CMSA

Geometry and Quantum Theory Seminar
2025-12-09 16:15 - 18:30 (America/New_York) | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speaker: Lorenzo Riva, CMSA
Title: Aganagic’s invariant is Khovanov homology
Abstract: Webster computed the Khovanov homology of (the closure of) a braid in terms of the action of that braid on a certain KLRW category. Aganagic proposed that the same computation could be done in the Fukaya-Seidel category of the multiplicative Coulomb branch associated to a weighted quiver. In this talk we will recap the story so far and then sketch LePage and Shende’s proof of Aganagic’s proposal.

Speaker: Bowen Yang, CMSA
Title: Some groups from Condensed matter physics
Abstract: I would like to talk about some groups coming from the study of quantum spin systems. They inspired a construction of generalized homology theories related to Azumaya algebras.

CMSA Q&A Seminar: Dan Freed, CMSA
2025-12-10 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q&A Seminar
Speaker: Dan Freed, CMSA
Topic: Constructions of homotopy types in geometry and physics

Covers of curves, Ceresa cycles, and unlikely intersections
2025-12-11 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Algebra Seminar
Speaker: Padamavathi Srinivasan, Boston University
Title: Covers of curves, Ceresa cycles, and unlikely intersections
Abstract: The Ceresa cycle is a canonical homologically trivial algebraic cycle associated to a curve in its Jacobian. In his 1983 thesis, Ceresa showed that this cycle is algebraically nontrivial for a very general complex curve of genus at least 3. In the last few years, there have been many new results shedding light on the locus in the moduli space of genus g curves where the Ceresa cycle becomes torsion. We will survey these recent results and provide new examples of positive dimensional families of curves where only finitely many members of the family have torsion Ceresa cycle. The main idea is to study covers of curves with many automorphisms, and we will explain how we use the covering maps together with results on unlikely intersections in abelian varieties to construct such families. This is joint work with Tejasi Bhatnagar, Sheela Devadas and Toren D’Nelly Warady.

The active Young-Dupré equation
2025-12-15 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Julien Tailleur, MIT
Title: The active Young-Dupré equation
Abstract: The Young-Dupré equation is a cornerstone of the equilibrium theory of capillary and wetting phenomena. In the biological world, interfacial phenomena are ubiquitous, from the spreading of bacterial colonies to tissue growth and flocking of birds, but the description of such active systems escapes the realm of equilibrium physics. I will show how a microscopic, mechanical definition of surface tension allows building an Active Young-Dupré equation able to account for the partial wetting observed in simulations of active particles interacting via pairwise forces. Remarkably, the equation shows that the corresponding steady interfaces do not result from a simple balance between the surface tensions at play but instead emerge from a complex feedback mechanism. The interfaces are indeed stabilized by a drag force due to the emergence of steady currents, which are themselves a by-product of the symmetry breaking induced by the interfaces. These currents also lead to new physics by selecting the sizes and shapes of adsorbed droplets, breaking the equilibrium scale-free nature of the problem. Finally, I will demonstrate a spectacular consequence of the negative value of the liquid-gas surface tensions in systems undergoing motility-induced phase separation: partially-immersed objects are expelled from the liquid phase, in stark contrast with what is observed in passive systems. These results lay the foundations for a theory of wetting in active systems.

Electrical networks, Grassmannians, and cluster algebras
2025-12-16 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Algebra Seminar
Speaker: Lazar Guterman, Hebrew University of Jerusalem
Title: Electrical networks, Grassmannians, and cluster algebras
Abstract: An electrical network with $n$ boundary vertices induces a matrix called the response matrix which measures the electrical properties of the network. The set of response matrices of all electrical networks has a characterization in terms of positivity of circular minors. Alman, Lian and Tran constructed a cluster algebra on the set of circular minors, which encodes the tests for positivity of these minors. Lam established the embedding of the set of electrical networks with $n$ boundary vertices into the totally nonnegative Grassmannian $Gr_{ge0}(n-1,2n)$. The coordinate ring of the Grassmannian has a cluster algebra structure as was proved by Scott. Given an electrical network, we find a relation between circular minors of its response matrix and Plücker coordinates of its image in the Grassmannian. Using this property, we prove that for an odd $n$ the two cluster algebras, on circular minors and on the Grassmanian, become isomorphic after a natural freezing and subsequent trivialization of certain variables in their initial seeds. We apply this isomorphism in order to relate the tests for positivity of circular minors to tests for positivity in the Grassmannian. The talk is based on a joint work with Boris Bychkov and Anton Kazakov.

Geometry and Quantum Theory Seminar
2025-12-16 16:15 - 18:30 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speaker: tba

The Quasi-Adiabatic Theorem and All That
2026-01-27 16:15 - 18:30 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speaker: Daniel Spiegel, Harvard
Title: The Quasi-Adiabatic Theorem and All That
Abstract: Yosuke Kubota has recently made progress on understanding Kitaev’s conjecture by constructing a loop spectrum consisting of spaces of quantum spin systems, indexed by spatial dimension of the lattice (arXiv: 2503.12618). After a brief reminder on the C*-algebraic formalism of quantum spin systems, I will discuss Section 2 of this paper, which covers some of the more analytical tools used to construct the loop spectrum. In particular, I will focus on the quasi-adiabatic theorem which roughly speaking states that a smooth path of gapped Hamiltonians with unique ground states gives rise to a path of nice automorphisms that map the ground state at time zero to the path of ground states.

Complete Calabi-Yau Metrics and Optimal Transport
2026-01-29 13:30 - 14:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Differential Geometry and Physics Seminar
Speaker: Tristan Collins, University of Toronto
Title: Complete Calabi-Yau Metrics and Optimal Transport
Abstract: I will discuss the connection between optimal transport and the existence of complete Calabi-Yau metrics on log Calabi-Yau varieties. I will explain how the geometric problem of constructing complete Calabi-Yau metrics gives rise to problems in the boundary regularity theory for optimal transport, and how ideas from geometry can be used to make progress on some of these problems. This talk will survey joint works with Li, Tong, Tong-Yau, Firester, and Tong-Firester.

Algebra Seminar
2026-01-29 16:00 - 17:00, 2026-02-05 16:00 - 17:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States

Some results about saturation
2026-01-30 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Stephen Landsittel
Title: Some results about saturation
Abstract: Given a local ring R we can ask when saturation of ideals in R commutes with other operations on ideals (such as extension to a ring containing R). We show that the condition that extension of ideals along a ring map R to S commutes with saturation controls inherent properties of the rings R & S, such as Cohen-Macaulayness and unramifiedness.

Freedman Seminar: Michael Freedman, CMSA & Slava Krushkal, University of Virginia
2026-01-30 13:30 - 16:30 | Hybrid
Freedman Seminar
Speakers: Michael Freedman, CMSA and Slava Krushkal, University of Virginia (2-3 pm and 3:15-4:15 pm)
Title: Formulating 4D surgery for AI agents
Abstract: The topological category surgery exact sequence is still open for free groups (and most groups of exponential growth). The lack of knowledge is about both surgery and s-cobordism; and the source of the mystery is the same in both cases. Thinking about how to present this problem to AIs has had its own value. In a pair of talks we will explain how we have thought about the problem in the past and how we are thinking about it now.

Reflexive Polytopes and the Convergence of Feynman Integrals
2026-02-02 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Pierre Vanhove (Institute of Theoretical Physics – Saclay)
Title: Reflexive Polytopes and the Convergence of Feynman Integrals
Abstract: In the parametric representation, Feynman integrals can be viewed as Euler integrals defined by the Symanzik polynomials of a graph. The convergence properties of these integrals are intimately tied to the combinatorial geometry of their associated Newton polytopes; specifically, finiteness is guaranteed when the polytope contains interior points. We present a classification of Feynman integrals associated with polytopes containing a unique interior point, identifying a subset that are reflexive. Our results show that such reflexive polytopes are surprisingly scarce within the space of Feynman graphs. We conclude by computing several infinite families of these integrals and exploring their connections to mirror symmetry and toric geometry. This is based on joint work with Leonardo de la Cruz and Pavel Novichkov.

Bijections for hyperplane arrangements of Coxeter type
2026-02-02 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Olivier Bernardi, Brandeis University
Title: Bijections for hyperplane arrangements of Coxeter type
Abstract: This talk is about real hyperplane arrangements whose hyperplanes are of the form {xi −xj = s} or {xi +xj = s}. We describe a bijective framework for a large family of such arrangements which we call transitive. For each transitive arrangement A, we give a bijection between the regions of A and a set of decorated trees. Particular cases include the families of Catalan, Shi, semiorder and Linial arrangements in type A, B, C, D and BC. We also derive some general enumerative formulas for such families of transitive arrangements.

More on Kubota's spectrum of invertible states
2026-02-03 16:15 - 18:00 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speakers: Dan Freed and Bowen Yang, Harvard CMSA
Title: More on Kubota’s spectrum of invertible states
Abstract: Bowen will explain a construction aptly dubbed “Kitaev’s pump” in Kubota’s paper. Time permitting, Bowen will demonstrate its ubiquity throughout the study of topological phases, where it appears under various guises. In the second hour, Dan will sketch Kubota’s construction of a spectrum from families of invertible quantum lattice systems.

CMSA Q&A Seminar: Ludmil Katzarkov, University of Miami
2026-02-04 13:00 - 14:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q&A Seminar
Speaker: Ludmil Katzarkov, University of Miami
Title: New Birational Invariants
Abstract: We will introduce the origins of the main ideas of the theory of atoms. Applications follow. Equivariant and mixed atoms will be considered.

Automated Theory Formation and Interestingness in Mathematics
2026-02-04 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
New Technologies in Mathematics Seminar
Speaker: George Tsoukalas, UT Austin Dept. of Computer Science and Google DeepMind.
Title: Automated Theory Formation and Interestingness in Mathematics
Abstract: Advances in modern learning systems are beginning to demonstrate utility for select problems in research mathematics. A broader challenge is that of developing new theories automatically. This area has a rich history, and is tied to some of the earliest work in AI. In particular, a central question in this study was measuring the “interestingness” of mathematical concepts.
In this talk, I will review this historical context and present our recent work on using large language models to synthesize interestingness measures that guide theory exploration in elementary number theory from scratch. I will conclude by outlining potential future research directions in this domain.
Joint work done at UT Austin with Rahul Saha, Amitayush Thakur, Sabrina Reguyal, and Swarat Chaudhuri.

Index from a point
2026-02-05 13:30 - 14:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Differential Geometry and Physics Seminar
Speaker: Monica Jinwoo Kang, Texas A&M University
Title: Index from a point
Abstract: We argue that protected data of 4d N=2 SCFTs admits a purely algebro-geometric characterization. We conjecture that both the Macdonald index (and hence the Schur index) and the Higgs branch are encoded by a bifiltered affine scheme determined by OPE nilpotency and decoupling relations. Focusing on Argyres–Douglas theories, where the Higgs branch is a point, we show that this geometric construction suffices to reconstruct the full Macdonald index. This is based on recent works with Craig Lawrie and Jaewon Song.

On E7+1/2 gauge theory
2026-02-05 14:45 - 15:45 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Differential Geometry and Physics Seminar
Speaker: Yinan Wang, Peking University
Title: On E7+1/2 gauge theory

Abstract: We propose that an exotic gauge theory based on the intermediate Lie algebra E7+1/2 naturally appears in the landscape of 6d F-theory. We give strong evidence of this proposal with 6d anomaly cancellation, dual M-theory geometry and elliptic genus of the single-string worldsheet CFT.

Lie algebra cohomology and Seiberg-Witten theory
2026-02-06 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Ahsan Khan, Harvard CMSA
Title: Lie algebra cohomology and Seiberg-Witten theory
Abstract: I will discuss how a certain (relative) Lie algebra cochain complex categorifies the Schur index of N=2 supersymmetric gauge theory. For the special case of Seiberg-Witten theory I will provide a conjectured description of this cohomology.

On the p-curvature of quantum connections of CY threefolds
2026-02-09 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Shaoyun Bai (MIT)
Title: On the p-curvature of quantum connections of CY threefolds
Abstract: The small quantum connection of Calabi-Yau varieties has integral coefficients, thus admits reduction mod a prime number p. A fundamental invariant associated with flat connections over characteristic p is the p-curvature, which lies at the heart of study of algebraic differential equations. I will explain how to identify the p-curvature of quantum connection of any compact Calabi-Yau threefold with the quantum Steenrod operation, thereby providing a modular description of the p-curvature in this setting. I will also discuss the role of BPS invariants and the mirror symmetry context. This is based on joint work with Jae Hee Lee.

Phase Transition to Chaos in Complex Ecosystems with Non-reciprocal Interactions
2026-02-09 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Pankaj Metha, Boston University
Title: Phase Transition to Chaos in Complex Ecosystems with Non-reciprocal Interactions
Abstract: Nonreciprocal interactions between microscopic constituents can profoundly shape the large-scale properties of complex systems. In this pedagogical chalk talk, I will discuss recent work from our group on phase transitions and chaos in high-dimensional ecosystems with non-reciprocal interactions. Our approach builds on a generalization of MacArthur’s consumer-resource model that incorporates asymmetric interactions between species and resources. I will highlight rich connections between this problem and the mathematics of disordered systems (cavity method and DMFT), random matrix theory, and constrained optimization.

CMSA Q&A Seminar: James Eldred Pascoe, Drexel University
2026-02-11 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q&A Seminar
Speaker: James Eldred Pascoe, Drexel University
Title: (What is) The tracial fundamental group and free universal monodromy?
Abstract: We introduce the tracial fundamental group to classify the analytic continuation of functions that are locally behave like the trace of natural matrix valued functions. While globally defined natural matrix-valued functions (known as free noncommutative functions, which roughly locally are defined by noncommutative power series) satisfy universal monodromy, we show that these tracial free functions exhibit a rigid but nontrivial structure governed by the aforementioned group. We prove that the tracial fundamental group is always a torsion-free, divisible abelian group, standing in sharp contrast to the non-abelian fundamental groups of classical domains.

ReLU and Softplus neural nets as zero-sum, turn-based, stopping games
2026-02-11 14:00 - 15:00 | Virtual
New Technologies in Mathematics Seminar
Speaker: Yiannis Vlassopoulos, Athena Research Center
Title: ReLU and Softplus neural nets as zero-sum, turn-based, stopping games
Abstract: Neural networks are for the most part treated as black boxes. In an effort to begin elucidating the mathematical structure they encode, we will explain how ReLU neural nets can be interpreted as zero-sum turn-based, stopping games. The game runs in the opposite direction to the net. The input to the net is the terminal reward of the game, the output of the net is the value of the game at its initial states. The bias at each neuron is used to define the reward and the weights are used to define state-transition probabilities. One player –Max– is trying to maximize reward and the other –Min-, to minimize it. Every neuron gives rise to two game states, one where Max plays and one where Min plays. In fact running the ReLU net is equivalent to the Shapley-Bellman backward recursion for the value of the game. As a corollary of this construction we get a path integral expression for the output of the net, given input. Moreover using the fact that the Shapley operator is monotonic (with respect to the coordinate-wise order) we get bounds for the output of the net, given bounds for the input. Adding an entropic regularization to the ReLU net game allows us to interpret Softplus neural nets as games in an analogous fashion.
This is joint work with Stéphane Gaubert.

Gromov-Hausdorff limits of collapsing Calabi-Yau fibrations
2026-02-12 13:30 - 14:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Differential Geometry and Physics Seminar
Speaker: Gabor Szekelyhidi, Northwestern University
Title: Gromov-Hausdorff limits of collapsing Calabi-Yau fibrations
Abstract: A well studied problem is the metric behavior of Calabi-Yau metrics on a fibration in a family of Kahler classes that collapses the fibers. I will discuss recent progress showing that the Gromov-Hausdorff limit can be identified with the base of the fibration, generalizing results of Gross-Tosatti-Zhang, Song-Tian-Zhang and Li-Tosatti. A new ingredient is to exploit the RCD property of the Gromov-Hausdorff limit.

A leisurely stroll through the theory of adjunctions
2026-02-13 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Lorenzo Riva, Harvard CMSA
Title: A leisurely stroll through the theory of adjunctions
Abstract: Adjoint functors (and, more generally, adjunctions in a 2-category) are ubiquitous in algebra and topology. In this talk I will give an overview of the basics of adjunctions, with the ultimate goal being understanding the statement of the cobordism hypothesis. Time permitting, I will talk about some recent work on a combinatorial construction yielding free adjunctions.

Geometric structures on gauge theoretic moduli spaces
2026-02-17 16:15 - 18:00 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speaker: Saman Habibi Esfahani (CMSA)
Title: Geometric structures on gauge theoretic moduli spaces
Abstract: Motivated by Witten’s study of instantons on S3 x S1, we survey some classical and recent results, programs, and conjectures on geometric structures, such as symplectic and hyperkahler, on moduli spaces of instantons and monopoles on various manifolds, from a mathematical perspective. This talk serves as background for Max’s talk on 2/24.

CMSA Q&A Seminar: Dan Freed, Harvard
2026-02-18 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q&A Seminar
Speaker: Dan Freed, Harvard
Topic: How does one navigate the job market as a postdoc in 2026?

Topics in the Relation of Four-Manifold Invariants and Supersymmetric Field Theory
2026-02-19 13:30 - 14:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Differential Geometry and Physics Seminar
Speaker: Greg Moore, Rutgers University
Title: Topics in the Relation of Four-Manifold Invariants and Supersymmetric Field Theory
Abstract: We will begin with a review of topological twisting as a choice of background fields. We then review the standard paradigm for the formulation of Donaldson invariants as correlation functions in twisted supersymmetric N=2 d=4 quantum field theory, together with the quantum field theory (QFT) derivation of the relation of the Donaldson invariants to Seiberg-Witten invariants. We then consider what can be said using other twisted QFTs. We present some new results on the four-manifold invariants derived from N=2 supersymmetric QCD. We then move on to 5d theories and the “K-theoretic Donaldson invariants” and comment briefly on the 6d theories and the “elliptic Donaldson invariants.” In the unlikely event that time permits we finish with the extension to families of four-manifolds, where the coupling to a suitably twisted and truncated superconformal gravity is expected to produce invariants valued in the cohomology of the classifying space of the diffeomorphism group of the four-manifold.

Constructing oriented TQFTs from twisted pivotal tensor categories
2026-02-19 15:30 - 16:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Geometry and Quantum Theory Seminar
Speaker: William Stewart
Title: Constructing oriented TQFTs from twisted pivotal tensor categories
Abstract: The cobordism hypothesis classifies n-dimensional oriented TQFTs in terms of SO(n) homotopy fixed point data. An SO(2) homotopy fixed point structure on a finite tensor category gives rise to a twisted pivotal structure (a more general notion than a pivotal structure). In this talk, I will illustrate how the usual skein theory (also called string nets) of a pivotal tensor category can be generalized to the twisted pivotal setting, yielding new 2d oriented TQFTs. This is joint work with Ben Haioun and Filippos Sytilidis.
