nd Floor

1:30 – 2:30pm

Anton Kapustin, California Institue of Technology
Fermionic phases of matter and spin-structures

Bob Room

2:30 – 3:00pm

Coffee Break

Bistro – 1st Floor

3:00 – 4:00pm

Fiona Burnell, University of Minnesota
Time reversal invariant gapped boundaries of the double semion state

Bob Room

 

Friday, October 23, 2015

Time

Event

Location

9:00 – 10:00am

Zhenghan Wang, Microsoft Station Q
(3+1)-TQFTs from G-crossed braided fusion categories and their lattice realization

Bob Room

10:00 – 10:30am

Coffee Break

Bistro – 1st Floor

10:30 – 11:30am

Theo Johnson-Freyd, Northwestern University
Spin--Statistics and Categorified Galois Groups

Bob Room

12:00 – 1:30pm

Lunch

Bistro – 2nd Floor

1:30 – 2:30pm

Ryan Thorngren, University of California, Berkeley
integrability and local formulas for spin TQFTs

Bob Room

2:30 – 3:00pm

Coffee Break

Bistro – 1st floor

3:00 – 4:00pm

Zheng-Cheng Gu, Perimeter Institute
Topological Quantum Field Theory approach for Bosonic Symmetry-Protected-Topological Phases with Abelian Symmetry in Three Dimensions 

Bob Room

 

Saturday, October 24, 2015

Time

Event

Location

9:00 – 10:00am

Shinsei Ryu, University of Illinois
Bulk/boundary correspondence in topological phases

Bob Room

10:00 – 10:30am

Coffee Break

Bistro – 1st Floor

10:30 – 11:30am

Max Melitski, Perimeter Institute
S-duality of u(1) gauge theory with θ = π on non-orientable manifolds: Applications to topological insulators and superconductors

Bob Room

12:00pm

Lunch

Bistro – 1st 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

 

 

Friday Oct 23, 2015
Speaker(s): 

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.

Scientific Areas: 
 

 

Friday Oct 23, 2015
Speaker(s): 

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.

Scientific Areas: 

Pages

Scientific Organizers:

  • Kevin Costello, Perimeter Institute
  • Davide Gaiotto, Perimeter Institute
  • Xiao-Gang Wen, Perimeter Institute & Massachusetts Institute of Technology