Calendar
- 19July 19, 2020No events
- 20July 20, 2020
CMSA Geometry and Physics Seminar: A geometric construction of orbifold Jacobian algebras
We review the definition of a twisted Jacobian algebra of a Landau-Ginzburg orbifold due to Kaufmann et al. Then we construct an A-infinity algebra of a weakly unobstructed Lagrangian submanifold in a symplectic orbifold. We work on an elliptic orbifold sphere and see that above two algebras are isomorphic, and furthermore their structure constants are related by a modular identity which was used to prove the mirror symmetry of closed string pairings. This is a joint work with Cheol-Hyun Cho.
- 21July 21, 2020
Applied von Neumann Algebra
We are interested in mathematical results which are stated entirely without reference to von Neumann algebras but whose proofs use von Neumann algebras in an essential way. The first stunning example is the Kaplansky result that ab=1 iff ba=1 in a group algebra over a field of characteristic zero. Connes’ noncommutative integration theory yields other examples. We will concentrate on a new example in the theory of zero sets of Bergman spaces where we are able to calculate a certain density of orbits of Fuchsian groups.
- 22July 22, 2020
CMSA Quantum Matter/Quantum Field Theory Seminar: Domain Wall Decorations, Anomalies, and Fermionic SPT
In the constructions of symmetry-protected topological (SPT) states, we usually decorate lower-dimensional states to higher codimensional domain walls of the system. In this talk, we will argue that domain wall decorations are basically equivalent to spectral sequences in algebraic topology. I will first illustrate this idea in bosonic systems, with explicit formulas for all differentials on all pages in the Lyndon-Hochschild-Serre spectral sequence. These results are useful in bosonic systems with Lieb-Schultz-Mattis (LSM) theorems, SPT-LSM theorems, and symmetry-enriched gauge theories. The second part of the talk will focus on fermionic SPT states. Using domain wall decorations, we will give a systematic construction and classification of fermionic SPT states in 3+1 or lower dimensions. We can obtain the full classifications for arbitrary finite unitary Abelian symmetries and interacting 10-fold way. All the classifications are consistent with known results from other approaches such as point/loop braiding statistics and spin cobordisms.
- 23July 23, 2020
CMSA Quantum Matter/Quantum Field Theory Seminar: Nonperturbative anomaly inflow for fermions and p-form fields
I will talk about a nonperturbative formulation of chiral fermions and chiral (self-dual) p-form fields, in terms of massive theories in one-higher dimensions. The introduction of the higher dimensional bulk is unavoidable due to the existence of anomalies, and I discuss the modern understanding of anomalies, which appears very naturally in our formulation of chiral theories.
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- 24July 24, 2020No events
- 25July 25, 2020No events