The 20192020 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 

1/31/2020 
Bogdan Stoica 
Title: From padic to Archimedean Physics: Renormalization Group Flow and Abstract: We introduce the padic particleinabox as a free particle with periodic boundary conditions in the padic spatial domain. We compute its energy spectrum, and show that the spectrum of the Archimedean particleinabox can be recovered from the padic spectrum via an Euler product formula. This product formula arises from a flow equation in Berkovich space, which we interpret as a space of theories connected by a kind of renormalization group flow. We propose that Berkovich spaces can be used to relate padic and Archimedean quantities generally. Talk based on arXiv:2001.01725. 
2/7/2020 
Sergiy Verstyuk 
Title: Some Shallow Explorations in Deep Learning for Finance Abstract: I will introduce the existing approaches to understanding (rather than predicting) prices on financial assets. I will then discuss some simple ways of improving upon them using modern machine learning methods. 
2/14/2020 
Yifan Wang 
Title: Modularity in Physics and Mathematics

2/21/2020 
Du Pei 

2/28/2020 
Yuewen Chen 

3/6/2020 G02 


3/13/2020 


3/20/2020 


3/27/2020 


4/3/2020 


4/10/2020 G02 


4/17/2020 


4/24/2020 


5/1/2020 G02 


5/8/2020 G02 


5/15/2020 G02 


Date  Speaker  Title/Abstract 

9/6/2019  Spiro Karigiannis  Title: Constructions of compact torsionfree $G_2$manifolds
Abstract: Compact torsionfree $G_2$manifolds are 7dimensional analogues of CalabiYau threefolds, being compact Ricciflat 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 CortiHaskinsNordstromPacini (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 4manifold with prescribed asymptotics at infinity. (arXiv: 1707.09325) 
9/13/2019  Wei Gu  Title: Sigma models and mirror symmetry
Abstract: In this talk, I will roughly review why physicists be interested in CalabiYau manfiolds, and will introduce some tools we used to probe CalabiYaus 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  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 timereversalinvariant GuWen fermionic SPT phases. In addition, we provide a lattice definition of (1+1)d pin− invertible theory whose partition function is the ArfBrownKervaire invariant, which generates the Z8 classification of (1+1)d topological superconductors. We also compute the indicator formula of Z16 valued timereversal anomaly for (2+1)d pin+ TQFT based on our construction. 
9/27/2019  Yun Shi  Title: On motivic DonaldsonThomas theory on local P2
Abstract: DonaldsonThomas (DT) theory is an enumerative theory which counts ideal sheaves of curves on a CalabiYau 3fold. Motivic DonaldsonThomas theory is a categorification of the DT theory. This categofication contains more refined information of the moduli space, just like the topological space or cohomology contains more information than an Euler characteristic. In this talk, I will give a brief introduction to motivic DT theory. I will also discuss some results on this theory for moduli spaces of sheaves on the local projective plane. 
10/4/2019  Yoosik Kim  Title: Towards SYZ mirror symmetry of flag varieties.
Abstract: SYZ mirror symmetry has provided a geometric way of understanding mirror symmetry via Tduality. In this talk, I will discuss how to obtain SYZ mirrors of partial flag varieties using Floer theory. 
10/11/2019  Rongxiao Mi  Title: On the change of GromovWitten theory under extremal transitions.
Abstract: Extremal transitions are a topological surgery that conjecturally connects the moduli space of CalabiYau 3folds (often known as “Reid’s Fantasy”). Through extremal transitions, we may be able to build new mirror pairs from old ones, provided we understand how mirror symmetry is preserved. In this talk, I will outline a conjectural framework that relates the genus zero GromovWitten theory under an extremal transition. I will explain how it works for a large family of extremal transitions among toric hypersurfaces. 
10/18/2019  No Seminar  
10/25/2019  Ruth J Williams  Title: Reflected Diffusions and (Bio)Chemical Reaction Networks
Abstract: Continuoustime Markov chain models are often used to describe them stochastic dynamics of networks of reacting chemical species, especially in the growing field of systems biology. Discreteevent stochastic simulation of these models rapidly becomes computationally intensive. Consequently, more tractable diffusion approximations are commonly used in numerical computation, even for modestsized networks. However, existing approximations (e.g., linear noise and Langevin), do not respect the constraint that chemical concentrations are never negative. In this talk, we propose an approximation for such Markov chains, via reflected diffusion processes, that respects the fact that concentrations of chemical species are nonnegative. This fixes a difficulty with Langevin approximations that they are frequently only valid until the boundary of the positive orthant is reached. Our approximation has the added advantage that it can be written down immediately from the chemical reactions. Some numerical examples illustrate the advantages of our approximation over direct simulation of the Markov chain or use of the linear noise approximation. 
11/1/2019  No Seminar  
11/8/2019  Zhengping Gui  Title: Deformation quantization and Algebraic index theorem
Abstract: Deformation quantization is one approach to encapsulating the algebraic aspects of observables in a quantum mechanical system. By constructing a trace map on the algebra of quantum observables, correlation functions are defined. Using this paradigm, an algebraic analogue of the AtiyahSinger index theorem was established by Fedosov and jointly by Nest and Tsygan. In this talk, I will discuss how to use topological quantum mechanics to prove the algebraic index theorem when quantum algebra is twisted by vector bundles. 
11/15/2019  Ryan Thorngren  Title: Introduction to BulkBoundary Correspondences in Condensed Matter Physics
Abstract: A hallmark of topological phases are featureless insulators which are metallic at their edges. The bulkboundary correspondence relates the ground state entanglement of the bulk with the anomalous properties of the boundary. I will give a gentle introduction to these ideas in a couple of simple models relevant to graphene and superconducting nanowires, respectively. If time permits, I will describe some recent work extending these ideas to bulk “phases” (actually critical points) described by conformal field theory. 
11/22/2019  Cancelled  
11/29/2019  Cancelled  
12/6/2019  Sergiy Verstyuk 