• December 11, 2023 04:30 PM
Speaker: Justin Moore
Title: Homology, higher derived limits, and set theory
Venue: CMSA Room G10

Colloquium Speaker: Justin Moore (Cornell University) Title: Homology, higher derived limits, and set theory Abstract: Singular homology has a number of well-known defects when used to study spaces such as the Hawaiian earring and solenoids. It may not reflect the “shape” of the space and can give counterintuitive information about its dimension. One remedy of this is to develop a homology theory based on approximating spaces by polyhedra, computing their homologies, and then taking a limit. This is the approach taken by Steenrod-Sitnikov homology and Lisica and Mardesic’s strong homology. Even within the class of locally compact second countable spaces though, the properties of these homology theories — and the higher derived limits which underly them — are dependent on…

  • December 04, 2023 04:30 PM
Speaker: Xuwen Zhu
Title: Analysis of ALH* gravitational instantons
Venue: CMSA Room G10

Speaker: Xuwen Zhu (Northeastern) Title: Analysis of ALH* gravitational instantons Abstract: Gravitational instantons are non-compact Calabi-Yau metrics with L^2 bounded curvature and are categorized into six types. We will discuss one such type called ALH* metrics which has a non-compact end modelled by the Calabi ansatz with inhomogeneous collapsing near infinity. Such metrics appeared recently in the works on SYZ conjecture, as well as the scaling bubble limits for codimension-3 collapsing of K3 surfaces, where the study of its Laplacian played a central role. In this talk I will talk about the Fredholm mapping property and L^2 cohomology of such metrics. This is ongoing work joint with Rafe Mazzeo.

  • November 27, 2023 04:30 PM
Speaker: Dana Bartosova
Title: What do topological dynamics, combinatorics, and model theory have in common?
Venue: CMSA Room G10

Speaker: Dana Bartosova (University of Florida) Title: What do topological dynamics, combinatorics, and model theory have in common? Abstract: A striking correspondence between dynamics of automorphism groups of countable first order structures and Ramsey theory of finitary approximation of the structures was established in 2005 by Kechris, Pestov, and Todocevic. Since then, their work has been generalized and applied in many directions. It also struck a fresh wave of interest in finite Ramsey theory.  Many classes of finite structures are shown to have the Ramsey property by encoding their problem in a known Ramsey class and translating a solution back. This is often a case-by-case approach and naturally there is a great need for abstracting the process. There has been…

  • November 20, 2023 04:30 PM
Speaker: Jeff W. Lichtman
Title: The analytical challenges of connectomics
Venue: CMSA Room G10

Speaker: Jeff W. Lichtman (Harvard University) Title: The analytical challenges of connectomics Abstract: Recent progress in generating synapse-level maps of brains, a field known as connectomics, brings both opportunities and challenges. The upside is that the biophysical instantiation of memories, behaviors, and knowledge will soon be before us. The downside is that no one knows exactly how to make sense of this data. I will show what connectomics data sets are and attempt to explain why it is so difficult to unravel their meaning.

  • November 13, 2023 04:30 PM
Speaker: Brian Williams
Title: Koszul duality in QFT
Venue: CMSA Room G10

Speaker: Brian Williams (Boston University) Title: Koszul duality in QFT Abstract: We will describe appearances of the algebraic phenomena of Koszul duality in the context of boundary conditions and defects in quantum field theory. Primarily motivated by topological string theory, this point of view was pioneered by Costello and Li in their proposal for a twisted version of the AdS/CFT correspondence. Since then, many important examples of (twisted) holographic dualities in string and M-theory have been studied in work of Costello, Gaiotto, Paquette and many others. I will survey some of these examples and some current work with Raghavendran and Saberi which uses this formalism to predict exceptional symmetries present in M-theory.  

  • November 06, 2023 04:30 PM
Speaker: Matthew Foreman
Title: Impossibility results in classical dynamical systems
Venue: CMSA Room G10

Speaker: Matthew Foreman (UC Irvine) Title: Impossibility results in classical dynamical systems Abstract: In 1932, motivated by questions in statistical and celestial mechanics, von Neumann proposed classifying the statistical behavior of dynamical systems. In the 1960’s, motivated by work of Poincaré, Smale proposed classifying the qualitative behavior of dynamical systems.  These questions laid the groundwork for enormous amounts of work, but the fundamental questions remain open. This talk shows that they are impossible to answer in a rigorous sense. The talk will discuss various kinds of impossibility results and describe how they apply to von Neumann’s program and Smale’s program.  

  • October 30, 2023 04:30 PM
Speaker: Manuel Cortés-Izurdiaga
Title: Homotopy categories of rings: some properties and consequences in module categories
Venue: CMSA Room G10

Speaker: Manuel Cortés-Izurdiaga (University of Malaga) Title:  Homotopy categories of rings: some properties and consequences in module categories Abstract: Given a non-necessarily commutative ring with unit and an additive subcategory of the category of right modules, one can consider complexes of modules in the subcategory and the corresponding homotopy category. Sometimes, these homotopy categories are the first step in studying other (algebraic) homotopy categories, such as those associated to a scheme. To study these categories, one can use results from the category of modules or the category of complexes. In the first part of the talk, we will see how some results of homotopy categories of complexes extend to homotopy categories of N-complexes, for a natural number N greater…

  • October 23, 2023 04:30 PM
Speaker: Boaz Barak
Title:  On Provable Copyright Protection for Generative Model
Venue: CMSA Room G10

Speaker: Boaz Barak (Harvard) Title: On Provable Copyright Protection for Generative Model Abstract: There is a growing concern that learned conditional generative models may output samples that are substantially similar to some copyrighted data C that was in their training set. We give a formal definition of near access-freeness (NAF) and prove bounds on the probability that a model satisfying this definition outputs a sample similar to C, even if C is included in its training set. Roughly speaking, a generative model p is k-NAF if for every potentially copyrighted data C, the output of p diverges by at most k-bits from the output of a model q that did not access C at all. We also give generative model learning…

  • October 16, 2023 04:30 PM
Speaker: Joel D. Hamkins
Title: An exploration of infinite games—infinite Wordle and the Mastermind numbers
Venue: CMSA Room G10

Speaker: Joel D. Hamkins (Notre Dame and Oxford) Title: An exploration of infinite games—infinite Wordle and the Mastermind numbers Abstract: Let us explore the nature of strategic reasoning in infinite games, focusing on the cases of infinite Wordle and infinite Mastermind. The familiar game of Wordle extends naturally to longer words or even infinite words in an idealized language, and Mastermind similarly has natural infinitary analogues. What is the nature of play in these infinite games? Can the codebreaker play so as to win always at a finite stage of play? The analysis emerges gradually, and in the talk I shall begin slowly with some easy elementary observations. By the end, however, we shall engage with sophisticated ideas in descriptive…

  • October 02, 2023 04:30 PM
Speaker: Yu-Shen Lin
Title: Gravitational Instantons
Venue: CMSA Room G10

Speaker: Yu-Shen Lin (Boston University) Title: Gravitational Instantons Abstract: Gravitational instantons were introduced by Hawking as building blocks of his Euclidean quantum gravity theory back in the 1970s. These are non-compact Calabi-Yau surfaces with L2 curvature and thus can be viewed as the non-compact analogue of K3 surfaces. K3 surfaces are 2-dimensional Calabi-Yau manifolds and are usually the testing stone before conquering the general Calabi-Yau problems. The moduli space of K3 surfaces and its compactification on their own form important problems in various branches in geometry. In this talk, we will discuss the Torelli theorem of gravitational instantons, how the cohomological invariants of a gravitational instanton determine them. As a consequence, this leads to a description of the…

  • September 25, 2023 04:30 PM
Speaker: Sean Cox
Title: Predicting non-continuous functions
Venue: CMSA Room G10

Speaker: Sean Cox, Virginia Commonwealth University Title: Predicting non-continuous functions Abstract: One of the strangest consequences of the Axiom of Choice is the following Hardin-Taylor 2008 result: there is a “predictor” such that for every function $f$ from the reals to the reals—even nowhere continuous $f$—the predictor applied to $f \restriction (-\infty,t)$ correctly predicts $f(t)$ for *almost every* $t \in R$. They asked how robust such a predictor could be, with respect to distortions in the time (input) axis; more precisely, for which subgroups $H$ of Homeo^+(R) do there exist $H$-invariant predictors? Bajpai-Velleman proved an affirmative answer when H=Affine^+(R), and a negative answer when H is (the subgroup generated by) C^\infty(R). They asked about the intermediate region; in particular,…

  • September 20, 2023 12:30 PM
Speaker: Tim Adamo
Title: An invitation to strong-field scattering
Venue: CMSA Room G10

Speaker: Tim Adamo, University of Edinburgh Title: An invitation to strong-field scattering Abstract: Scattering amplitudes in strong background fields provide an arena where perturbative and non-perturbative physics meet, with important applications ranging from laser physics to black holes, but their study is hampered by the cumbersome nature of QFT in the background field formalism. In this talk, I will try to convince you that strong-field scattering amplitudes contain a wealth of physical information which cannot be obtained with standard perturbative techniques, ranging from all-order classical observables to constraints on exact solutions. Furthermore, I will discuss how amplitudes in certain chiral strong fields can be obtained to all-multiplicity twistor and string methods.

  • May 03, 2023 12:30 PM
Speaker: Xin Guo
Title: Generative Adversarial Networks (GANs): An Analytical Perspective
Venue: CMSA Room G10

Speaker: Xin Guo, UC Berkeley Title: Generative Adversarial Networks (GANs): An Analytical Perspective Abstract: Generative models have attracted intense interests recently. In this talk, I will discuss one class of generative models, Generative Adversarial Networks (GANs).  I will first provide a gentle review of the mathematical framework behind GANs. I will then proceed to discuss a few challenges in GANs training from an analytical perspective. I will finally report some recent progress for GANs training in terms of its stability and convergence analysis.  

  • April 26, 2023 12:30 PM
Speaker: Max Metlitski
Title: Boundary behavior at classical and quantum phase transitions
Venue: CMSA Room G10

Speaker: Max Metlitski (MIT) Title: Boundary behavior at classical and quantum phase transitions Abstract: There has been a lot of recent interest in the boundary behavior of materials. This interest is driven in part by the field of topological states of quantum matter, where exotic protected boundary states are ubiquitous. In this talk, I’ll ask: what happens at a boundary of a system, when the bulk goes through a phase transition. While this question was studied in the context of classical statistical mechanics in the 70s and 80s, basic aspects of the boundary phase diagram for the simplest classical phase transitions have been missed until recently. I’ll describe progress in this field, as well as some extensions to quantum phase transitions….

  • April 20, 2023 01:30 PM
Speaker: Julio Parra Martinez
Title: Black hole collider physics
Venue: CMSA Room G10

Speaker: Julio Parra Martinez, Caltech Title: Black hole collider physics Abstract: Despite more than a century since the development of Einstein’s theory, the general relativistic two-body problem remains unsolved. A precise description of its solution is now essential, as it is necessary for understanding the strong-gravity dynamics of compact binaries observed at LIGO/VIRGO/KAGRA and in future gravitational wave observatories. In this talk, I will describe how considering the scattering of black holes and gravitons can shed new light on this problem. I will explain how using modern ideas from collider and particle physics we can calculate scattering observables in classical gravity, and extract the basic ingredients that describe the bound binary dynamics. Such calculations have produced state-of-art predictions…

  • April 12, 2023 12:30 PM
Speaker: James Halverson
Title: Unexpected Uses of Neural Networks: Field Theory and Metric Flows  
Venue: CMSA Room G10

Speaker: James Halverson (Northeastern University)   Title: Unexpected Uses of Neural Networks: Field Theory and Metric Flows Abstract:  We are now quite used to the idea that deep neural networks may be trained in a variety of ways to tackle cutting-edge problems in physics and mathematics, sometimes leading to rigorous results. In this talk, however, I will argue that breakthroughs in deep learning theory are also useful for making progress, focusing on applications to field theory and metric flows. Specifically, I will introduce a neural network approach to field theory with a different statistical origin, that exhibits generalized free field behavior at infinite width and interactions at finite width, and that allows for the study of symmetries via the study of correlation functions…

  • April 03, 2023 11:00 AM
Speaker: Luca Iliesiu
Title: Black hole microstate counting from the gravitational path integral
Venue: CMSA Room G10

Colloquium Speaker: Luca Iliesiu, Stanford Title: Black hole microstate counting from the gravitational path integral Abstract: Reproducing the integer count of black hole micro-states from the gravitational path integral is an important problem in quantum gravity. In the first part of the talk, I will show that, by using supersymmetric localization, the gravitational path integral for 1/16-BPS black holes in supergravity can reproduce the index obtained in the string theory construction of such black holes. A more refined argument then shows that not only the black hole index but also the total number of black hole microstates within an energy window above extremality that is polynomially suppressed in the charges also matches this string theory index. In the second part of the talk, I will…

  • March 29, 2023 12:30 PM
Speaker: Ruth Britto
Title: Scattering amplitudes in quantum field theory
Venue: CMSA Room G10

Speaker: Ruth Britto (Trinity College Dublin) Title: Scattering amplitudes in quantum field theory Abstract: Particle collider experiments require a detailed description of scattering events, traditionally computed through sums of Feynman diagrams. However, it is not practical to evaluate Feynman diagrams directly for all significant scattering processes. Moreover, adding all diagrams reveals many cancellations: scattering amplitudes in theories such as QCD take remarkably simple forms. This simplicity is a clue that the perturbative theory is perhaps best understood without reference to Feynman diagrams. In fact, it has recently become possible to explain some of this simplicity. I will show how to derive many amplitudes efficiently and elegantly, and propose taming the remaining complexity with ideas drawn from combinatorics and…

  • March 22, 2023 12:30 PM
Speaker: Mete Soner
Title: Synchronization in a Kuramoto Mean Field Game
Venue: CMSA Room G10

Speaker: Mete Soner (Princeton University) Title: Synchronization in a Kuramoto Mean Field Game Abstract:  Originally motivated by systems of chemical and biological oscillators, the classical Kuramoto model has found an amazing range of applications from neuroscience to Josephson junctions in superconductors, and has become a  key mathematical model to describe self organization in complex systems. These autonomous oscillators are coupled through a nonlinear interaction term which plays a central role in the long term behavior of the system. While the system is not synchronized when this term is not sufficiently strong, fascinatingly, they exhibit an abrupt transition to a full synchronization above a critical value of the interaction parameter.  We explore this system in the mean field formalism.  We treat the system…

  • March 08, 2023 12:30 PM
Speaker: Ning Su
Title: Conformal symmetry, Optimization algorithms and the Critical Phenomena
Venue: CMSA Room G10

Speaker: Ning Su, University of Pisa Title: Conformal symmetry, Optimization algorithms and the Critical Phenomena Abstract: In the phase diagram of many substances, the critical points have emergent conformal symmetry and are described by conformal field theories. Traditionally, physical quantities near the critical point can be computed by perturbative field theory method, where conformal symmetry is not fully utilized. In this talk, I will explain how conformal symmetry can be used to determine certain physical quantities, without even knowing the fine details of the microscopic structure. To compute the observables precisely, one needs to develop powerful numerical techniques. In the last few years, we have invented many computational tools and algorithms, and predicted critical exponents of Helium-4 superfluid…