Members’ Seminar

The 2019-2020 CMSA Members’ Seminar will occur every Friday at 5pm in CMSA G10. The Schedule will be updated below. Previous seminars can be found here.

Date Speaker Title/Abstract
9/6/2019 Spiro Karigiannis Title: Constructions of compact torsion-free $G_2$-manifolds

Abstract: Compact torsion-free $G_2$-manifolds are 7-dimensional analogues of Calabi-Yau threefolds, being compact Ricci-flat Riemannian manifolds with reduced holonomy that are important ingredients in theories of physics. All known constructions use an abstract existence theorem of Dominic Joyce to perturb “almost” solutions of a quasilinear elliptic PDE to honest solutions, and construct the “almost” solutions via glueing methods. I will first summarize some basic facts about $G_2$-manifolds and Joyce’s existence theorem, and then briefly mention the previous constructions by Joyce (1994), Kovalev (2003), and Corti-Haskins-Nordstrom-Pacini (2014). Then I will focus on a new construction (joint work of myself and Joyce, to appear in JDG) that is significantly more involved for several reasons, which I will elucidate. In particular one key step in our construction involves solving a linear first order elliptic PDE on a noncompact 4-manifold with prescribed asymptotics at infinity. (arXiv: 1707.09325)

9/13/2019 Wei Gu (CMSA) Title: Sigma models and mirror symmetry

Abstract: In this talk, I will roughly review why physicists be interested in Calabi-Yau manfiolds, and will introduce some tools we used to probe Calabi-Yaus and other spaces like Fanos which we called sigma models.  I will also briefly mention how physicists using sigma models to study mirror symmetry. This is not a technical talks, rather, I will just focus on the pictures of the connections between math and physics from sigma models.

9/20/2019 Ryohei Kobayashi (U of Tokyo)
Title: Fermionic phases of matter on unoriented spacetime
Abstract: We discuss a recipe to produce a lattice construction of fermionic phases of matter on unoriented manifolds. This is performed by extending the construction of spin TQFT via the Grassmann integral proposed by Gaiotto and Kapustin, to the unoriented pin± case. As an application, we construct gapped boundaries for time-reversal-invariant Gu-Wen fermionic SPT phases. In addition, we provide a lattice definition of (1+1)d pin− invertible theory whose partition function is the Arf-Brown-Kervaire invariant, which generates the Z8 classification of (1+1)d topological superconductors. We also compute the indicator formula of Z16 valued time-reversal anomaly for (2+1)d pin+ TQFT based on our construction.

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