CMSA

Compression Is All You Need: Modeling Mathematics
2026-04-24 14:00 - 16:30 (America/New_York) | Virtual
Freedman Seminar
Speaker: Mike Freedman, Harvard CMSA
Title: Compression Is All You Need: Modeling Mathematics
Abstract: The talk will exposit a recent eponymous arXiv posting with coauthors Vitaly Aksenov, Eve Bodnia, and Mike Mulligan. The approach is to think like a physicist and model a seemingly complex bit of reality: mathematics, by a simple toy model where exact computations can be carried out and then compared with observation. The models are finitely generated monoids and the data is derived from MathLib a large Lean-based repository. The hierarchical nature of definitions and lemmas in math is modeled by adding redundant generators to the monoids – think of the powers of 10 within the natural numbers which support place notation. Place notation confers an exponential compression of how we describe numbers; exploration of MathLib shows that this theme persists to (human) mathematics writ large. We hope that the observables we describe will help our agents navigate to interesting mathematical destinations.

Higher current algebras and chiral algebras
2026-04-27 15:00 - 16:00 | CMSA G102, 20 Garden Street, Cambridge, MA, 02138
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Charles Young (University of Hertfordshire)
Title: Higher current algebras and chiral algebras
Abstract: Vertex algebras capture physicists’ notion of OPEs in chiral CFTs, in complex dimension one. For various motivations, one would like to have analogs of vertex algebras in higher dimensions. Chiral algebras, in the sense of Beilinson-Drinfeld and Francis-Gaitsgory, provide a natural framework here, because they re-express the vertex algebra axioms (which are rather sui generis, and therefore hard to generalize) as something more recognizable (a chiral algebra is a Lie algebra, of a sort).
I will review this, and then go on to introduce a certain concrete model of the unit chiral algebra in higher dimensions. In higher dimensions one is forced to work up to coherent homotopy in some fashion; in this model it turns out to be in the mildest fashion one could hope for: namely, one moves from Lie algebras to their homotopy analogs, L-infinity algebras, and from chiral algebras to homotopy chiral algebras in a sense introduced by Malikov-Schechtman.
The main tool in the talk will be a strict cdga model — the polysimplicial model — of derived global sections of the structure sheaf on configuration space. The hope is that this model will prove well-adapted to doing concrete calculations, and in that direction, I will gesture towards a homotopy version of the usual Arnold/Orlik-Solomon relations for broken circuits.
This is joint work with Zhengping Gui and Laura Felder and is based largely on the preprint 2506.09728

Enacted collective cognition: Brainless problem-solving in weaver ants
2026-04-27 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Ofer Feinerman, Weizmann Institute of Science
Title: Enacted collective cognition: Brainless problem-solving in weaver ants
Abstract: Unlike most ants, weaver ants construct their nests by pulling together leaves. Because individual ants are small relative to the leaves, they assemble their bodies into temporary tools that bend the leaves into a hollow structure, later stabilized with larval silk. Remarkably, they achieve functional nests across a wide range of leaf shapes and configurations, suggesting that this distributed system is capable of solving complex, open-ended problems.
To understand how this is possible, we performed laboratory experiments using controlled leaf configurations. In simple cases, we show that ants can rely on a zipping heuristic that produces closed nests, and we use differential geometry to demonstrate how flexible leaves are transformed into rigid structures. Crucially, this zipping behavior forms a feedback loop in which ants continuously read and modify the evolving structure. In this sense, the nest itself functions as a shared physical information system.
This suggests that cognition in this system is not located within individual ants, but is enacted through the co-dynamics of the colony and the structure it builds. We present preliminary experiments with more complex leaf configurations, showing that this process can solve increasingly challenging construction problems. Together, these results point to a distributed, brainless, and enactive form of cognition.

The classifying space of a Morse flow category
2026-04-28 16:15 - 18:00 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Joint Math/CMSA Geometry and Quantum Theory Seminar
Speaker: Lorenzo Riva, Harvard CMSA
Title: The classifying space of a Morse flow category

Abstract: Following a paper of Calle and Liu we show that, under suitable tameness assumptions, the classifying space of the Morse category associated to a manifold M with a Morse function recovers the homotopy type of M, thereby addressing a gap in a preprint of Cohen-Jones-Segal. We also give a counterexample when those assumptions are not satisfied.

Transcendental Epsilon Multiplicity via Divisor Volumes
2026-04-30 16:00 - 17:00 | CMSA Room G02, 20 Garden Street, Cambridge, MA, 02138
Algebra Seminar
Speaker: Sudipta Das, Tata Institute of Fundamental Research
Title: Transcendental Epsilon Multiplicity via Divisor Volumes
Abstract: In this talk, our goal is to establish a structural bridge between asymptotic commutative algebra and transcendence theory to show that there exists an ideal in a Noetherian local ring whose epsilon multiplicity is transcendental. By equating the local-cohomological definition of epsilon multiplicity to a global divisorial volume integral on a projective bundle, we apply Baker’s theorem on linear forms in logarithms to prove that the resulting arithmetic invariant falls strictly outside the field of algebraic numbers. This talk is based on collaborative work with Vinh Pham and Stephen Landsittel.

note room change to G02

Lifting F-split surfaces to the Witt vectors
2026-05-01 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Iacopo Brivio, CMSA
Title: Lifting F-split surfaces to the Witt vectors

Abstract: Algebraic varieties in positive characteristic are ill behaved compared to characteristic zero ones. Several important tools available over the complex numbers, such as the Hodge decomposition theorem, are either not available or straight-away false. There are two important classes of positive characteristic varieties which have better behavior: Witt liftable varieties and Frobenius split varieties. A folklore conjecture predicts that the latter class is contained in the former. In a joint work with Bernasconi, Kawakami and Witaszek we proved that this is the case for surfaces. I will give an overview of this result as well as some applications thereof.

Twisted D-branes and TQFTs valued in Calabi-Yau categories
2026-05-04 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Surya Raghavendran, Yale University
Title: Twisted D-branes and TQFTs valued in Calabi-Yau categories
Abstract: Recently, Bozec–Calaque–Scherotzke have articulated a noncommutative version of the AKSZ construction, which associates to a smooth Calabi–Yau category a fully extended TQFT valued in a category of iterated Calabi–Yau cospans. In this talk, I will study a class of examples of such theories which arise in the context of conjectures of Costello and Li, which describe Type II strings in certain Ramond–Ramond backgrounds as topological strings. These TQFTs capture structural features of the BPS physics of D-branes that are universal in Chan–Paton factors. Conjecturally commutative limits of the values of such theories on closed manifolds can sometimes be geometrically quantized to yield algebraic structures with Hall-type products. Examples of this paradigm include CoHAs associated to complex 3-folds, CoHAs attached to local systems on 3-manifolds, and the categorified Hall algebras of Porta–Sala.

Dynamics as intersection problem
2026-05-04 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Nikita Nekrasov, Simons Center
Title: Dynamics as intersection problem
Abstract: Most classical and quantum field theories are based on an action principle. However, there are important exceptions to this — hydrodynamics and the theory of self-dual fields. In this talk we formulate the covariant relativistic fluid dynamics, with or without magnetic fields, as well as the theory of chiral boson in 1+1 dimensions, self-dual tensor in 1+5 dimensions, and self-dual four-form of IIB supergravity, in terms of intersection theory of an auxiliary phase space. This provides a common covariant geometric framework for systems without a conventional action, while at the same time laying the groundwork for quantization via the Kontsevich approach. Joint work with Paul Wiegmann.

New directions in synthetic data
2026-05-06 14:00 - 15:00 | Virtual
New Technologies in Mathematics Seminar
Speaker: Tatsunori Hashimoto, Stanford
Title: New directions in synthetic data
Abstract: Synthetic data has been an effective, if boring set of techniques: prompt some language model to restructure your corpus to match some downstream task, with occasionally some distillation. In this talk, we will take a more expansive view of synthetic data as a general algorithmic tool for generative modeling, arguing that the design space and possibilities of synthetic data are much bigger than it might seem. Through a few recent works, we will show that synthetic data has major benefits beyond transforming the data – improving in-domain perplexities, and enabling unique algorithmic primitives, such as neighborhood smoothing and concatenated ‘mega’ documents. With this broader view, we will point towards a nascent but interesting possibility of treating data itself as an algorithmic object to be engineered and optimized end-to-end.

From Poincaré/Koszul duality to (twisted) AdS/CFT correspondence
2026-05-08 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Keyou Zeng
Title: From Poincaré/Koszul duality to (twisted) AdS/CFT correspondence
Abstract: Poincaré duality is a fundamental result in the (co)homology theory of manifolds. It has many applications in topology and vast generalizations to other types of “spaces,” such as singular/stratified spaces and schemes. In this talk, I will discuss a variant of Poincaré duality for factorization algebras, also known as Koszul duality. At the end of the talk, I will relate this notion to a mathematical formulation of what physicists call the AdS/CFT correspondence, as proposed by Costello and Li.

When do anomalous finite symmetries in (3+1)d enforce gaplessness?
2026-05-11 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 (University of Oxford)
Title: When do anomalous finite symmetries in (3+1)d enforce gaplessness?
Abstract: I will explain a comprehensive framework for characterizing the infrared (IR) phases of a fermionic QFTs in (3+1)d, based on their quantum anomalies associated with a finite symmetry. We uncover a fundamental dichotomy among these anomalies: the first class of anomalies can always be realized by symmetric gapped states, while the second class can never be realized by gapped states without breaking the given symmetry, establishing the phenomenon of symmetry-enforced gaplessness in these settings. Using the construction of symmetry extension afforded to us by new developments in fusion 2-categories, we construct the candidate gapped states that theories with the first class of anomalies can flow to in the IR. As an application, I will provide examples of concrete predictions for the candidate IR phases of (3+1)d gauge theories based on our results.

Statistical Shape Analysis of Complex Natural Structures
2026-05-11 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Anuj Srivastava, Johns Hopkins University
Title: Statistical Shape Analysis of Complex Natural Structures
Abstract: Statistical modeling and analysis of structured data is a fast-growing field in Statistics and Data Science. Rapid advances in imaging techniques have led to tremendous amounts of data for analyzing imaged objects across several scientific disciplines. Examples include shapes of cancer cells, botanical trees, human biometrics, 3D genome, brain anatomical structures, crowd videos, nano-manufacturing, and so on. Shapes are relevant even in non-imaging data contexts, e.g., the shapes of COVID rate curves or the shapes of activity cycles in lifestyle data. Imposing statistical models and inferences on shapes seems daunting because the shape is an abstract notion and one requires precise mathematical representations to quantify shapes. This talk has two parts. In the first part, I will present some recent developments in “elastic representations” of structures such as functions, curves, surfaces, and graphs. In the second part, I will focus on statistical analyses: computing shape summaries, estimation under shape constraints, hypothesis testing, time-series models, and regression models involving shapes.

Polynomial invariants of conjugation over finite fields
2026-05-14 16:00 - 17:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Algebra Seminar
Speaker: Aryaman Maithani, University of Utah
Title: Polynomial invariants of conjugation over finite fields

Abstract: Consider the conjugation action of GL₂(K) on the polynomial ring K[X₂ₓ₂].
When K is an infinite field, the ring of invariants is a polynomial ring generated by the trace and the determinant.
We describe the ring of invariants when K is a finite field, and show that it is a hypersurface.

Abelian duality via derived geometry
2026-05-18 15:00 - 16:00 | CMSA Room G02, 20 Garden Street, Cambridge, MA, 02138
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Owen Gwilliam, UMass Amherst
Title: Abelian duality via derived geometry
Abstract: We discuss how to synthesize differential cohomology and the BV formalism to describe generalized Maxwell theories (or abelian p-form gauge theories), and how this framework allows a succinct formulation of abelian duality. Given time, we will discuss how these methods apply to the 6d self-dual 2-form gauge theory that appears as part of the 6d N=(1,0) and (2,0) superconformal theories known as abelian tensor multiplets. This is joint work in progress with Chris Elliott, Ingmar Saberi, and Brian Williams.

Geometry and Quantum Theory Seminar
2026-05-19 16:15 - 18:00 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Joint Math/CMSA Geometry and Quantum Theory Seminar
Speaker: Vasily Krylov, Harvard

Separation of timescales controls feature learning and overfitting in large neural networks
2026-05-20 14:00 - 15:00 | Virtual
New Technologies in Mathematics Seminar
Speaker: Pierfrancesco Urbani, Universite Paris-Saclay, CNRS, CEA, Institut de physique theorique
Title: Separation of timescales controls feature learning and overfitting in large neural networks
Abstract: To understand the inductive bias and generalization capabilities of large, overparameterized machine learning models, it is essential to analyze the dynamics of their training algorithms. Using dynamical mean field theory we investigate the learning dynamics of large two-layer neural networks. Our findings reveal that, for networks with a large width, the training process exhibits a separation of timescales phenomenon. This leads to several key observations:
1. The emergence of a slow timescale linked to the growth in Gaussian/Rademacher complexity of the network;
2. An inductive bias favoring low complexity when the initial model complexity is sufficiently small;
3. A dynamical decoupling between feature learning and overfitting phases;
4. A non-monotonic trend in test error, characterized by a “feature unlearning” regime at later stages of training.
Joint work with Andrea Montanari.

Quasi-local algebras and invertible phases of matter
2026-09-08 16:15 - 18:00 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speaker: Nikita Sopenko, CMSA
Title: Quasi-local algebras and invertible phases of matter
Abstract: In the algebraic approach to quantum field theory, observables localized in bounded regions form a net of von Neumann algebras generating what is known as a quasi-local algebra. I will discuss the classification of quasi-local algebras under a notion of equivalence that generalizes Brauer equivalence and captures only large-scale properties. I will argue that this problem coincides with the classification of invertible phases of lattice systems in one dimension higher, providing a way to relate quantum field-theoretic and microscopic descriptions. As a byproduct, I will describe a candidate for the generalized cohomology theory associated with invertible phases, as conjectured by Kitaev.

New Technologies in Mathematics Seminar
2026-09-09 14:00 - 15:00, 2026-09-16 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
New Technologies in Mathematics Seminar
Speaker: tba

Working with LLMs to do high quality math
2026-09-09 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
AI for the Working Mathematician
Speaker: Daniel Litt, University of Toronto
Title: Working with LLMs to do high quality math
Abstract: Much hay has been made of the capabilities of LLMs to do math autonomously, and indeed frontier models have resolved some long-standing, interesting open questions. But our goal is not to produce papers, but rather to do high quality mathematics. I’ll discuss some experiments over the past year in trying to get LLMs to help with producing high quality mathematics, non-autonomously, and speculate a bit about the future.

Geometry and Mathematical Physics Seminar
2026-09-10 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Geometry and Mathematical Physics Seminar
Speaker: Brian Williams, Boston University

Member Seminar
2026-09-11 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Elena Kim

Colloquium
2026-09-14 16:30 - 17:30, 2026-09-21 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States

Geometry and Quantum Theory Seminar
2026-09-15 16:15 - 18:00, 2026-09-22 16:15 - 18:00 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Joint Math/CMSA Geometry and Quantum Theory Seminar

Geometry and Mathematical Physics Seminar
2026-09-17 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States

Member Seminar
2026-09-18 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States

CMSA Special Seminar: Deformations to the Complex Plane, Novel Asymptotic Techniques, and the Large t- Asymptotics of the Riemann Zeta Function
2026-09-22 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Special Seminar

Speaker: Thanasis Fokas, University of Cambridge
Title: Deformations to the Complex Plane, Novel Asymptotic Techniques, and the Large t-
Asymptotics of the Riemann Zeta Function
Abstract: The Unified Transform (also known as the Fokas method) is a powerful new method for
solving boundary value problems for linear and for integrable nonlinear PDEs. For linear
PDEs, the relevant transform is based on appropriate deformations of certain integrals from
the real line to the complex plane. After briefly reviewing this transform, it will be shown
that combining this idea with novel asymptotic techniques has recently led to unexpected
and exciting results regarding the large t-asymptotic analysis of the celebrated Riemann zeta
function. The following two results will be discussed. First, a simple formula will be
presented for the difference of the functions defining the error terms in two historic
problems: in Atkinson’s formula and in the formula for the Dirichlet divisor problem; it will
be shown that this difference equals π/ 2 plus a function which is simply related to the
square of the Riemann zeta function. Second, a remarkable integral identity satisfied by the
Riemann zeta function will be presented; this identity is obtained from an earlier identity
derived by the speaker via contour deformation in the complex plane. Making crucial use of
novel asymptotic techniques obtained jointly with Jonatan Lenells, the asymptotic analysis
of this integral equation gives rise to an interesting identity satisfied, for large t, by a sum
generalizing the Dirichlet divisor sum. Also, and more importantly, it gives rise to a specific
integral transform suitable for the large t-asymptotic analysis of the Riemann zeta function.

CMSA Q&A Seminar: Hugh Woodin, Harvard
2026-09-23 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q&A Seminar
Speaker: Hugh Woodin, Harvard
Title: Truth, proof, and AI
