CMSA

The Extended Vertex Algebra of 4d N = 2 SCFTs and their Higher Products
2025-04-14 15:00 - 16:00 (America/New_York) | 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.

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.

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.

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?

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

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.

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).

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

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.

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

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.

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.

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?

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

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.

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

Asset pricing with heterogeneous agents
2025-05-09 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Sergiy Verstyuk, Harvard CMSA
Title: Asset pricing with heterogeneous agents
Abstract: This talk will introduce the basics of continuous-time finance, discuss important existing theories and models, as well as present some new asset pricing results in a setting with many heterogeneous investors. (Joint work with Puskar Mondal.)

An index for 2d invertible phases of quantum many-body systems
2025-05-12 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Nikita Sopenko, IAS
Title: An index for 2d invertible phases of quantum many-body systems

Factorizations for data analysis
2025-05-12 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Anna Seigal, Harvard University
Title: Factorizations for data analysis
Abstract: We can find structure in data by factoring it into building blocks, which should be interpretable for the context at hand. A classical example is principal component analysis (PCA), which uses the eigendecomposition of the covariance matrix to find axes of variation in a dataset. Starting from PCA, I will discuss matrix and tensor factorizations for data analysis, and the linear and multilinear algebra that underpins their theoretical properties. We will see examples from causal inference, independent component analysis, and dimensionality reduction.

Report on the Perimeter Institute Theory+AI Workshop
2025-05-14 12:00 - 13:00 | CMSA 20 Garden Street Cambridge, Massachusetts 02138 United States
Conference Reports
Speaker: Hugo Cui, Harvard CMSA
Title: Report on the Perimeter Institute Theory+AI Workshop
Abstract: I will give a survey and brief summary of some of the talks given at the Theory+AI Workshop: Theoretical Physics for AI event organized by Perimeter Institute in April, on approaches to machine learning theory inspired from physics.
Link : https://events.perimeterinstitute.ca/event/993/

Echo Chamber: RL Post-training Amplifies Behaviors Learned in Pretraining
2025-05-16 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Samy Jelassi, CMSA
Title: Echo Chamber: RL Post-training Amplifies Behaviors Learned in Pretraining
Abstract: Reinforcement Learning has become a crucial step in training state-of-the-art language models such as DeepSeek-R1 for solving mathematical problems. In this talk, I will first review the mechanisms of Reinforcement Learning fine-tuning. Then, I will present a systematic end-to-end study of RL fine-tuning for mathematical reasoning, training models entirely from scratch on different mixtures of fully open datasets and fine-tuning them with RL. Doing so allows us to investigate the effects of the pretraining data mixture on the behavior of RL, and its interaction with the model size and choices of the algorithm hyperparameters. Our study reveals that RL algorithms consistently converge towards a dominant output distribution, amplifying patterns in the pretraining data. We also find that models of different scales trained on the same data mixture will converge to distinct output distributions, suggesting that there are scale-dependent biases in model generalization.
The second part of the talk is based on a joint work with Rosie Zhao, Alex Meterez, Cengiz Pehlevan, Sham Kakade and Eran Malach: https://arxiv.org/abs/2504.07912

Joint BHI/CMSA Foundation Seminar: The semiclassical energy outflux emerging from a collapsing shell
2025-07-31 11:00 - 12:00 | Black Hole Initiative, 20 Garden Street, Cambridge MA, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Joint BHI/CMSA Foundation Seminar
Location: BHI seminar room
Speaker: Noa Zilberman (Princeton University)
Title: The semiclassical energy outflux emerging from a collapsing shell
Abstract: When a compact object collapses to form a black hole, quantum field theory predicts the emission of an energy outflux to future null infinity, which later relaxes to Hawking radiation. Within the semiclassical framework, we derive a simple, closed form, analytical expression for the energy outflux emitted from a spherical thin null shell collapsing to form a black hole. In particular, this energy outflux vanishes (quadratically in r-2M) as the shell approaches the horizon. This result refutes claims that the Hawking energy outflux originates from the collapsing body, showing instead that it develops in a broad strong-field region. Additionally, this vanishing implies that semiclassical backreaction cannot prevent or significantly affect the classical process of gravitational collapse and horizon formation (as sometimes claimed).

Fukaya category and gauge theory
2025-09-02 16:15 - 18:30 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speaker: Saman Habibi Esfahani, Harvard CMSA
Title: Fukaya category and gauge theory
Abstract: After setting up some background, I will discuss the Fukaya $A_ infty$-category and several instances where it appears in gauge theory, such as in the study of flat connections on Riemann surfaces, holomorphic sections of some hyperkähler bundles, and instantons and holomorphic curves in K3 surfaces. If time permits, I will also outline potential applications of these ideas to the study of 3-manifolds and manifolds with special holonomy.

Higher categories of cobordisms
2025-09-09 16:15 - 18:30 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speaker: Lorenzo Riva
Title: Higher categories of cobordisms
Abstract: I will give a brief introduction to topological field theories from a higher categorical perspective. After saying a few things about higher categories, I will define a family of n-categories of bordisms and talk about their universal properties. I will try to squeeze in the canonical example — representations of the 2-dimensional oriented bordism 2-category are separable symmetric Frobenius algebras — and, time permitting, talk about my current work.

Orientifolds for F-theory on K3 Surfaces
2025-09-15 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Chuck Doran (Alberta/CMSA)
Title: Orientifolds for F-theory on K3 Surfaces
Abstract: Compactification of F-theory on an elliptically fibered K3 surface provides a framework to encode type IIB string theory on elliptic curves, with the Kaehler modulus of the elliptic curve encoded in the complex structure of the elliptic fibers. In work with Malmendier, Mendez-Diez, and Rosenberg we extend that perspective by examining F-theory orientifolds on elliptically fibered K3 surfaces and connecting them to D-brane classifications using real K-theory (KR-theory). The real structures—antiholomorphic involutions—on our K3 surfaces connect the geometry with the physics, providing a natural setting for understanding the interplay between elliptic fibration structures and D-brane classifications in F-theory. We construct Real normal forms with their associated antiholomorphic involutions and use this to make explicit the 2-torsion Brauer twist that relates our normal forms to the Jacobian (Weierstrass normal form) elliptic fibration, including the realization of a representative for the twisting class as an Azumaya algebra. This all connects back to the physics by considering three families of real K3 surfaces whose string limits give the three diﬀerent type IIB theories on P1 with four type I_0^∗ Kodaira fibers.

Topological Manifolds – The First 100 Years
2025-09-15 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Michael Freedman (Harvard CMSA and Logical Intelligence)
Title: Topological Manifolds – The First 100 Years
Abstract: I’ll review manifold topology in the topological category from its start with work of Rado (1925) and Kneser (1926) to the present. Work of Moise, Mazur, Kirby, Siebenmann, Sullivan, Kruskal, and the speaker will be discussed. In my view there is one pressing open question (the A-B slice problem). I will end with some thoughts on putting an AI to work on it.

Moduli spaces of 4d N=2 quantum field theories
2025-09-18 16:00 - 17:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Differential Geometry and Physics Seminar
Speaker: Robert Moscrop, CMSA
Title: Moduli spaces of 4d N=2 quantum field theories
Abstract: Supersymmetry endows quantum field theories with several rich algebraic and geometric structures associated to their moduli space of vacua, providing powerful tools to study such theories non-perturbatively. For example, in four-dimensional theories with eight supercharges, the low energy dynamics of the theory is captured by an algebraic completely integrable system whose base is the Coulomb branch– a particular distinguished submanifold of the moduli space. This structure is so tightly constrained, that there is an ongoing program to classify such theories purely by understanding their Coulomb branch geometry. In this talk, I will give a gentle introduction to the geometry of the moduli spaces of 4d N=2 theories and, time permitting, discuss some recent results showcasing how the geometry of the Coulomb branch can be used to constrain certain physical quantities of the theory.

Top-Down Perspectives on Symmetry Theories
2025-09-19 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Max Hubner
Title: Top-Down Perspectives on Symmetry Theories
Abstract: I will review the construction and utility of symmetry theories for string constructed quantum field theories. Symmetry theories are extra-dimensional auxiliary theories separating aspects of a quantum field theory’s symmetries from many of its more messy features. For QFTs with extra-dimensional string constructions the symmetry theory derives directly from the extra-dimensional geometry. This perspective allows for the study of symmetries of famously string engineered systems, such as SCFTs in 5D and 6D, which we will discuss on an example by example basis.

Non-Supersymmetric Orbifolds, Quivers and Chen-Ruan Orbifold Cohomology
2025-09-22 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Max Hübner (Uppsala & CMSA)
Title: Non-Supersymmetric Orbifolds, Quivers and Chen-Ruan Orbifold Cohomology
Abstract: We consider D3-brane probes of non-supersymmetric orbifolds and IIA on the same class of non-supersymmetric orbifolds. Both setups are characterized, in part, by quivers (which in the latter case relate for example to D0-brane probes) from which symmetries constraining the scale-dependence and tachyonic instabilities of the two systems, respectively, can be derived. We demonstrate that these considerations can be matched via a geometric analysis of the asymptotic boundary of the relevant orbifolds, in all cases, via considerations centered on Chen-Ruan orbifold cohomology.

Turbulent Mixing and Antagonistic Microorganisms
2025-09-22 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: David Nelson, Harvard
Title: Turbulent Mixing and Antagonistic Microorganisms
Abstract: Unlike coffee and cream that homogenize when stirred, growing micro-organisms (e.g., bacteria and baker’s yeast) can actively kill each other and avoid mixing. How do such antagonistic interactions impact the growth and survival of competing strains, while being spatially advected by turbulent flows? By using analytic arguments and numerical simulations of a continuum model, we describe the dynamics of two antagonistic strains that are dispersed by both compressible and incompressible turbulent flows in two spatial dimensions. A key parameter is the ratio of the fluid transport time to that of biological reproduction, which determines the winning organism that ultimately takes over the whole population from an initial heterogeneous state, a process known as fixation. By quantifying the probability and mean time for fixation, we discuss how turbulence raises the threshold for biological nucleation and antagonism suppresses flow-induced mixing by depleting the population at interfaces. We highlight the unusual biological consequences of the interplay of turbulent fluid flows with antagonistic population dynamics, with potential implications for marine microbial ecology and origins of biological chirality.
