During the 2022–23 academic year, the CMSA will be hosting a Member Seminar, organized by Freid Tong and Benjamin McKenna in the Fall 2022 semester and Gabriel Wong and Damian van de Heisteeg Spring 2023. This seminar will take place on Fridays at 11:00 am – 12:00 pm (Boston time). All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. The meetings will take place in Room G10 at the CMSA, 20 Garden Street, Cambridge MA 02138. The schedule will be updated as talks are confirmed.

CMSA COVID-19 Policies

• December 09, 2022 11:00 AM
##### Speaker: Faidra Monachou
###### Venue: CMSA Room G10

Member Seminar Speaker: Faidra Monachou

• December 02, 2022 11:00 AM
##### Speaker: Alejandro Poveda
###### Venue: CMSA Room G10

Member Seminar Speaker: Alejandro Poveda Title: Compactness and Anticompactness Principles in Set Theory Abstract: Several fundamental properties in Topology, Algebra or Logic are expressed in terms of Compactness Principles.For instance, a natural algebraic question is the following: Suppose that G is an Abelian group whose all small subgroups are free – Is the group G free? If the answer is affirmative one says that compactness holds; otherwise, we say that compactness fails. Loosely speaking, a compactness principle is anything that fits the following slogan: Suppose that M is a mathematical structure (a group, a topological space, etc) such that all of its small substructures N have certain property $\varphi$; then the ambient structure M has property $\varphi$, as well….

• November 18, 2022 11:00 AM
##### Speaker: Damian van de Heisteeg
###### Venue: CMSA Room G10

Member Seminar Speaker: Damian van de Heisteeg Title: Light states in the interior of CY moduli spaces Abstract: In string theory one finds that states become massless as one approaches boundaries in Calabi-Yau moduli spaces. In this talk we look in the opposite direction, that is, we search for points where the mass gap for these light states is maximized — the so-called desert. In explicit examples we identify these desert points, and find that they correspond to special points in the moduli space of the CY, such as orbifold points and rank two attractors.

• November 11, 2022 11:00 AM
##### Speaker: Mauricio Romo
###### Venue: CMSA Room G10

Member Seminar Speaker: Mauricio Romo Title: Quantum trace and length conjecture for hyperbolic knot Abstract: I will define the quantum trace map for an ideally triangulated hyperbolic knot complement on S^3. This map assigns an operator to each element L of  the Kauffman Skein module of knot complement.  Motivated by an interpretation of this operator in the context of SL(2,C) Chern-Simons theory, one can formulate a ‘length conjecture’ for the hyperbolic length of L.

• October 28, 2022 11:00 AM
##### Speaker: Shuaijie Qian
###### Venue: CMSA Room G10

Member Seminar Speaker: Shuaijie Qian (Harvard CMSA) Title: Some non-concave dynamic optimization problems in finance Abstract: Non-concave dynamic optimization problems appear in many areas of finance and economics. Most of existing literature solves these problems using the concavification principle, and derives equivalent, concave optimization problems whose value functions are still concave. In this talk, I will present our recent work on some non-concave dynamic optimization problems, where the concavification principle may not hold and the resulting value function is indeed non-concave. The first work is about the portfolio selection model with capital gains tax and a bitcoin mining model with exit options and technology innovation, where the average tax basis and the average mining cost serves as an approximation, respectively….

• October 21, 2022 11:00 AM
##### Speaker: David Zuckerman
###### Venue: CMSA Room G10

Speaker: David Zuckerman, Harvard CMSA/University of Texas at Austin Title: Explicit Ramsey Graphs and Two Source Extractors Abstract: Ramsey showed that any graph on N nodes contains a clique or independent set of size (log N)/2.  Erdos showed that there exist graphs on N nodes with no clique or independent set of size 2 log N, and asked for an explicit construction of such graphs.  This turns out to relate to the question of extracting high-quality randomness from two independent low-quality sources.  I’ll explain this connection and our recent exponential improvement in constructing two-source extractors.

• October 14, 2022 11:00 AM
##### Speaker: Leonid Rybnikov
###### Venue: CMSA Room G10

Speaker: Leonid Rybnikov, Harvard CMSA/National Research University Higher School of Economics Title: Quantum magnet chains and Kashiwara crystals Abstract: Solutions of the algebraic Bethe ansatz for quantum magnet chains are, generally, multivalued functions of the parameters of the integrable system. I will explain how to compute some monodromies of solutions of Bethe ansatz for the Gaudin magnet chain. Namely, the Bethe eigenvectors in the Gaudin model can be regarded as a covering of the Deligne-Mumford moduli space of stable rational curves, which is unramified over the real locus of the Deligne-Mumford space. The monodromy action of the fundamental group of this space (called cactus group) on the eigenlines can be described very explicitly in purely combinatorial terms of Kashiwara crystals –…

• October 07, 2022 11:00 AM
##### Speaker: Zhigang Yao
###### Venue: CMSA Room G10

Member Seminar  Speaker: Zhigang Yao Title: Principal flow, sub-manifold and boundary Abstract: While classical statistics has dealt with observations which are real numbers or elements of a real vector space, nowadays many statistical problems of high interest in the sciences deal with the analysis of data which consist of more complex objects, taking values in spaces which are naturally not (Euclidean) vector spaces but which still feature some geometric structure. I will discuss the problem of finding principal components to the multivariate datasets, that lie on an embedded nonlinear Riemannian manifold within the higher-dimensional space. The aim is to extend the geometric interpretation of PCA, while being able to capture the non-geodesic form of variation in the data. I will…

• September 30, 2022 11:00 AM
##### Speaker: Jie Wang
###### Venue: CMSA Room G10

Member Seminar Speaker: Jie Wang Title: Kahler geometry in twisted materials Abstract: Flatbands are versatile platform for realizing exotic quantum phases due to the enhanced interactions. The canonical example is Landau level where fractional quantum Hall physics exists. Although interaction is strong, the fractional quantum Hall effect is relatively well understood thanks to its model wavefunction, exact parent Hamiltonian, conformal field theory analogous and other exact aspects. In generic flatbands, the interacting physics is controlled by the interplay between the interaction scale and intrinsic quantum geometries, in particular the Berry curvature and the Fubini-Study metric, which are in general spatially non-uniform. It is commonly believed that the non-uniform geometries destroy these exact properties of fractional quantum Hall physics, making…

• September 23, 2022 11:00 AM
##### Speaker: Ben McKenna
###### Venue: CMSA Room G10

Member Seminar Speaker: Ben McKenna Title: Random determinants, the elastic manifold, and landscape complexity beyond invariance Abstract: The Kac-Rice formula allows one to study the complexity of high-dimensional Gaussian random functions (meaning asymptotic counts of critical points) via the determinants of large random matrices. We present new results on determinant asymptotics for non-invariant random matrices, and use them to compute the (annealed) complexity for several types of landscapes. We focus especially on the elastic manifold, a classical disordered elastic system studied for example by Fisher (1986) in fixed dimension and by Mézard and Parisi (1992) in the high-dimensional limit. We confirm recent formulas of Fyodorov and Le Doussal (2020) on the model in the Mézard-Parisi setting, identifying the boundary…

• September 16, 2022 11:00 AM
##### Speaker: Shai Chester
###### Venue: CMSA Room G10

Member Seminar Speaker: Shai Chester Title: Derivation of AdS/CFT for Vector Models Abstract: We derive an explicit map at finite N between the singlet sector of the free and critical O(N) and U(N) vector models in any spacetime dimension above two, and a bulk higher spin theory in anti-de Sitter space in one higher dimension. For the boundary theory, we use the bilocal formalism of Jevicki et al to restrict to the singlet sector of the vector model. The bulk theory is defined from the boundary theory via our mapping, and is a consistent quantum higher spin theory with a well defined action. Our mapping relates bilocal operators in the boundary theory to higher spin fields in the bulk, while single trace local operators…

• September 09, 2022 12:00 PM
##### Speaker: Uri Kol
###### Venue: CMSA Room G10

Title: Duality in Einstein’s Gravity Abstract: Electric-Magnetic duality has been a key feature behind our understanding of Quantum Field Theory for over a century. In this talk I will describe a similar property in Einstein’s gravity. The gravitational duality reveals, in turn, a wide range of new IR phenomena, including aspects of the double copy for scattering amplitudes, asymptotic symmetries and more.

• May 13, 2022 09:30 AM
##### Speaker: Juven Wang
###### Venue: Virtual

Member Seminar Speaker: Juven Wang Title: Cobordism and Deformation Class of the Standard Model and Beyond: Proton Stability and Neutrino Mass Abstract: ‘t Hooft anomalies of quantum field theories (QFTs) with an invertible global symmetry G (including spacetime and internal symmetries) in a d-dim spacetime are known to be classified by a d+1-dim cobordism group TPd+1(G), whose group generator is a d+1-dim cobordism invariant written as a d+1-dim invertible topological field theory. Deformation class of QFT is recently proposed to be specified by its symmetry G and a d+1-dim invertible topological field theory. Seemly different QFTs of the same deformation class can be deformed to each other via quantum phase transitions. We ask which deformation class controls the 4d ungauged…

• April 29, 2022 09:30 AM
##### Speaker: Sergiy Verstyuk
###### Venue: virtual

Member Seminar Speaker: Sergiy Verstyuk Title: Machine Learning the Gravity Equation for International Trade Abstract: We will go through modern deep learning methods and existing approaches to their interpretation. Next, I will describe a graph neural network framework. You will also be introduced to an economic analog of gravity. Finally, we will see how these tools can help understand observed trade flows between 181 countries over 68 years. [Joint work with Michael R. Douglas.]

• April 08, 2022 08:45 AM
##### Speaker: Jorn Boehnke
###### Venue: virtual

Speaker: Jörn Boehnke Title: Synthetic Regression Discontinuity: Estimating Treatment Effects using Machine Learning Abstract:  In the standard regression discontinuity setting, treatment assignment is based on whether a unit’s observable score (running variable) crosses a known threshold.  We propose a two-stage method to estimate the treatment effect when the score is unobservable to the econometrician while the treatment status is known for all units.  In the first stage, we use a statistical model to predict a unit’s treatment status based on a continuous synthetic score.  In the second stage, we apply a regression discontinuity design using the predicted synthetic score as the running variable to estimate the treatment effect on an outcome of interest.  We establish conditions under which the…

• April 01, 2022 09:00 AM
##### Speaker: Farzan Vafa
###### Venue: virtual

Member Seminar Speaker: Farzan Vafa Title: Diffusive growth sourced by topological defects Abstract: In this talk, we develop a minimal model of morphogenesis of a surface where the dynamics of the intrinsic geometry is diffusive growth sourced by topological defects. We show that a positive (negative) defect can dynamically generate a cone (hyperbolic cone). We analytically explain features of the growth profile as a function of position and time, and predict that in the presence of a positive defect, a bump forms with height profile h(t) ~ t^(1/2) for early times t. To incorporate the effect of the mean curvature, we exploit the fact that for axisymmetric surfaces, the extrinsic geometry can be deduced entirely by the intrinsic…

• March 25, 2022 06:04 PM
##### Speaker: Tsung-Ju Lee
###### Venue: Virtual

Member Seminar Speaker: Tsung-Ju Lee Title: Periods for singular CY families and Riemann–Hilbert correspondence Abstract: A GKZ system, introduced by Gelfand, Kapranov, and Zelevinsky, is a system of partial differential equations generalizing the hypergeometric structure studied by Euler and Gauss. The solutions to GKZ systems have been found applications in various branches of mathematics including number theory, algebraic geometry and mirror symmetry. In this talk, I will explain the details and demonstrate how to find the Riemann–Hilbert partner of the GKZ system with a fractional parameter which arises from the B model of singular CY varieties. This is a joint work with Dingxin Zhang.

• March 18, 2022 09:30 AM
##### Speaker: Yingying Wu
###### Venue: virtual

Member Seminar Speaker: Yingying Wu Title: Moduli Space of Metric SUSY Graphs Abstract: SUSY curves are algebraic curves with additional supersymmetric or supergeometric structures. In this talk, I will present the construction of dual graphs of SUSY curves with Neveu–Schwarz and Ramond punctures. Then, I will introduce the concept of the metrized SUSY graph and the moduli space of the metric SUSY graphs. I will outline its geometric and topological properties, followed by a discussion on the connection with the classical case.

• March 04, 2022 09:30 AM
##### Speaker: Martin Lesourd
###### Venue: Hybrid- G10

Member Seminar Speaker: Martin Lesourd Title: Positive Mass, Density, and Scalar Curvature on Noncompact Manifolds Abstract: I’ll describe some recent work spanning a couple of different papers on the topics mentioned in the title: Positive Mass, Density, and Scalar Curvature on Noncompact Manifolds. Two of these are with R. Unger, Prof. S-T. Yau, and two others are with R. Unger, and Prof. D. A. Lee.

• February 18, 2022 09:30 AM
##### Speaker: An Huang
###### Venue: Virtual

Member Seminar Speaker:An Huang Title: Quadratic reciprocity from a family of adelic conformal field theories Abstract: This talk aims to provide a physics framework to understand quadratic reciprocity. Specifically, we consider a deformation of the two-dimensional free scalar field theory by raising the Laplacian to a positive real power. It turns out that the resulting non-local generalized free action is invariant under two commuting actions of the global conformal symmetry algebra, although it is no longer invariant under the full Witt algebra. The deformation is also closely related to dimensional regularization. Furthermore, there is an adelic version of this family of conformal field theories, parameterized by the choice of a number field, together with a Hecke character. Tate’s thesis…