CMSA

Birkhoff’s conjecture on integrable billiards and Kac’s problem “hearing the shape of a drum”
2022-03-15 10:00 - 23:00 (America/New_York) | MA
Abstract: Billiards on an elliptical billiard table are completely integrable: phase space is foliated by invariant submanifolds for the billiard flow. Birkhoff conjectured that ellipses are the only plane domains with integrable billiards. Avila-deSimoi- Kaloshin proved the conjecture for ellipses of sufficiently small eccentricity. Kaloshin-Sorrentino proved local results for all eccentricities. On the quantum level, the analogous conjecture is that ellipses are uniquely determined by their Dirichlet (or, Neumann) eigenvalues. Using the results on the Birkhoff conjecture, Hamid Hezari and I proved that for ellipses of small eccentricity are indeed uniquely determined by their eigenvalues. Except for disks, which Kac proved to be uniquely determined, these are the only domains for which it is known that one can hear their shape.

2-categorical 3d mirror symmetry
2022-03-15 09:30 - 10:30 | Virtual
Abstract: It is by now well-known that mirror symmetry may be expressed as an equivalence between categories associated to dual Kahler manifolds. Following a proposal of Teleman, we inaugurate a program to understand 3d mirror symmetry as an equivalence between 2-categories associated to dual holomorphic symplectic stacks. We consider here the abelian case, where our theorem expresses the 2-category of spherical functors as a 2-category of coherent sheaves of categories. Applications include categorifications of hypertoric category O and of many related constructions in representation theory. This is joint work with Justin Hilburn and Aaron Mazel-Gee.

Moduli space of tropical curves, graph Laplacians and physics
2022-03-15 09:00 - 10:00 | MA
Abstract: I will first review the construction of the moduli space of tropical curves (or metric graphs), and its relation to graph complexes. The graph Laplacian may be interpreted as a tropical version of the classical Torelli map and its determinant is the Kirchhoff graph polynomial (also called 1st Symanzik), which is one of the two key components in Feynman integrals in high energy physics.The other component is the so-called 2nd Symanzik polynomial, which is defined for graphs with external half edges and involves particle masses (edge colourings). I will explain how this too may be interpreted as the determinant of a generalised graph Laplacian, and how it leads to a volumetric interpretation of a certain class of Feynman integrals.

Resonant side-jump thermal Hall effect of phonons coupled to dynamical defects
2022-03-10 20:00 - 21:30 | Virtual
Abstract: We present computations of the thermal Hall coefficient of phonons scattering off defects with multiple energy levels. Using a microscopic formulation based on the Kubo formula, we find that the leading contribution perturbative in the phonon-defect coupling is of the ‘side-jump’ type, which is proportional to the phonon lifetime. This contribution is at resonance when the phonon energy equals a defect level spacing. Our results are obtained for different defect models, and include models of an impurity quantum spin in the presence of quasi-static magnetic order with an isotropic Zeeman coupling to the applied field.
This work is based on arxiv: 2201.11681

Virtual Teams in Gig Economy — An End-to-End Data Science Approach
2022-03-10 15:13 - 16:13 | MA
Abstract: The gig economy provides workers with the benefits of autonomy and flexibility, but it does so at the expense of work identity and co-worker bonds. Among the many reasons why gig workers leave their platforms, an unexplored aspect is the organization identity. In a series of studies, we develop a team formation and inter-team contest at a ride-sharing platform. We employ an end-to-end data science approach, combining methodologies from randomized field experiments, recommender systems, and counterfactual machine learning. Together, our results show that platform designers can leverage team identity and team contests to increase revenue and worker engagement in a gig economy.
Bio: Wei Ai is an Assistant Professor in the College of Information Studies (iSchool) and the Institute for Advanced Computer Studies (UMIACS) at the University of Maryland. His research interest lies in data science for social good, where the advances of machine learning and data analysis algorithms translate into measurable impacts on society. He combines machine learning, causal inference, and field experiments in his research, and has rich experience in collaborating with industrial partners. He earned his Ph.D. from the School of Information at the University of Michigan. His research has been published in top journals and conferences, including PNAS, ACM TOIS, WWW, and ICWSM.

The Einstein-flow on manifolds of negative curvature
2022-03-10 13:00 - 14:00 | MA
Abstract: We consider the Cauchy problem for the Einstein equations for cosmological spacetimes, i.e. spacetimes with compact spatial hypersurfaces. Various classes of those dynamical spacetimes have been constructed and analyzed using CMC foliations or equivalently the CMC-Einstein flow. We will briefly review the Andersson-Moncrief stability result of negative Einstein metrics under the vacuum Einstein flow and then present various recent generalizations to the nonvacuum case. We will emphasize what difficulties arise in those generalizations, how they can be handled depending on the matter model at hand, and what implications we can draw from these results for cosmology. We then turn to a scenario where the CMC Einstein flow leads to a large data result in 2+1-dimensions.

Machine Learning 30 STEM Courses in 12 Departments
2022-03-09 14:00 | MA
Speaker: Iddo Drori, MIT EE&CS and Columbia School of Engineering
Title: Machine Learning 30 STEM Courses in 12 Departments
Abstract: We automatically solve, explain, and generate university-level course problems from thirty STEM courses (at MIT, Harvard, and Columbia) for the first time.
We curate a new dataset of course questions and answers across a dozen departments: Aeronautics and Astronautics, Chemical Engineering, Chemistry, Computer Science, Economics, Electrical Engineering, Materials Science, Mathematics, Mechanical Engineering, Nuclear Science, Physics, and Statistics.
We generate new questions and use them in a Columbia University course, and perform A/B tests demonstrating that these machine generated questions are indistinguishable from human-written questions and that machine generated explanations are as useful as human-written explanations, again for the first time.
Our approach consists of five steps:
(i) Given course questions, turn them into programming tasks;
(ii) Automatically generate programs from the programming tasks using a Transformer model, OpenAI Codex, pre-trained on text and fine-tuned on code;
(iii) Execute the programs to obtain and evaluate the answers;
(iv) Automatically explain the correct solutions using Codex;
(v) Automatically generate new questions that are qualitatively indistinguishable from human-written questions.
This work is a significant step forward in applying machine learning for education, automating a considerable part of the work involved in teaching.
Our approach allows personalization of questions based on difficulty level and student backgrounds, and scales up to a broad range of courses across the schools of engineering and science.
This is joint work with students and colleagues at MIT, Harvard University, Columbia University, Worcester Polytechnic Institute, and the University of Waterloo.

Anomalies, topological insulators and Kaehler-Dirac fermions
2022-03-09 10:30 - 12:00 | Virtual
Abstract: Motivated by a puzzle arising from recent work on staggered lattice fermions we introduce Kaehler-Dirac fermions and describe their connection both to Dirac fermions and staggered fermions. We show that they suffer from a gravitational anomaly that breaks a chiral U(1) symmetry specific to Kaehler-Dirac fermions down to Z_4 in any even dimension. In odd dimensions we show that the effective theory that results from integrating out massive Kaehler-Dirac fermions is a topological gravity theory. Such theories generalize Witten’s construction of (2+1) gravity as a Chern Simons theory. In the presence of a domain wall massless modes appear on the wall which can be consistently coupled to gravity due to anomaly inflow from the bulk gravitational theory. Much of this story parallels the usual discussion of topological insulators. The key difference is that the twisted chiral symmetry and anomaly structure of Kaehler-Dirac theories survives intact under discretization and governs the behavior of the lattice models. $Z_4$ invariant four fermion interactions can be used to gap out states in such theories without breaking symmetries and in flat space yields the known constraints on the number of Majorana fermions needed symmetric mass generation namely eight and sixteen Majorana spinors in two and four dimensions.

Side-effects of Learning from Low Dimensional Data Embedded in an Euclidean Space
2022-03-09 09:30 - 10:30 | MA
Abstract: The low dimensional manifold hypothesis posits that the data found in many applications, such as those involving natural images, lie (approximately) on low dimensional manifolds embedded in a high dimensional Euclidean space. In this setting, a typical neural network defines a function that takes a finite number of vectors in the embedding space as input. However, one often needs to consider evaluating the optimized network at points outside the training distribution. We analyze the cases where the training data are distributed in a linear subspace of Rd. We derive estimates on the variation of the learning function, defined by a neural network, in the direction transversal to the subspace. We study the potential regularization effects associated with the network’s depth and noise in the codimension of the data manifold.

Greedy maximal independent sets via local limits
2022-03-08 09:00 - 10:00 | MA
Abstract: The random greedy algorithm for finding a maximal independent set in a graph has been studied extensively in various settings in combinatorics, probability, computer science, and chemistry. The algorithm builds a maximal independent set by inspecting the graph’s vertices one at a time according to a random order, adding the current vertex to the independent set if it is not connected to any previously added vertex by an edge.
In this talk, I will present a simple yet general framework for calculating the asymptotics of the proportion of the yielded independent set for sequences of (possibly random) graphs, involving a valuable notion of local convergence. I will demonstrate the applicability of this framework by giving short and straightforward proofs for results on previously studied families of graphs, such as paths and various random graphs, and by providing new results for other models such as random trees.
If time allows, I will discuss a more delicate (and combinatorial) result, according to which, in expectation, the cardinality of a random greedy independent set in the path is no larger than that in any other tree of the same order.
The talk is based on joint work with Michael Krivelevich, Tamás Mészáros and Clara Shikhelman.

4d strings at strong coupling
2022-03-07 10:00 - 11:30 | Virtual
Speakers: Fernando Marchesano (UAM-CSIC, Madrid) and Max Wiesner (Harvard CMSA)

Title: 4d strings at strong coupling

As usual, the format will be 45 min talk + 30 min discussion, to encourage participation from the audience.
Looking forward to seeing you there!

Positive Mass, Density, and Scalar Curvature on Noncompact Manifolds
2022-03-04 09:30 - 10:30 | 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.

Towards Understanding Training Dynamics for Mildly Overparametrized Models
2022-03-03 15:11 - 16:11 | MA
Abstract: While over-parameterization is widely believed to be crucial for the success of optimization for the neural networks, most existing theories on over-parameterization do not fully explain the reason — they either work in the Neural Tangent Kernel regime where neurons don’t move much, or require an enormous number of neurons. In this talk I will describe our recent works towards understanding training dynamics that go beyond kernel regimes with only polynomially many neurons (mildly overparametrized). In particular, we first give a local convergence result for mildly overparametrized two-layer networks. We then analyze the global training dynamics for a related overparametrized tensor model. For both works, we rely on a key intuition that neurons in overparametrized models work in groups and it’s important to understand the behavior of an average neuron in the group. Based on two works: https://arxiv.org/abs/2102.02410 and https://arxiv.org/abs/2106.06573.
Bio: Professor Rong Ge is Associate Professor of Computer Science at Duke University. He received his Ph.D. from the Computer Science Department of Princeton University, supervised by Sanjeev Arora. He was a post-doc at Microsoft Research, New England. In 2019, he received both a Faculty Early Career Development Award from the National Science Foundation and the prestigious Sloan Research Fellowship. His research interest focus on theoretical computer science and machine learning. Modern machine learning algorithms such as deep learning try to automatically learn useful hidden representations of the data. He is interested in formalizing hidden structures in the data and designing efficient algorithms to find them. His research aims to answer these questions by studying problems that arise in analyzing text, images, and other forms of data, using techniques such as non-convex optimization and tensor decompositions.

Callan Rubakov Effect and Higher Charge Monopoles
2022-03-03 09:30 - 11:00 | Virtual
Abstract: In this talk we will discuss the interaction between magnetic monopoles and massless fermions. In the 1980’s Callan and Rubakov showed that in the simplest example and that fermion-monopole interactions catalyze proton decay in GUT completions of the standard model. Here we will explain how fermions in general representations interact with general spherically symmetric monopoles and classify the types of symmetries that are broken: global symmetries with ABJ-type anomalies.

Scaling Laws and Their Implications for Coding AI
2022-03-02 14:00 - 15:00 | Virtual
Speaker: Jared Kaplan, Johns Hopkins Dept. of Physics & Astronomy
Title: Scaling Laws and Their Implications for Coding AI
Abstract: Scaling laws and associated downstream trends can be used as an organizing principle when thinking about current and future ML progress. I will briefly review scaling laws for generative models in a number of domains, emphasizing language modeling. Then I will discuss scaling results for transfer from natural language to code, and results on python programming performance from “codex” and other models. If there’s time I’ll discuss prospects for the future — limitations from dataset sizes, and prospects for RL and other techniques.

Exactly Solvable Lattice Hamiltonians and Gravitational Anomalies
2022-03-02 10:30 - 12:00 | MA
Abstract: We construct infinitely many new exactly solvable local commuting projector lattice Hamiltonian models for general bosonic beyond group cohomology invertible topological phases of order two and four in any spacetime dimensions, whose boundaries are characterized by gravitational anomalies. Examples include the beyond group cohomology invertible phase “w2w3” in (4+1)D that has an anomalous boundary topological order with fermionic particle and fermionic loop excitations that have mutual statistics. Finally, we will demonstrate a few examples of fermionic loop excitations.

Tropical Lagrangian multi-sections and locally free sheaves
2022-03-02 09:30 - 22:30 | MA
Abstract: The SYZ proposal suggests that mirror symmetry is T-duality. It is a folklore that locally free sheaves are mirror to a Lagrangian multi-section of the SYZ fibration. In this talk, I will introduce the notion of tropical Lagrangian multi-sections and discuss how to obtain from such object to a class of locally free sheaves on the log Calabi-Yau spaces that Gross-Siebert have considered. I will also discuss a joint work with Kwokwai Chan and Ziming Ma, where we proved the smoothability of a class of locally free sheaves on some log Calabi-Yau surfaces by using combinatorial data obtained from tropical Lagrangian multi-sections.

Dimers and webs
2022-03-02 09:30 - 10:30 | Virtual
Speaker: Richard Kenyon (Yale)
Title: Dimers and webs
Abstract: We consider SL_n-local systems on graphs on surfaces and show how the associated Kasteleyn matrix can be used to compute probabilities of various topological events involving the overlay of n independent dimer covers (or “n-webs”).
This is joint work with Dan Douglas and Haolin Shi.

General Relativity Program Minicourses
2022-03-01 10:00 - 2022-05-17 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Minicourses
General Relativity Program Minicourses

During the Spring 2022 semester, the CMSA hosted a program on General Relativity.
This semester-long program included four minicourses running in March, April, and May; a conference April 4–8, 2022; and a workshop from May 2–5, 2022.

Schedule
Speaker
Title
Abstract

March 1 – 3, 2022
10:00 am – 12:00 pm ET, each dayLocation: Hybrid. CMSA main seminar room, G-10.
Dr. Stefan Czimek
Characteristic Gluing for the Einstein Equations
Abstract: This course serves as an introduction to characteristic gluing for the Einstein equations (developed by the lecturer in collaboration with S. Aretakis and I. Rodnianski). First we set up and analyze the characteristic gluing problem along one outgoing null hypersurface. Then we turn to bifurcate characteristic gluing (i.e. gluing along two null hypersurfaces bifurcating from a spacelike 2-sphere) and show how to localize characteristic initial data. Subsequently we turn to applications for spacelike initial data. Specifically, we discuss in detail our alternative proofs of the celebrated Corvino-Schoen gluing to Kerr and the Carlotto-Schoen localization of spacelike initial data (with improved decay).

March 22 – 25, 2022
22nd & 23rd, 10:00 am – 11:30am ET
24th & 25th, 11:00 am – 12:30pm ETLocation: Hybrid. CMSA main seminar room, G-10.
Prof. Lan-Hsuan Huang
Existence of Static Metrics with Prescribed Bartnik Boundary Data
Abstract: The study of static Riemannian metrics arises naturally in general relativity and differential geometry. A static metric produces a special Einstein manifold, and it interconnects with scalar curvature deformation and gluing. The well-known Uniqueness Theorem of Static Black Holes says that an asymptotically flat, static metric with black hole boundary must belong to the Schwarzschild family. In the same vein, most efforts have been made to classify static metrics as known exact solutions. In contrast to the rigidity phenomena and classification efforts, Robert Bartnik proposed the Static Vacuum Extension Conjecture (originating from his other conjectures about quasi-local masses in the 80’s) that there is always a unique, asymptotically flat, static vacuum metric with quite arbitrarily prescribed Bartnik boundary data. In this course, I will discuss some recent progress confirming this conjecture for large classes of boundary data. The course is based on joint work with Zhongshan An, and the tentative plan is
1. The conjecture and an overview of the results
2. Static regular: a sufficient condition for existence and local uniqueness
3. Convex boundary, isometric embedding, and static regular
4. Perturbations of any hypersurface are static regular
Video on Youtube: March 22, 2022

March 29 – April 1, 2022 10:00am – 12:00pm ET, each day
Location: Hybrid. CMSA main seminar room, G-10.
Prof. Martin Taylor
The nonlinear stability of the Schwarzschild family of black holes
Abstract: I will present aspects of a theorem, joint with Mihalis Dafermos, Gustav Holzegel and Igor Rodnianski, on the full finite codimension nonlinear asymptotic stability of the Schwarzschild family of black holes.

April 19 & 21, 2022
10 am – 12 pm ET, each dayZoom only
Prof. Håkan Andréasson
Two topics for the Einstein-Vlasov system: Gravitational collapse and properties of static and stationary solutions.
Abstract: In these lectures I will discuss the Einstein-Vlasov system in the asymptotically flat case. I will focus on two topics; gravitational collapse and properties of static and stationary solutions. In the former case I will present results in the spherically symmetric case that give criteria on initial data which guarantee the formation of black holes in the evolution. I will also discuss the relation between gravitational collapse for the Einstein-Vlasov system and the Einstein-dust system. I will then discuss properties of static and stationary solutions in the spherically symmetric case and the axisymmetric case. In particular I will present a recent result on the existence of massless steady states surrounding a Schwarzschild black hole.
Video 4/19/2022
Video 4/22/2022

May 16 – 17, 2022
10:00 am – 1:00 pm ET, each dayLocation: Hybrid. CMSA main seminar room, G-10.
Prof. Marcelo Disconzi
A brief overview of recent developments in relativistic fluids
Abstract: In this series of lectures, we will discuss some recent developments in the field of relativistic fluids, considering both the motion of relativistic fluids in a fixed background or coupled to Einstein’s equations. The topics to be discussed will include: the relativistic free-boundary Euler equations with a physical vacuum boundary, a new formulation of the relativistic Euler equations tailored to applications to shock formation, and formulations of relativistic fluids with viscosity.
1. Set-up, review of standard results, physical motivation.
2. The relativistic Euler equations: null structures and the problem of shocks.
3. The free-boundary relativistic Euler equations with a physical vacuum boundary.
4. Relativistic viscous fluids.
Video 5/16/2022
Video 5/17/2022

Virtual localization for Artin stacks
2022-03-01 09:30 - 10:30 | Virtual
Abstract: This is a report about work in progress with: Adeel Khan, Aloysha Latyntsev, Hyeonjun Park and Charanya Ravi. We will describe a virtual Atiyah-Bott formula for Artin stacks. In the Deligne-Mumford case our methods allow us to remove the global resolution hypothesis for the virtual normal bundle.

Rational Polypols
2022-03-01 09:00 - 10:00 | MA
Abstract: Eugene Wachspress introduced polypols as real bounded semialgebraic sets in the plane that generalize polygons. He aimed to generalize barycentric coordinates from triangles to arbitrary polygons and further to polypols. For this, he defined the adjoint curve of a rational polypol. In the study of scattering amplitudes in physics, positive geometries are real semialgebraic sets together with a rational canonical form. We combine these two worlds by providing an explicit formula for the canonical form of a rational polypol in terms of defining equations of the adjoint curve and the facets of the polypol. For the special case of polygons, we show that the adjoint curve is hyperbolic and provide an explicit description of its nested ovals. Finally, we discuss the map that associates the adjoint curve to a given rational polypol, in particular the cases where this map is finite. For instance, using monodromy we find that a general quartic curve is the adjoint of 864 heptagons.
This talk is based on joint work with R. Piene, K. Ranestad, F. Rydell, B. Shapiro, R. Sinn, M.-S. Sorea, and S. Telen.

Generalized Global Symmetries and the Weak Gravity Conjecture
2022-02-28 13:00 - 14:00 | MA

Bridging three-dimensional coupled-wire models and cellular topological states
2022-02-24 20:00 - 21:30 | MA
Abstract: Three-dimensional (3d) gapped topological phases with fractional excitations are divided into two subclasses: One has topological order with point-like and loop-like excitations fully mobile in the 3d space, and the other has fracton order with point-like excitations constrained in lower-dimensional subspaces. These exotic phases are often studied by exactly solvable Hamiltonians made of commuting projectors, which, however, are not capable of describing those with chiral gapless surface states. Here we introduce a systematic way, based on cellular construction recently proposed for 3d topological phases, to construct another type of exactly solvable models in terms of coupled quantum wires with given inputs of cellular structure, two-dimensional Abelian topological order, and their gapped interfaces. We show that our models can describe both 3d topological and fracton orders and even their hybrid and study their universal properties such as quasiparticle statistics and topological ground-state degeneracy.

Singular Set in Obstacle Problems
2022-02-24 15:08 - 16:08 | MA
Abstract: In this talk we describe a new method to study the singular set in the obstacle problem. This method does not depend on monotonicity formulae and works for fully nonlinear elliptic operators. The result we get matches the best-known result for the case of Laplacian.

Taming Active Matter: from ordered topological defects to autonomous shells
2022-02-24 13:00 - 14:30 | MA
Abstract: The spontaneous emergence of collective flows is a generic property of active fluids and often leads to chaotic flow patterns characterized by swirls, jets, and topological
disclinations in their orientation field. I will first discuss two examples of these collective features helping us understand biological processes: (i) to explain the tortoise & hare story in bacterial competition: how motility of Pseudomonas aeruginosa bacteria leads to a slower invasion of bacteria colonies, which are individually faster, and
(ii) how self-propelled defects lead to finding an unanticipated mechanism for cell death.
I will then discuss various strategies to tame, otherwise chaotic, active flows, showing how hydrodynamic screening of active flows can act as a robust way of controlling and guiding active particles into dynamically ordered coherent structures. I will also explain how combining hydrodynamics with topological constraints can lead to further control of exotic morphologies of active shells.

Extreme Black Holes: Anabasis and Accidental Symmetry
2022-02-24 13:00 - 14:00 | Virtual
Speaker: Achilleas Porfyriadis, Harvard Black Hole Initiative
Title: Extreme Black Holes: Anabasis and Accidental Symmetry
Abstract: The near-horizon region of black holes near extremality is universally AdS_2-like. In this talk I will concentrate on the simplest example of AdS_2 x S^2 as the near-horizon of (near-)extreme Reissner-Nordstrom. I will first explain the SL(2)transformation properties of the spherically symmetric linear perturbations of AdS_2 x S^2 and show how their backreaction leads to the Reissner-Nordstrom black hole. This backreaction with boundary condition change is called an anabasis. I will then show that the linear Einstein equation near AdS_2 x S^2, with or without additional matter, enjoys an accidental symmetry that may be thought of as an on-shell large diffeomorphism of AdS_2.

Donaldson-Thomas invariants and hyperkahler manifolds: the example of theories of class S[A1]
2022-02-23 16:00 - 17:00 | MA
Abstract: I will report on a project which aims to encode the DT invariants of a CY3 triangulated category in a geometric structure on its stability space. I will focus on a class of categories whose stability spaces were studied in previous joint work with Ivan Smith, and which correspond in physics to theories of class S[A1]. I will describe the resulting geometric structures using a kind of complexified Hitchin system parameterising bundles on curves equipped with pencils of flat connections.

Topological Quantum Gravity and the Ricci Flow – Part II
2022-02-23 10:30 - 12:00 | MA
Abstract: In this sequence of talks, I will describe our work with Alexander Frenkel and Stephen Randall, in which we presented a novel topological quantum gravity, relating three previously unrelated fields: Topological quantum field theories (of the cohomological type), the theory of Ricci flows on Riemannian manifolds, and nonrelativistic quantum gravity. The remarkable richness of results produced in the recent decades by mathematicians studying the Ricci flow promises to shed new light on the physics of the path integral in quantum gravity (at least in the topological regime). In the opposite direction, the techniques of quantum field theory and path integrals may end up putting some of the mathematical results in the Ricci flow theory in a new perspective as well.

Holographic Cone of Average Entropies and Universality of Black Holes
2022-02-23 09:30 - 10:30 | Virtual
Speaker: Bartek Czech, Tsinghua University
Title: Holographic Cone of Average Entropies and Universality of Black Holes
Abstract: In the AdS/CFT correspondence, the holographic entropy cone, which identifies von Neumann entropies of CFT regions that are consistent with a semiclassical bulk dual, is currently known only up to n=5 regions. I explain that average
entropies of p-partite subsystems can be checked for consistency with a semiclassical bulk dual far more easily, for an arbitrary number of regions n. This analysis defines the “Holographic Cone of Average
Entropies” (HCAE). I conjecture the exact form of HCAE, and find that it has the following properties: (1) HCAE is the simplest it could be, namely it is a simplicial cone. (2) Its extremal rays represent stages of thermalization (black hole formation). (3) In a time-reversed picture, the extremal rays of HCAE represent stages of unitary black hole evaporation, as stipulated by the island solution of the black hole information paradox. (4) HCAE is bound by a novel, infinite family of holographic entropy inequalities. (5) HCAE is the simplest it could be also in its dependence on the number of regions n, namely its bounding inequalities are n-independent. (6) In a precise sense I describe, the bounding inequalities of HCAE unify (almost) all previously discovered holographic inequalities and strongly constrain future inequalities yet to be discovered. I also sketch an interpretation of HCAE in terms of error correction and the holographic Renormalization Group. The big lesson that HCAE seems to be teaching us is about the universality of black hole physics.

Higgs-Coulomb correspondence in abelian GLSM
2022-02-22 09:30 - 10:30 | Virtual
Abstract: We construct a certain type of Gauged Linear Sigma Model quasimap invariants that generalize the original ones and are easier to compute. Higgs-Coulomb correspondence provides identification of generating functions of our invariants with certain analytic functions that can be represented as generalized inverse Mellin transforms. Analytic continuation of these functions provides wall-crossing results for GLSM and generalizes Landau- Ginzburg/Calabi-Yau correspondence. The talk is based on a joint work in progress with Melissa Liu.
