CMSA

Residues and homotopy Lie algebras
2025-05-08 10:00 - 11:00 (America/New_York) | Virtual
Mathematical Physics and Algebraic Geometry Seminar
Speaker: Zhenping Gui, Shanghai Institute for Mathematics and Interdisciplinary Sciences
Title: Residues and homotopy Lie algebras
Abstract: I will introduce the notion of a chiral operad for any compact Riemann surface. This operad consists of compositions of residue operations, which give rise to the Chevalley-Cousin complex and lead to the definition of chiral homology (derived conformal blocks). I will explain how to use this machinery to rigorously define certain Feynman integrals in 2D chiral CFTs. Subsequently, I will present a polysimplicial construction of a series of chain models for the configuration space of points in an affine space and study residue operations. These residue operations can be described by a homotopy Lie algebra structure, and the latter defines a higher-dimensional analog of the Chevalley-Cousin complex. This is based on joint work in progress with Charles Young and Laura Felder.

Geometry and Quantum Theory Seminar
2025-05-06 16:15 - 18:15 | Science Center 507, 1 Oxford Street, Cambridge, 02138

Thinking Outside the Ballot Box
2025-05-05 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Ariel Procaccia, Harvard University
Title: Thinking Outside the Ballot Box
Abstract: How should one design unprecedented democratic processes capable of handling enormous sets of alternatives like all possible policies, bills, or statements? I argue that this challenge can be addressed through a framework called generative social choice, which fuses the rigor of social choice theory with the flexibility and power of large language models. I then explore an application of generative social choice to the problem of identifying a proportionally representative slate of opinion statements. This includes a discussion of desired properties, an algorithm that provably achieves them, an implementation using GPT, and insights from an end-to-end pilot. By providing guarantees, generative social choice could alleviate concerns about AI-driven democratic innovation and help unlock its potential.

Quantum Field Theory and Physical Mathematics
2025-05-05 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar

Incentives for data sharing in federated learning
2025-05-02 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Han Shao, Harvard CMSA
Title: Incentives for data sharing in federated learning
Abstract: Federated learning has recently emerged as a powerful approach for enabling collaboration across large populations of learning agents. However, agents may have incentives to defect from the collaboration—that is, to withdraw or contribute less data than expected—due to the costs of data curation and privacy concerns. This raises several key questions: What happens when agents defect, and how can we prevent such defections?

From superspace to twisted supergravity
2025-05-01 10:00 - 11:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Mathematical Physics and Algebraic Geometry Seminar
Speaker: Fabian Hahner, University of Washington
Title: From superspace to twisted supergravity
Abstract: In this talk, I will present a geometric perspective on the pure spinor superfield formalism, which proves fruitful for studying twisted supergravity. For eleven-dimensional supergravity, we use this technique to construct the full interacting theory together with all its twists in a uniform and geometric way as homotopy Poisson–Chern–Simons theories. In addition to simplifying the computation of twists immensely, this also provides fresh insights into the supergeometric origin of supergravity. Building on these ideas, we further construct local dg Lie algebras that recover conformal supergravity multiplets and their twists in terms of a geometric moduli problem on superspace.

Algebraic approach to the bow construction
2025-04-29 16:15 - 18:15 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speakers: Anadil Saeed Rao (Northeastern) and Vasily Krylov (CMSA/Harvard)
Title: Algebraic approach to the bow construction
Abstract: Anadil will finish his part of the talk. Vasily will then explain how to understand moduli spaces of instantons on R^4, monopoles on R^3, and instantons on Taub-NUT spaces algebraically as so-called bow varieties. We will see how affine type A Nakajima quiver varieties and Slodowy slices arise as special cases of bow varieties. Time permitting, we will also discuss applications to 3D mirror symmetry and Coulomb branches.

Bass-Note Spectra of locally uniform geometries
2025-04-28 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Peter Sarnak, IAS & Princeton University
Title: Bass-Note Spectra of locally uniform geometries
Abstract: We formulate and report on the problem of the Bass-Note Spectrum of an invariant operator as one varies over locally uniform geometries. In the Euclidean setting this recasts classical problems of Mahler from the geometry of numbers in a new light. For certain operators homogeneous dynamics can be used decisively. In the non-Euclidean setting of hyperbolic manifolds we review some recent developments using the conformal bootstrap method and of random covers to study the Bass-Note spectra. We highlight the theme and impact of rigidity.

Adversarial KA
2025-04-25 03:00 - 16:00 | Virtual
Freedman CMSA Seminar
Speaker: Slava Dzhenzher, MIPT
Title: Adversarial KA
Abstract: Regarding the representation theorem of Kolmogorov and Arnold (KA) as an algorithm for representing or «expressing» functions, we test its robustness by analyzing its ability to withstand adversarial attacks. We find KA to be robust to countable collections of continuous adversaries, but unearth a question about the equi-continuity of the outer functions that, so far, obstructs taking limits and defeating continuous groups of adversaries. This question on the regularity of the outer functions is relevant to the debate over the applicability of KA to the general theory of NNs. Based on https://arxiv.org/abs/2504.05255

Mass gap in AdS space
2025-04-24 10:00 - 11:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Mathematical Physics and Algebraic Geometry Seminar
Speaker: Ziming Ji, Northeastern University
Title: Mass gap in AdS space
Abstract: AdS space can be used as an IR regulator of QFT. The asymptotic conformal boundary in AdS space provides rich, unique observables. We study asymptotic free theories in two-dimensional AdS space. By changing the AdS curvature scale Lambda L, we observe boundary signals of quantum phase transitions where mass gaps are dynamically generated in the bulk. We also utilize supersymmetry to study gauge theories in AdS4. We argue a connection between the AdS partition function and the prepotential and use the F-maximization of the Nekrasov partition function to study supersymmetric boundary conditions and its connection to the Seiberg-Witten theory.

Machine learning for analytic calculations in theoretical physics
2025-04-23 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
New Technologies in Mathematics Seminar
Speaker: Matthias Wilhelm (University of Southern Denmark)
Title: Machine learning for analytic calculations in theoretical physics
Abstract: In this talk, we will present recent progress on applying machine-learning techniques to improve calculations in theoretical physics, in which we desire exact and analytic results. One example are so-called integration-by-parts reductions of Feynman integrals, which pose a frequent bottleneck in state-of-the-art calculations in theoretical particle and gravitational-wave physics. These reductions rely on heuristic approaches for selecting a finite set of linear equations to solve, and the quality of the heuristics heavily influences the performance. In this talk, we investigate the use of machine-learning techniques to find improved heuristics. We use funsearch, a genetic programming variant based on code generation by a Large Language Model, in order to explore possible approaches, then use strongly typed genetic programming to zero in on useful solutions. Both approaches manage to re-discover the state-of-the-art heuristics recently incorporated into integration-by-parts solvers, and in one example find a small advance on this state of the art.

CMSA Q&A Seminar: Alexei Borodin
2025-04-23 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q&A Seminar
Speaker: Alexei Borodin (MIT)
Topic: Connections between physics and probability

Classifying Space for Phases of Matrix Product States
2025-04-22 16:15 - 18:15 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speakers: Bryan Wang Peng Jun (Harvard) and Bowen Yang (CMSA)
Title: Classifying Space for Phases of Matrix Product States
Abstract: In this talk we will introduce recent work of Beaudry-Hermele-Pflaum-Qi-Spiegel-Stephen (arXiv:2501.14241), on constructing a classifying space for phases of matrix product states (MPS).

Hyperbolic equations in a double null gauge
2025-04-22 11:00 - 12:00 | CMSA G102, 20 Garden Street, Cambridge, MA, 02138
General Relativity Seminar
Speaker: Christopher Stith, University of Michigan
Title: Hyperbolic equations in a double null gauge
Abstract: The hyperbolic nature of the Einstein equations is well-known and has been used in many different contexts. More recently, the double null gauge has proven to be a powerful tool for quantitative analysis of the Einstein equations. It has the advantage of reducing the equations for many dynamical quantities to ODEs along null curves, and the Bianchi equations to a first-order hyperbolic system. The double null gauge has been used extensively and to great effect in analyzing the structure of spacetime for many purposes, including (for instance) stability problems and trapped surface formation. However, the local existence problem for the Einstein equations in a double null gauge has never been treated in full in its own right. In this talk, we discuss how to formulate a general procedure for solving the linearized problem, namely, the local existence theory for systems of first-order hyperbolic equations in a double null gauge.

Modeling the emergence of complex cortical structure from simple precursors in the brain: maps, hierarchies, and modules
2025-04-21 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Ila Fiete, MIT
Title: Modeling the emergence of complex cortical structure from simple precursors in the brain: maps, hierarchies, and modules
Abstract: Modular and hierarchical structures are ubiquitous in the brain. Two distinct hypotheses for such morphogenesis involve genetic specification (the positional information hypothesis) or spontaneous structure emergence from symmetry breaking (the pattern formation hypothesis). Indeed, there is rich evidence supporting both hypotheses in different systems, and more recently evidence that both systems might interact, for instance with genetic specification providing an initial but relatively low-information scaffold of positional guidance and pattern formation constructing sharper structures by bootstrapping from this guidance. In this talk, I will consider the emergence of two systems in the brain: the visual processing hierarchy with topographic structure, and a modular cognitive circuit consisting of functionally independent grid cell networks that compute spatial location from velocity cues as animals move and navigate the world. I will describe how simple activity-driven growth and competition rules can lead to the emergence of topographically ordered sensory processing hierarchies, and how genetically specified smooth gradients with purely local recurrent interactions on two scales can lead to global module emergence. In sum, simple growth rules, local interactions and smooth gradients can interact to produce rich emergent order on multiple scales in the form of maps, modules, and hierarchies, with predictions that bridge scales from genes to connectivity to function.

Member Seminar
2025-04-18 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Han Shao

Fifth Annual Yip Lecture | Scott Aaronson (UT Austin): How Much Math Is Knowable?
2025-04-17 16:00 - 17:00 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
Speaker: Scott Aaronson, Department of Computer Science, University of Texas, Austin
Scott Aaronson is the founding director at the Quantum Information Center at the University of Texas at Austin.
Date: April 17, 2025
Time: 4:00-5:00 pm ET (Reception following in the Math Common Room)
Location: Harvard Science Center Hall A

Title: How Much Math Is Knowable?
Abstract: Theoretical computer science has over the years sought more and more refined answers to the question of which mathematical truths are knowable by finite beings like ourselves, bounded in time and space and subject to physical laws. I’ll tell a story that starts with Gödel’s Incompleteness Theorem and Turing’s discovery of uncomputability. I’ll then introduce the spectacular Busy Beaver function, which grows faster than any computable function. Work by me and Yedidia, along with recent improvements by O’Rear and Riebel, has shown that the value of BB(745) is independent of the axioms of set theory; on the other end, an international collaboration proved last year that BB(5) = 47,176,870. I’ll speculate on whether BB(6) will ever be known, by us or our AI successors. I’ll next discuss the P!=NP conjecture and what it does and doesn’t mean for the limits of machine intelligence. As my own specialty is quantum computing, I’ll summarize what we know about how scalable quantum computers, assuming we get them, will expand the boundary of what’s mathematically knowable. I’ll end by talking about hypothetical models even beyond quantum computers, which might expand the boundary of knowability still further, if one is able (for example) to jump into a black hole, create a closed timelike curve, or project oneself onto the holographic boundary of the universe.

The Yip Lecture takes place thanks to the support of Dr. Shing-Yiu Yip.

The previous Yip Lecture featured Josh Tenenbaum (MIT) who spoke on How to grow a mind from a brain: From guessing and betting to thinking and talking

CMSA Q&A Seminar: Noah Golowich
2025-04-16 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q&A Seminar
Speaker: Noah Golowich (MIT)
Topic: What is length generalization in large language models?

Instantons on Taub-NUT space and Bow Construction
2025-04-15 16:15 - 18:15 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speaker: Anadil Saeed Rao, Northeastern University
Title: Instantons on Taub-NUT space and Bow Construction
Abstract: In this talk I will discuss Yang-Mills Instantons in a very special geometric setting: the Taub-NUT space, which itself is a Gravitational Instanton. In the first part of the talk I will review the essentials of gravitational instanton theory from the differential geometry/physics perspective and discuss the geometry of Taub-NUT space in detail. Then I will review the essentials of the ADHM-Nahm construction which describe Instantons and Monopoles in Euclidean R^4 and R^3 respectively. In the second part of my talk I will extend the ADHM-Nahm description to Instantons on Taub-NUT space and show how the ADHM-Nahm data may be presented in terms of combinatorial diagrams called Bows and their representations.

Positive mass theorem for ALE(AE) and ALF(AF) Toric 4-Manifolds
2025-04-15 11:00 - 12:00 | CMSA G102, 20 Garden Street, Cambridge, MA, 02138
General Relativity Seminar
Speaker: Aghil Alaee, Clark University
Title: Positive mass theorem for ALE(AE) and ALF(AF) Toric 4-Manifolds
Abstract: One of the fundamental conjectures in mathematical relativity is the positivity of total mass (if it is defined!) for complete non-compact Riemannian manifolds assuming appropriate lower bounds on scalar curvature. This conjecture has been proved for AE manifolds using several techniques, starting with the celebrated results of Schoen-Yau and Witten. There are counter-examples to this conjecture in the AF, ALF, and ALE cases. In this talk, we will refine this conjecture and prove it for toric 4-manifolds. The proof is robust and can be extended to higher dimensions if additional assumptions are added. This is a joint work with Marcus Khuri and Hari Kunduri.

Quantum K-theory at roots of unity
2025-04-14 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Andrey Smirnov, University of North Carolina at Chapel Hill
Title: Quantum K-theory at roots of unity
Abstract: In this talk, I will discuss a version of quantum K-theory introduced by A.Okounkov, which can be defined through quasimap counts. In this framework, the quantum K-theory ring is obtained as a specialization of the equivariant quasimap count at $q=1$, where $q$ is the equivariant parameter associated with the torus action on the source of the quasimaps. A related, but less explored, structure emerges when $q$ is specialized at the roots of unity. I will outline the key ideas behind this construction and its implications. As an application, I’ll also describe the spectrum of $p$-curvature for the quantum connection, which offers a new proof of a recent result by P.Etingof and A.Varchenko. This talk is based on joint work with P. Koroteev.

The Extended Vertex Algebra of 4d N = 2 SCFTs and their Higher Products
2025-04-14 15:00 - 16:00 | Hybrid – G10
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Mitch Weaver, KAIST
Title: The Extended Vertex Algebra of 4d N = 2 SCFTs and their Higher Products
Abstract: Every 4d N=2 superconformal field theory contains a BPS protected sub-algebra of local operators that has the structure of a vertex operator algebra (VOA). This VOA is identified by passing to the cohomology of a nilpotent supercharge, T, whose local operator cohomology is represented by twist-translated Schur operators with support in a Euclidean two-plane. When working in 4d Minkowski space, this cohomology admits a web of three extended operators (called descent operators) that are constructed from each Schur operator in the VOA, have worldvolume support in the Lorentzian two-plane that is transverse to the Euclidean plane supporting the VOA, and behave as point-like insertions in the plane of the VOA, i.e. as new chiral operators. The combined result is the extended vertex algebra (EVA): a universal extension of the VOA that canonically has the structure of a quasi-VOA, i.e. a vertex algebra (VA) with no conformal vector but which still possesses a representation of sl(2). After reviewing the VOA of Schur operators, I will explain the origin of the descent operators and present the OPEs for a subsector of the EVA in the free hyper SCFT.
Time permitting, I will also describe the construction and basic properties of a set of higher products that are associated to each descent operator. Such products function as higher dimensional versions of 2d chiral algebra λ-brackets, i.e. positive mode operators: they are defined on the EVA and map to the operators appearing in the singular terms of OPEs involving descent operators. Their existence offers a route toward sl(2) symmetry enhancement of the EVA and suggests the latter has structural properties that are common to the higher dimensional chiral algebras describing the minimal twists of 3d N = 2 and 4d N = 1 SQFTs. This talk is based on [2211.04410] and forthcoming work.

Homological Invariants in Translation-Invariant Pauli Stabilizer Codes
2025-04-11 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Bowen Yang
Title: Homological Invariants in Translation-Invariant Pauli Stabilizer Codes
Abstract: Pauli stabilizer codes serve as foundational models in quantum error correction and the study of exotic quantum phases. In this talk, we explore the application of homological methods to translationally invariant Pauli stabilizer codes with qudits of varying dimensions. We introduce a series of invariants, termed charge modules, and delve into their properties and physical interpretations. A key focus is on codes whose charge modules exhibit zero Krull dimension, a condition indicative of the mobility of excitations. Notably, we demonstrate that this condition is universally met in two-dimensional codes with a unique ground state in infinite volume, extending prior findings beyond the realm of uniform, prime qudit dimensions. For systems where all excitations are mobile, we establish the existence of p-dimensional excitations and associated (D−p−1)-form symmetries corresponding to each element of the p-th charge module. Additionally, we define a braiding pairing between charge modules in complementary degrees.

3d Mirror Symmetry is 2d Mirror Symmetry
2025-04-10 10:00 - 11:00 | Virtual
Mathematical Physics and Algebraic Geometry Seminar
Speaker: Ki Fung Chan (Chinese University of Hong Kong)
Title: 3d Mirror Symmetry is 2d Mirror Symmetry
Abstract: We introduce an approach to studying 3d mirror symmetry via 2d mirror symmetry. The main observations are: (1) 3d brane transforms are given by SYZ-type transforms; (2) the exchange of symplectic and complex structures in 2d mirror symmetry induces the exchange of Kähler and equivariant parameters in 3d mirror symmetry; and (3) the functionalities of 2d mirror symmetry control the gluing of 3d mirrors. If time permits, we will also discuss some applications to 2d mirror symmetry at the end of the talk. Joint works with Naichung Conan Leung.

Can Transformers Do Enumerative Geometry?
2025-04-09 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
New Technologies in Mathematics Seminar
Speaker: Baran Hashemi, Technical University of Munich
Title: Can Transformers Do Enumerative Geometry?
Abstract: How can Transformers model and learn enumerative geometry? What is a systematic procedure for using Transformers in abductive knowledge discovery within a mathematician-machine collaboration? In this work, we introduce a Neural Enumerative Reasoning model for computation of ψ-class intersection numbers on the moduli space of curves. By reformulating the problem as a continuous optimization task, we compute intersection numbers across a wide value range from 10e-45 to 10e45. To capture the recursive nature inherent in these intersection numbers, we propose the Dynamic Range Activator (DRA), a new activation function that enhances the Transformer’s ability to model recursive patterns and handle severe heteroscedasticity. Given precision requirements for computing the intersections, we quantify the uncertainty of the predictions using Conformal Prediction with a dynamic sliding window adaptive to the partitions of equivalent number of marked points. Beyond simply computing intersection numbers, we explore the enumerative “world-model” of Transformers. Our interpretability analysis reveals that the network is implicitly modeling the Virasoro constraints in a purely data-driven manner. Moreover, through abductive hypothesis testing, probing, and causal inference, we uncover evidence of an emergent internal representation of the large-genus asymptotic of ψ-class intersection numbers. This opens up new possibilities in inferring asymptotic closed-form expressions directly from limited amount of data.
This talk is based on https://openreview.net/pdf?id=4X9RpKH4Ls.

CMSA Q&A Seminar: Eric Maskin
2025-04-09 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q&A Seminar
Speaker: Eric Maskin, Harvard University
Topic: The Mathematics of Voting

CMSA/Tsinghua Math-Science Literature Lecture: Scott Sheffield (MIT): Yang-Mills theory and random surfaces
2025-04-08 09:00 - 10:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA/Tsinghua Math-Science Literature Lecture
Date: April 8, 2025
Time: 9:00 – 10:30 am ET
Location: CMSA G10, 20 Garden Street, Cambridge MA & via Zoom
Speaker: Scott Sheffield (MIT)
Title: Yang-Mills theory and random surfaces
Abstract: The Clay Institute famously offered one million dollars to anyone who could mathematically construct and understand a certain continuum version of “Yang-Mills gauge theory.” This theory is the basis of the standard model of physics, and the heart of the problem is to understand the so-called “Wilson loop expectations.” Following recent work with Sky Cao and Minjae Park, I will explain how the “Wilson loop expectations” in a lattice Yang-Mills model are equivalent to “insertion costs” of loops in a related random-closed-surface-ensemble model. In a sense, these results allow us to convert one famously hard problem into another presumably hard problem. But the new problem is all about random surfaces and random permutations, and it has a lot of relationships with and similarities to other problems we understand (think domino tilings, random planar maps, Young tableaux and symmetric group representation theory, and the Weingarten calculus). It gives us some intuition for *why* certain things should be true like the “area law” or “exponential correlation decay” (what physicists call “quark confinement” or “mass gap”) even if we can’t prove all of them yet.

Beginning in Spring 2020, the CMSA began hosting a lecture series on literature in the mathematical sciences, with a focus on significant developments in mathematics that have influenced the discipline, and the lifetime accomplishments of significant scholars.

3-d Mirror Symmetry
2025-04-07 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Ben Webster, University of Waterloo & Perimeter Institute
Title: 3-d Mirror Symmetry
Abstract: I’ll give an introduction (or update, for those who’ve been introduced) to 3d mirror symmetry from the perspective of a mathematician.

Quantum Field Theory and Physical Mathematics
2025-04-07 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Matthew Yu (Oxford)
Title: A new tangential structure for type IIA string theory
Abstract: The Green-Schwarz anomaly cancellation condition says that the target space of heterotic string theory must come with a string structure for the theory to be consistent. In this talk we discuss a new tangential structure called string^h, first introduced by Devalapurkar, as a spin^c analogue of string. Approximating the correct tangential structure of string theory has many implications, primarily is the Swampland program via the cobordism conjecture of Mcnamara and Vafa. We will show that the spectrum of string^h has the notable property that it orients tmf_1(n), just like how the spectrum of string orients tmf, by the work of Ando-Hopkins-Rezk. Finally we will show that the anomaly condition of the partition function of M-theory, studied by Diaconescu-Moore-Witten is implied by a string^h structure on the target space of type IIA, in parallel to the Green-Schwarz anomaly for heterotic string theory, and discuss applications for anomaly cancellation.

Learning diffusion models in high-dimensions
2025-04-04 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Hugo Cui
Title: Learning diffusion models in high-dimensions
Abstract: We consider the problem of learning a generative model parametrized by a two-layer auto-encoder, and trained with online stochastic gradient descent, to sample from a high-dimensional data distribution with an underlying low-dimensional structure. We provide a tight asymptotic characterization of low-dimensional projections of the resulting generated density, and evidence how mode(l) collapse can arise. On the other hand, we discuss how in a case where the architectural bias is suited to the target density, these simple models can efficiently learn to sample from a binary Gaussian mixture target distribution.
