CMSA

Geometry at Strong coupling for amplitudes/Wilson loops
2023-09-26 11:00 - 12:00 (America/New_York) | MA
General Relativity Seminar
Speaker: Lionel Mason (Oxford)
Title: Geometry at Strong coupling for amplitudes/Wilson loops
Abstract: The amplitude/Wilson loop correspondence identifies planar N=4 super-Yang-Mills amplitudes with certain null polygonal Wilson loops at all the values of the coupling. At strong coupling this equates the amplitude/Wilson loop computed by Alday & Maldacena in terms of the area of a minimal surface in AdS_5. To do so they developed a `Y-system’ for computing the amplitude. This talk re-interprets their construction as providing the underlying twistor space for a hyperKahler structure on the corresponding space of kinematic data. In particular, the area is given by a Kahler scalar for the pseudo-hyperkahler structure and satisfies a version of the Plebanski equations, a well-known completely integrable system. This geometry encodes the properties of the space of kinematic data on which the amplitude depends as a cluster variety tying into its positive geometry and cluster variety structure. Similar constructures are possible for other cluster varieties corresponding to form factors and beyond.

CMSA Q and A Seminar 9/26/2023
2023-09-26 12:30 - 13:30 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q and A Seminar
Speakers: Michael Douglas (CMSA) and Mayuko Yamashita (Kyoto University)
Topics:
Michael Douglas: “What is non-commutative field theory?”

Mayuko Yamashita: “What is differential cohomology?”

Transformers for maths, and maths for transformers
2023-09-27 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
New Technologies in Mathematics Seminar
Speaker: François Charton, Meta AI
Title: Transformers for maths, and maths for transformers
Abstract: Transformers can be trained to solve problems of mathematics. I present two recent applications, in mathematics and physics: predicting integer sequences, and discovering the properties of scattering amplitudes in a close relative of Quantum ChromoDynamics.
Problems of mathematics can also help understand transformers. Using two examples from linear algebra and integer arithmetic, I show that model predictions can be explained, that trained models do not confabulate, and that carefully choosing the training distributions can help achieve better, and more robust, performance.

Large deviations for the 3D dimer model
2023-09-27 15:30 - 16:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Probability Seminar
Speaker: Catherine Wolfram (MIT)
Title: Large deviations for the 3D dimer model
Abstract: A dimer tiling of Z^d is a collection of edges such that every vertex is covered exactly once. In 2000, Cohn, Kenyon, and Propp showed that 2D dimer tilings satisfy a large deviations principle. In joint work with Nishant Chandgotia and Scott Sheffield, we prove an analogous large deviations principle for dimers in 3D. A lot of the results for dimers in two dimensions use tools and exact formulas (e.g. the height function representation of a tiling or the Kasteleyn determinant formula) that are specific to dimension 2. In this talk, I will try to give some intuition for why three dimensions is different from two, explain how to formulate the large deviations principle in 3D, show simulations, and explain some of the ways that we use a smaller set of tools (e.g. Hall’s matching theorem or a double dimer swapping operation) in our arguments.

Strongly driven mixtures and membranes: Out of equilibrium surprises
2023-09-28 13:00 - 14:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Active Matter Seminar

Speaker: Max Lavrentovich, Worcester State University
Title: Strongly driven mixtures and membranes: Out of equilibrium surprises
Abstract: The more prosaic cousin of active matter, driven inactive matter, is still full of unexpected phenomena. I will discuss two projects involving two seemingly mundane systems, a phase-separating colloidal mixture and a lipid membrane, which demonstrate counterintuitive properties when driven out of equilibrium. We will see that the phase separating mixture, when driven by a uniform force, develops (in simulations) an intriguing pattern with a characteristic length scale set by the magnitude of the drive. We will look at some theoretical approaches to understanding the pattern formation and possible experimental realizations. The membrane, when driven by an oscillatory electric field, develops (in experiments) a long-lived metastable state with a decreased capacitance and increased dissipation. This state may have implications for neuronal processing and memory formation.

Quantum field theory approach to quantum information
2023-09-28 16:30 - 18:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter Seminar
Speaker: Cenke Xu (UCSB)
Title: Quantum field theory approach to quantum information
Abstract: We apply the formalism of quantum field theory and Euclidean space-time path integral to investigate a class of quantum information problems. In particular, we investigate quantum many-body systems under weak-measurement and decoherence. The Euclidean space-time path integral allows us to map this problem to a quantum field theory with (temporal) boundary or defects. We therefore investigate two types of quantum many-body systems with nontrivial boundary physics: quantum critical points, and states with nontrivial topology, such as Chern insulator and symmetry protected topological states. For example, we demonstrate that a Wilson-Fisher quantum critical point can be driven into an “extraordinary-log” phase after weak-measurement. Another example is that, we argue that a system with higher form symmetry may be driven to a self-dual phase transition under weak measurement.

Moduli of vector bundles on curve and semiorthogonal decomposition
2023-09-29 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Kai Xu (CMSA)
Title: Moduli of vector bundles on curve and semiorthogonal decomposition
Abstract: In this talk we construct semiorthogonal decompositions of moduli of vector bundles on a curve into its symmetric powers. The essential ingredients in the proof include Borel-Weil-Bott theory for loop groups, derived Schur-Weyl duality for current groups and derived Θ-stratification.

Topological modular forms and heretoric string theory
2023-09-29 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Special Seminar

Speaker: Mayuko Yamashita, Kyoto University

Title: Topological modular forms and heretoric string theory
Abstract: In this talk I will explain my works with Y. Tachikawa to study anomaly in heterotic string theory via homotopy theory, especially the theory of Topological Modular Forms (TMF). TMF is an E-infinity ring spectrum which is conjectured by Stolz-Teichner to classify two-dimensional supersymmetric quantum field theories in physics. In the previous work (https://arxiv.org/abs/2108.13542), we proved the vanishing of anomalies in heterotic string theory mathematically by using TMF.
Furthermore, we have a recent update (https://arxiv.org/abs/2305.06196) on the previous work. Because of the vanishing result, we can consider a secondary transformation of spectra, which is shown to coincide with the Anderson self-duality morphism of TMF. This allows us to detect subtle torsion phenomena in TMF by differential-geometric ways, and leads us to new conjectures on the relation between VOAs and TMF.

Motivic decomposition of moduli space from brane dynamics
2023-10-02 10:30 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Algebraic Geometry in String Theory Seminar

Pre-talk Speaker: Kai Xu (CMSA): 10:00-10:30 am

Speaker: Kai Xu (CMSA)
Title: Motivic decomposition of moduli space from brane dynamics
Abstract: Supersymmetric gauge theories encode deep structures in algebraic geometry, and geometric engineering gives a powerful way to understand the underlying structures by string/M theory. In this talk we will see how the dynamics of M5 branes tell us about the motivic and semiorthogonal decompositions of moduli of bundles on curves.

Gravitational Instantons
2023-10-02 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
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 moduli space of gravitational instantons.

A Smooth Horizon without a Smooth Horizon
2023-10-03 11:00 - 12:00 | MA
General Relativity Seminar
Speaker: Chethan Krishnan (IISc Bangalore)
Title: A Smooth Horizon without a Smooth Horizon
Abstract: I will talk about some work that is about to appear, where we note one precise way in which the stretched horizon can simulate a smooth horizon. I will also make an effort to put things in some perspective (brickwalls, fuzzballs, Type I algebras,…)

CMSA Q and A Seminar 10/3/2023
2023-10-03 12:30 - 13:30 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q and A Seminar
Speakers: Dan Freed (Harvard Math & CMSA) and Dan Berwick-Evans (University of Illinois at Urbana-Champaign)

Topics:
Dan Freed: What is framing anomaly? How is it different from other anomalies?
Dan Berwick-Evans: What is Atiyah-Singer index theorem?

Dipolar and modulated symmetry protected topological phases
2023-10-04 10:30 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Topological Quantum Matter Seminar
Speaker: Ho Tat Lam, MIT
Title: Dipolar and modulated symmetry protected topological phases
Abstract: Modulated symmetries are symmetries whose symmetry generators exhibit spatial modulations. We will discuss one-dimensional symmetry protected topological (SPT) phases protected by modulated symmetries. We will present a simple recipe for constructing modulated SPT models by generalizing the concept of decorated domain walls. We will then focus on the simplest modulated SPT protected by dipolar symmetries, classify them using matrix product states and construct their response field theories using twisted finite tensor gauge theories.

Random matrices and large deviations
2023-10-06 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Benjamin McKenna
Title: Random matrices and large deviations
Abstract: We give a generalist overview of random matrices and their (a)typical behaviors. In recent years, classical results have been complemented by a variety of new ones, in both the math and physics literatures, whose proofs leverage connections with special integrals over matrix groups. Some of these models exhibit interesting transition points, whose motivating relationships to eigenvector (de)localization are not yet fully understood. Based on joint work with Jonathan Husson.

Tidal Squeezing of Black Holes
2023-10-10 11:00 - 12:00 | MA
General Relativity Seminar
Speaker: Maria Rodriguez (Utah)
Title: Tidal Squeezing of Black Holes
Abstract: Recent developments indicate that Kerr black holes do not deform when perturbed by a static external gravitational field. Relying on hidden symmetries, compelling progress has been achieved to explain that Love numbers for Kerr black holes vanish. How does the phenomenon of tidal squeezing manifest in broader contexts? An elementary presentation of dynamical tidal squeezing of Kerr black holes will be given.

CMSA Q and A Seminar 10/10/23
2023-10-10 12:30 - 13:30 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q and A Seminar
Speakers: Dan Freed (Harvard Math and CMSA) and Sunghyuk Park (CMSA)
Topics:
Dan Freed: What is Dijkgraaf-Witten theory?
Sunghyuk Park: What happened at the Clay Math Institute Workshop?

LeanDojo: Theorem Proving with Retrieval-Augmented Language Models
2023-10-11 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
New Technologies in Mathematics Seminar
Speaker: Alex Gu, MIT Dept. of EE&CS
Title: LeanDojo: Theorem Proving with Retrieval-Augmented Language Models
Abstract: Large language models (LLMs) have shown promise in proving formal theorems using proof assistants such as Lean. However, existing methods are difficult to reproduce or build on, due to private code, data, and large compute requirements. This has created substantial barriers to research on machine learning methods for theorem proving. We introduce LeanDojo: an open-source Lean playground consisting of toolkits, data, models, and benchmarks. LeanDojo extracts data from Lean and enables interaction with the proof environment programmatically. It contains fine-grained annotations of premises in proofs, providing valuable data for premise selection: a key bottleneck in theorem proving. Using this data, we develop ReProver (Retrieval-Augmented Prover): the first LLM-based prover that is augmented with retrieval for selecting premises from a vast math library. It is inexpensive and needs only one GPU week of training. Our retriever leverages LeanDojo’s program analysis capability to identify accessible premises and hard negative examples, which makes retrieval much more effective. Furthermore, we construct a new benchmark consisting of 96,962 theorems and proofs extracted from Lean’s math library. It features a challenging data split requiring the prover to generalize to theorems relying on novel premises that are never used in training. We use this benchmark for training and evaluation, and experimental results demonstrate the effectiveness of ReProver over non-retrieval baselines and GPT-4. We thus provide the first set of open-source LLM-based theorem provers without any proprietary datasets and release it under a permissive MIT license to facilitate further research.

Non-invertible symmetries, leptons, quarks, and why multiple generations
2023-10-11 16:30 - 18:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter Seminar
Speaker: Seth Koren (Notre Dame)
Title: Non-invertible symmetries, leptons, quarks, and why multiple generations
Abstract: Generalized global symmetries are present in theories of particle physics, and understanding their structure can give insight into these theories and UV completions thereof. After discussing the generalized symmetries of the Standard Model, we will go Beyond and show that the identification of a non-invertible symmetry of Z’ models of L_µ – L_τ reveals the existence of non-Abelian horizontal gauge theories which naturally produce exponentially small Dirac neutrino masses. Next we will uncover a subtler non-invertible symmetry in horizontal gauge theories of the quark sector which will lead us to a massless down-type quarks solution to strong CP in color-flavor unification. Intriguingly, this theory works by virtue of the SM having the same numbers of colors and generations.

Contractility, structure formation and fluctuations in active gels, with and without molecular motors
2023-10-12 13:00 - 14:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Active Matter Seminar

Speaker: Fred MacKintosh (Rice University)
Title: Contractility, structure formation and fluctuations in active gels, with and without molecular motors
Abstract: Various processes in living cells depend on contractile forces that are often generated by myosin motors in concert with polar actin filaments. A textbook example of this is the actomyosin contractile ring that forms during cell division. Recent evidence, however, has begun to suggest alternate or redundant mechanisms that do not depend on myosin. Experiments on simplified, reconstituted systems also point to contractility and structure formation in disordered, apolar arrays of filaments. We propose a motor-free mechanism that can generate contraction in biopolymer networks without the need for motors such as myosin or polar filaments such as actin. This mechanism is based on active binding and unbinding of cross-linkers that breaks the principle of detailed balance, together with the asymmetric force-extension response of semiflexible biopolymers. We discuss the resulting force-velocity relation and other implications of this, as well as possible evidence for non-motor force generation.

On the Breakdown of Einstein's Gravity
2023-10-13 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Puskar Mondal (CMSA)
Title: On the Breakdown of Einstein’s Gravity
Abstract: It is important to understand under which conditions, the solutions of non-linear hyperbolic PDEs break down in finite time. In the context of Einstein’s gravity, this is very closely tied to naked singularity formation and Penrose’s weak cosmic censorship conjecture. In this talk, I will give sharp estimates on the relevant geometric entities that allow one to continue the solutions of Einstein’s equations indefinitely in the future in a ‘time’ direction without forming a naked singularity.

Moduli of boundary polarized Calabi-Yau pairs
2023-10-16 10:00 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Algebraic Geometry in String Theory Seminar
Pre-talk Speaker: Rosie Shen (Harvard): 10:00-10:30 am
Pre-talk Title: Introduction to the singularities of the MMP

Speaker: Dori Bejleri (Harvard Math & CMSA)
Title: Moduli of boundary polarized Calabi-Yau pairs
Abstract: The theories of KSBA stability and K-stability furnish compact moduli spaces of general type pairs and Fano pairs respectively. However, much less is known about the moduli theory of Calabi-Yau pairs. In this talk I will present an approach to constructing a moduli space of Calabi-Yau pairs which should interpolate between KSBA and K-stable moduli via wall-crossing. I will explain how this approach can be used to construct projective moduli spaces of plane curve pairs. This is based on joint work with K. Ascher, H. Blum, K. DeVleming, G. Inchiostro, Y. Liu, X. Wang.

Breaking ergodicity: quantum scars and regular eigenstates
2023-10-16 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Topological Quantum Matter Seminar
Speaker: Ceren Dag, Harvard
Title: Breaking ergodicity: quantum scars and regular eigenstates
Abstract: Quantum many-body scars (QMBS) consist of a few low-entropy eigenstates in an otherwise chaotic many-body spectrum and can weakly break ergodicity resulting in robust oscillatory dynamics. The notion of QMBS follows the original single-particle scars introduced within the context of quantum billiards, where scarring manifests in the form of a quantum eigenstate concentrating around an underlying classical unstable periodic orbit (UPO). A direct connection between these notions remains an outstanding problem. Here, we study a many-body spinor condensate that, owing to its collective interactions, is amenable to the diagnostics of scars. We characterize the system’s rich dynamics, spectrum, and phase space, consisting of both regular and chaotic states. The former are low in entropy, violate the Eigenstate Thermalization Hypothesis (ETH), and can be traced back to integrable effective Hamiltonians, whereas most of the latter are scarred by the underlying semiclassical UPOs, while satisfying ETH. We outline an experimental proposal to probe our theory in trapped spin-1 Bose-Einstein condensates. If time permits, I will also mention our latest efforts in introducing spatial dimension to this model with a true semiclassical limit, and how quantum scars persist to exist in a many-body system. Reference: arXiv 2306.10411, in peer review.

An exploration of infinite games—infinite Wordle and the Mastermind numbers
2023-10-16 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
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 set theory, a kind of infinitary information theory. Some assertions about the minimal size of winning sets of guesses, for example, turn out to be independent of the Zermelo-Fraenkel ZFC axioms of set theory. Some questions remain open.

Composite fermions and the fractional quantum anomalous Hall effect
2023-10-18 12:30 - 13:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Topological Quantum Matter Seminar
Speaker: Hart Goldman, University of Chicago
Title: Composite fermions and the fractional quantum anomalous Hall effect
Abstract: Recent experiments have revealed evidence for fractional quantum anomalous Hall (FQAH) states at zero magnetic field in a growing number of moire materials. In this talk, I will argue that a composite fermion description, already a unifying framework for the phenomenology of 2d electron gases at high magnetic fields, provides a similarly powerful perspective in this new zero-field context. In particular, a central prediction of the composite fermion framework is a non-Fermi liquid metal of composite fermions at even-denominator fillings. To this end, I will present exact diagonalization evidence for such composite Fermi liquid states at zero magnetic field in twisted MoTe2 bilayers, at fillings n = 1/2 and n = 3/4. Dubbing these states anomalous composite Fermi liquids (ACFLs), I will argue that they play a central organizing role in the FQAH phase diagram. I will also develop a long wavelength theory for this ACFL state, which offers concrete experimental predictions that I will discuss in relation to current measurements. For example, upon doping the composite Fermi sea, one obtains a Jain sequence of FQAH states consistent with those observed experimentally, as well as a new type of commensurability oscillations originating from the superlattice potential intrinsic to the system. Finally, I will discuss opportunities for new physics not possible in quantum Hall systems at finite magnetic field.

Physics of Language Models: Knowledge Storage, Extraction, and Manipulation
2023-10-18 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
New Technologies in Mathematics Seminar
Speaker: Yuanzhi Li, CMU Dept. of Machine Learning and Microsoft Research
Title: Physics of Language Models: Knowledge Storage, Extraction, and Manipulation
Abstract: Large language models (LLMs) can memorize a massive amount of knowledge during pre-training, but can they effectively use this knowledge at inference time? In this work, we show several striking results about this question. Using a synthetic biography dataset, we first show that even if an LLM achieves zero training loss when pretraining on the biography dataset, it sometimes can not be finetuned to answer questions as simple as “What is the birthday of XXX” at all. We show that sufficient data augmentation during pre-training, such as rewriting the same biography multiple times or simply using the person’s full name in every sentence, can mitigate this issue. Using linear probing, we unravel that such augmentation forces the model to store knowledge about a person in the token embeddings of their name rather than other locations.
We then show that LLMs are very bad at manipulating knowledge they learn during pre-training unless a chain of thought is used at inference time. We pretrained an LLM on the synthetic biography dataset, so that it could answer “What is the birthday of XXX” with 100% accuracy. Even so, it could not be further fine-tuned to answer questions like “Is the birthday of XXX even or odd?” directly. Even using Chain of Thought training data only helps the model answer such questions in a CoT manner, not directly.
We will also discuss preliminary progress on understanding the scaling law of how large a language model needs to be to store X pieces of knowledge and extract them efficiently. For example, is a 1B parameter language model enough to store all the knowledge of a middle school student?

Geometry of the doubly periodic Aztec dimer model
2023-10-18 15:30 - 16:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Probability Seminar
Speaker: Tomas Berggren (MIT)
Title: Geometry of the doubly periodic Aztec dimer model
Abstract: Random dimer models (or equivalently tiling models) have been a subject of extensive research in mathematics and physics for several decades. In this talk, we will discuss the doubly periodic Aztec diamond dimer model of growing size, with arbitrary periodicity and only mild conditions on the edge weights. In this limit, we see three types of macroscopic regions — known as rough, smooth and frozen regions. We will discuss how the geometry of the arctic curves, the boundary of these regions, can be described in terms of an associated amoeba and an action function. In particular, we determine the number of frozen and smooth regions and the number of cusps on the arctic curves. We will also discuss the convergence of local fluctuations to the appropriate translation-invariant Gibbs measures. Joint work with Alexei Borodin.

CMSA Director Dan Freed featured in Harvard Gazette
2023-10-20 09:00 | MA
CMSA Director Dan Freed featured in Harvard Gazette
“Center welcomes new director, a Harvard alum who will explore ‘beautiful, deep’ interactions between mathematics, science.”
Link to article.
Story by Anne J. Manning, Harvard Staff Writer
Photo courtesy of Niles Singer, Harvard University.

Black Holes as Quantum Systems
2023-10-20 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Daniel Kapec (CMSA)
Title: Black Holes as Quantum Systems
Abstract: To an outside observer, a black hole appears to be an ordinary quantum mechanical system with finite entropy and highly chaotic internal dynamics. Nevertheless, the low-temperature thermodynamics of the Kerr black hole presents several puzzles. For instance, the leading order semiclassical approximation to the black hole density of states predicts a surprisingly large ground state degeneracy, while poorly understood quantum corrections are known to become increasingly important at low temperatures. I will review the modern picture of black holes as quantum systems and then discuss a recent result on the leading correction to the low-temperature thermodynamics of the Kerr black hole that resolves many of the old puzzles.

Gauged Linear Sigma Models and Cohomological Field Theories
2023-10-23 10:30 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Algebraic Geometry in String Theory Seminar

Speaker: David Favero, University of Minnesota

Title: Gauged Linear Sigma Models and Cohomological Field Theories
Abstract: This talk is dedicated to the memory of my friend and collaborator Bumsig Kim and based on joint work with Ciocan-Fontanine-Guere-Kim-Shoemaker. Gauged Linear Sigma Models (GLSMs) serve as a means of interpolating between Kahler geometry and singularity theory. In enumerative geometry, they should specialize to both Gromov-Witten and Fan-Jarvis-Ruan-Witten theory. In joint work with Bumsig Kim (see arXiv:2006.12182), we constructed such enumerative invariants for GLSMs. Furthermore, we proved that these invariants form a Cohomological Field Theory. In this lecture, I will describe GLSMs and Cohomological Field Theories, review the history of their development in enumerative geometry, and discuss the construction of these general invariants. Briefly, the invariants are obtained by forming the analogue of a virtual fundamental class which lives in the twisted Hodge complex over a certain “moduli space of maps to the GLSM”. This virtual fundamental class roughly comes as the Atiyah class of a “virtual matrix factorization” associated to the GLSM data.

On Provable Copyright Protection for Generative Model
2023-10-23 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
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 algorithms, which efficiently modify the original generative model learning algorithm in a black box manner, that output generative models with strong bounds on the probability of sampling protected content. Furthermore, we provide promising experiments for both language (transformers) and image (diffusion) generative models, showing minimal degradation in output quality while ensuring strong protections against sampling protected content.
Joint work with Nikhil Vyas and Sham Kakade. Paper appeared in ICML 2023 and is on https://arxiv.org/abs/2302.10870
