CMSA

Classification of 2D Stabilizer States
2025-11-07 12:00 - 13:00 (America/New_York) | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Bowen Yang
Title: Classification of 2D Stabilizer States
Abstract: I will explain how translation-invariant two-dimensional stabilizer states are completely classified by finite abelian groups with nondegenerate quadratic forms—that is, by abelian anyon theories. The proof uses the algebraic structure of stabilizer codes as modules over Laurent polynomial rings, revealing how their physical features reflect in this module-theoretic framework. arXiv:2509.10418

The Moyal bracket and the BV cohomology of the spinning particle
2025-11-10 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Ezra Getzler, Northwestern
Title: The Moyal bracket and the BV cohomology of the spinning particle
Abstract: The spinning particle is the one-dimensional reduction of the Neveu-Schwartz-Ramond superstring. It consists of a supersymmetric particle moving in a one-dimensional supergravity background, and its quantization is the Hilbert superspace of harmonic spinors. (These models are classified by N, the number of copies of fermionic fields. In this talk, N=1. The extension to N=2 is work in progress with Ivo.) It is actually an AKSZ model (so a generalization of one-dimensional Chern-Simons), and so associated to a differential graded symplectic supermanifold, by which we mean a pair (ω,Q), where ω is a(n exact) symplectic form and Q is an odd function of degree 1. The cohomology of the ring of functions of this supermanifold with differential the Poisson bracket with Q determines the classical BV cohomology of the spinning particle, so is important for understanding perturbative BV quantization of this model. I calculated this cohomology in earlier work for N=1, and showed that it is somewhat bizarre, with two series of cohomology classes in arbitrary negative degrees, each a copy of the functions on the target manifold.
In the study of quantum BFV, we should instead consider the Moyal bracket on the target, and lift Q to an element Q satisfying [Q,Q]=0. The cohomology of the differential [Q,-] is the Moyal cohomology of the differential graded symplectic supermanifold. (This lift corresponds to the choice of a Spinc structure on the target manifold.) In this talk, I prove that the Moyal cohomology, unlike the Poisson cohomology, is well-behaved: in the spectral sequence from Poisson to Moyal cohomology, the extra cohomology classes of negative degree cancel each other pairwise at the E1 page.

Khovanov homology from KLRW algebras
2025-11-11 16:15 - 18:30 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speaker: Sunghyuk Park, CMSA
Title: Khovanov homology from KLRW algebras
Abstract: This is the first in a four-part series, organized together with Vasily Krylov, Sebastian Haney, and Lorenzo Riva, aimed at understanding Aganagic’s categorification of quantum link invariants through Coulomb branches and homological mirror symmetry. In this first talk, I will lay the algebraic background for this story by explaining how Khovanov homology can be understood in terms of higher representation theory via Khovanov-Lauda-Rouquier-Webster (KLRW) algebras.

Freedman Seminar: Michael Freedman, CMSA & Bowen Yang, CMSA
2025-11-14 13:00 - 16:00 | Virtual
Freedman Seminar
Speaker: Michael Freedman, Harvard CMSA
Title: Sullivan’s work on Lipschitz structures Part II (but self-contained)

Speaker: Bowen Yang, CMSA
Title: Deligne and Sullivan’s work on complex bundles with discrete structure group

BV and the ThimTFT
2025-11-17 15:00 - 16:00 | CMSA Room G02, 20 Garden Street, Cambridge, MA, 02138
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Justin Kulp, Stony Brook
Title: BV and the ThimTFT
Abstract: The SymTFT (or “quiche”) construction relates different global forms of d-dimensional QFTs with discrete symmetry: realizing different global forms as a (d+1)-dimensional TFT on an interval, with a common “physical” boundary condition on one side, and different topological boundary conditions on the other. In my talk, I will describe an analogue of the SymTFT which relates theories with the same “perturbative equations of motion”, but different non-perturbative completions.
I will start with a lightning overview of conformal blocks and relative QFT, then explain the BV formalism in some detail—focusing on the elegant (super)geometric story in 0d for simplicity. I will argue that there is a natural 1d cohomological TFT (called the ThimTFT) associated to the classical action S, with different topological boundary conditions described by convergent path-integral contours in a complexified field space. Time permitting, I will discuss extensions to higher dimensions. Based on WIP.

Interaction of Statistics and Geometry: A New Landscape for Data Science
2025-11-17 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Zhigang Yao (National University of Singapore)
Title: Interaction of Statistics and Geometry: A New Landscape for Data Science
Abstract: Classical statistics views data as real numbers or vectors in Euclidean space, but modern challenges increasingly involve data with intrinsic geometric structures. A central problem in this direction is manifold fitting, with origins in H. Whitney’s work of the 1930s. The Geometric Whitney Problems ask: given a set, when can we construct a smooth 𝑑-dimensional manifold that approximates it, and how accurately can we estimate it?
In this talk, I will discuss recent progress on manifold fitting and its role in bridging geometry and data science. While many existing methods rely on restrictive assumptions, the manifold hypothesis—that data often lie near non-Euclidean structures—remains fundamental in modern statistical learning. I will highlight both theoretical insights and algorithmic challenges, drawing on recent works with, as well as ongoing research.

Differentials and Singularities
2025-11-20 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Algebra Seminar
Speaker: Dawei Chen, Boston College
Title: Differentials and Singularities
Abstract: Given a holomorphic differential on a smooth algebraic curve, we associate to it a Gorenstein curve singularity with Gm-action. Conversely, we show that every isolated Gorenstein curve singularity with Gm-action appears in this way. This construction reveals a fascinating relation between differentials and singularities, where the zero orders of the differentials determine the combinatorial data of the singularities. In this talk, I’ll provide many concrete examples of such singularities, and explain how the study of deformations of these singularities can help us better understand the geometry of moduli spaces of differentials. This is based on joint work with Fei Yu (Zhejiang University).

Tropical-Topological(Tropological) Sigma Models
2025-11-20 16:00 - 17:00 | Virtual
Differential Geometry and Physics Seminar
Speaker: Andrés Franco Valiente, UC Berkeley
Title: Tropical-Topological (Tropological) Sigma Models
Abstract: Tropical geometry provides a powerful bridge between complex and combinatorial worlds, allowing certain curve-counting invariants to be computed in a piecewise-linear “tropical” limit. Building on Mikhalkin’s insight that Gromov–Witten invariants can be recovered from tropical curves, this talk revisits Mikhalkin’s result from the viewpoint of topological field theory and functional integration. I will first review the topological sigma model and explain how the localization equations admit a natural notion of tropicalization which allows us to reproduce the Gromov-Witten invariants using standard cohomological BRST methods without having to reformulate the functional integral in terms of the tropical semifield. We find that the relevant geometries associated to the tropical limit of the topological sigma models no longer require a complex structure but they are instead based on nilpotent structures on singular foliated manifolds. We close with a discussion on recent progress on how the tropological sigma model has a close connection to Hořava’s topologicial quantum gravity for Ricci Flow in a joint work with Emil Albrychiewicz and Viola Zixin Zhao.

Optimal learning protocols via statistical physics and control theory
2025-11-21 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Francesco Mori, CMSA
Title: Optimal learning protocols via statistical physics and control theory
Abstract: Behind the impressive performance of modern machine learning lies a toolkit of training tricks, from tuning learning rates to curating training data. These heuristics are powerful but hard to interpret and possibly suboptimal, leaving open the challenge of finding general principles for protocol design. In this talk, I will present a framework that combines tools from statistical physics and control theory to identify optimal training strategies in simple yet insightful neural network models. In the high-dimensional limit, the training dynamics can be reduced to closed-form ordinary differential equations for a small set of order parameters that track learning. This reduction allows us to pose the design of training protocols as an optimal control problem directly on the order-parameter dynamics, with the objective of minimizing the generalization error. This formulation encompasses a variety of learning scenarios and yields principled training strategies that clarify, and in some cases improve upon, standard heuristic practices.

Geometric Simplicity in Quantum Field Theory and Gravity
2025-11-24 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Thomas Grimm, Utrecht University
Title: Geometric Simplicity in Quantum Field Theory and Gravity
Abstract: In physics we attribute much value to the emergence of simplicity, both conceptually and for computations. Familiar examples include algebraic relations among Feynman amplitudes, the surprising descriptions arising in large-N or duality limits, and the central role played by symmetries. In this colloquium we discuss how tame geometry allows one to quantitatively describe such simplifications by introducing a measure of complexity. This framework relies on finiteness: the information content of the functions and domains required to specify a theory, or an observable is finite. A key strength of the proposal is its generality as it applies to any physical quantity and can therefore be used both to analyze complexities within an individual Quantum Field Theory and to study the entire space of such theories. We present several applications and explain how this perspective ties in with our understanding of the expected properties of effective theories that can be coupled to Quantum Gravity.

Coulomb branches and KLRW algebras
2025-11-25 16:15 - 18:30 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speaker:Vasily Krylov, CMSA
Title: Coulomb branches and KLRW algebras
Abstract: I will introduce Coulomb branches associated to a pair of a reductive group G and its complex representation N. We will discuss their main geometric properties and examine explicit examples. I will also highlight the connection to the moduli space of monopoles. Time permitting, we will see how KLRW naturally arise in this context.

Asymptotic Theory of Attention: In-Context Learning and Sparse Token Detection
2025-12-01 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Yue M. Lu, Harvard University
Title: Asymptotic Theory of Attention: In-Context Learning and Sparse Token Detection
Abstract: Attention-based architectures exhibit striking emergent abilities—from learning tasks directly from context to detecting rare, weak features in long sequences—yet a rigorous theory explaining these behaviors remains limited. In this talk, I will present two recent exactly solvable models that develop a high-dimensional asymptotic theory of attention.
(i) In-context learning. For linear attention pretrained on linear regression tasks, we derive sharp asymptotics in a regime where token dimension, context length, and task diversity all scale proportionally, while the number of pretraining examples scales quadratically. The resulting learning curve exhibits double descent and a phase transition separating a low-diversity memorization regime from a high-diversity regime of genuine in-context generalization. These predictions closely track empirical behavior in both linear-attention models and nonlinear Transformer architectures.
(ii) Sparse-token classification. For detecting weak signals embedded in a small, randomly located subset of tokens, we analyze a single-layer attention classifier and determine its representational and learnability thresholds. Attention succeeds with only logarithmic signal scaling in the sequence length L, outperforming linear baselines that require √L scaling. In a proportional high-dimensional regime, we prove that two gradient descent steps yield nontrivial alignment between the query vector and the hidden signal, leading to signal-adaptive attention. Exact formulas for the test error, training loss, and separability capacity quantify this advantage.

Homological mirror symmetry for Coulomb branches
2025-12-02 16:15 - 18:30 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speaker: Sebastian Haney, Harvard
Title: Homological mirror symmetry for Coulomb branches
Abstract: I will describe a result of Aganagic, Danilenko, Li, Shende, and Zhou which constructs a embeddings of certain cylindrical KLRW categories into Fukaya-Seidel categories of multiplicative Coulomb branches. This can be thought of as a homological mirror symmetry statement relating the Fukaya category of a multiplicative Coulomb branch to the derived category of a resolved additive Coulomb branch. I will describe the construction of the relevant Fukaya–Seidel categories, and explain how the KRLW relations are realized by counts of holomorphic disks in symmetric products of surfaces.

Machine learning tools for mathematical discovery
2025-12-03 14:00 - 15:00 | Virtual
New Technologies in Mathematics Seminar
Speaker: Adam Zsolt Wagner, Google DeepMind
Title: Machine learning tools for mathematical discovery
Abstract: I will discuss various ML tools we can use today to try to find interesting constructions to various mathematical problems. I will briefly mention simple reinforcement learning setups and PatternBoost, but the talk will mainly focus on LLM-based tools such as FunSearch and AlphaEvolve. We will discuss the pros and cons of several of these methods, and try to figure out which one is best for the problems we care about.
Joint work with François Charton, Jordan Ellenberg, Bogdan Georgiev, Javier Gómez-Serrano, Terence Tao, and Geordie Williamson.

Towards a Dolbeault AGT correspondence
2025-12-04 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Differential Geometry and Physics Seminar
Speaker: Surya Raghavendran, Yale
Title: Towards a Dolbeault AGT correspondence
Abstract: The AGT correspondence and its extensions propose geometric constructions of vertex algebras and their modules from the cohomology of various moduli spaces of sheaves on surfaces. Physically, the correspondence is illuminated throgh the holomorphic–topological twist of the six-dimensional N=(2,0) superconformal field theories. In this talk, I will describe a variant of AGT arising instead from the so-called minimal twist of these theories. In this setting, the natural algebraic structures are holomorphic factorization algebras in three complex dimensions. From these, one can extract an associative algebra together with a natural module, which we conjecture to coincide with a quantization of the moduli of Higgs sheaves on surfaces. In examples, this pair is furthermore expected to admit a Hodge–de Rham deformation to the Heisenberg algebra and its action on the cohomology of Hilbert schemes of surfaces, as constructed by Grojnowski and Nakajima.

A combinatorial formula for interpolation Macdonald polynomials
2025-12-05 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Houcine Ben Dali, Harvard CMSA
Title: A combinatorial formula for interpolation Macdonald polynomials
Abstract: In 1996, Knop and Sahi introduced a remarkable family of inhomogeneous symmetric polynomials, defined via vanishing conditions, whose top homogeneous parts are exactly the Macdonald polynomials. Like the Macdonald polynomials, these interpolation Macdonald polynomials are closely connected to the Hecke algebra, and admit nonsymmetric versions, which generalize the nonsymmetric Macdonald polynomials. I will present a combinatorial formula for interpolation Macdonald polynomials in terms of signed multiline queues. This formula generalizes the combinatorial formula for Macdonald polynomials in terms of multiline queues given by Corteel–Mandelshtam–Williams. This is based on a joint work with Lauren Williams.

Computing WKB periods
2025-12-08 15:00 - 16:00 | CMSA Room G02, 20 Garden Street, Cambridge, MA, 02138
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Max Meynig, University of Connecticut
Title: Computing WKB periods
Abstract: In one dimensional quantum mechanics, the all-orders WKB method leads to ‘quantum periods’ which are formal power series in hbar whose coefficients are certain period integrals. These periods, which limelight in supersymmetric/string theories, have rich structure and can be computed in a number of ways. I will discuss a new perspective on them and their computation.

Recent Advances in Probabilistically Checkable Proofs
2025-12-08 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Dor Minzer (MIT)
Title: Recent Advances in Probabilistically Checkable Proofs
Abstract: The PCP Theorem is a cornerstone of computer science, with applications to hardness of approximation, verification, interactive protocols and more. It asserts a witness for the satisfiability of a given 3CNF formula can be encoded in a robust way that allows local checking.In this talk we discuss recent developments in PCPs, and their connection with distributed protocols, high-dimensional expanders and discrete Fourier analysis. Based on joint works with Kai Zhe Zheng, Mitali Bafna, Noam Lifshitz, Nikhil Vyas.

Geometry and Quantum Theory Seminar
2025-12-09 16:15 - 18:30 | 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 | 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.
