Geometry and Quantum Theory Seminar
2025-10-14 16:15 - 18:30 (America/New_York) | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speaker: Dylan Galt, Harvard
(60 minute talk)
Title: What is a “nonlinear” near-symplectic form?
Abstract: In this talk, I will explain how one might understand this question and why a possible answer can be found in the geometry of coassociative 4-folds, a special class of minimal submanifolds discovered by Harvey and Lawson.

Speaker: Keyou Zeng, CMSA
(30 minute talk)
Title: Cohomology of configuration space of points
Abstract: Configuration space of points is an interesting and important subject in mathematics and physics. I’ll review some classical results computing cohomology of configuration space of points. I’ll also introduce some recent progress in computing sheaf cohomology of configuration space of affine space.

Lech's inequality and stability of local rings
2025-10-16 14:00 - 15:00 | Virtual
Algebra Seminar
Speaker: Linquan Ma (Purdue University)
Title: Lech’s inequality and stability of local rings
Abstract: We explore Lech’s inequality relating the colength and multiplicity of m-primary ideals in a Noetherian local ring (R,m). We introduce a natural invariant that measures the sharpness of Lech’s inequality and show its connections with singularities of asymptotically semistable varieties and singularities arising from the MMP. We compute this invariant in various examples. This is joint work with Ilya Smirnov.

Differential Geometry and Physics Seminar
2025-10-16 16:00 - 17:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Differential Geometry and Physics Seminar
Speaker: Andy Neitzke, Yale
Title: Abelianization of tau functions
Abstract: The symplectic and hyperkahler geometry of moduli spaces of flat connections over Riemann surfaces is in a sense quantized by the theory of isomonodromic tau functions. These functions in turn arise as partition functions in the conformal field theory of twisted free fermions. I will describe a new scheme for computing these tau functions via abelianization, and what it produces in one simple example, related to the Painleve I equation. This scheme is joint work with Qianyu Hao. The talk is intended to be self-contained (you don’t have to know in advance what a tau function or a conformal field theory is).

DMFT, Two Point Correlations of Resolvents, and Applications to Machine Learning Theory
2025-10-17 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Blake Bordelon
Title: DMFT, Two Point Correlations of Resolvents, and Applications to Machine Learning Theory
Abstract: Machine learning algorithms evolve the parameters of a model in a high dimensional and disordered loss landscape. To characterize the effects of random initialization of model parameters, randomly sampled training data, and the effect of SGD noise, it often is useful to invoke ideas from random matrix theory and the physics of disordered systems. In this seminar, I describe a general idea, known as dynamical mean field theory (DMFT) which describes the evolution of a disordered dynamical system in infinite dimensions. I will briefly describe simple examples of interest to theoretical neuroscientists and machine learning theorists. For linear dynamical systems, I will show that this method characterizes the typical case trajectory in terms of two point correlations of resolvent matrices evaluated at different frequencies. This bispectral object can account for puzzling effects such as late time divergence of gradient descent at the interpolation threshold (when parameters = dataset size) despite the Jacobian of the dynamics having real and non-positive eigenvalues. I will then describe a novel two point correlation result for general free products of the form M = O B O^T A for O sampled from the Haar measure. I will use this result to characterize the exact asymptotics of the performance of a linear transformer trained to perform in-context linear regression on “generic” (randomly rotated) covariance matrices.

Freedman Seminar: Michael Freedman, CMSA & Bowen Yang, CMSA
2025-10-17 13:00 - 16:00 | Virtual
Freedman Seminar
Speaker: Michael Freedman, Harvard CMSA
Title: Sullivan’s work on Lipschitz structures
Abstract: I’ll begin with an elementary, but now little known, piece of PL topology: engulfing. John Stalling used it to give an alternative proof of the high dimensional Poincare conjecture. Then I’ll explain Dennis Sullivan’s enhancement of Kirby’s torus trick (which relies on engulfing.) I’ll note an open question regarding Lipschitz structures on 4-manifolds.

Speaker: Bowen Yang, CMSA
Title: Quantum Cellular Automata and Algebraic L-Theory
Abstract: Quantum cellular automata (QCAs) are models of reversible quantum dynamics that preserve locality; they can be thought of as quantum analogues of classical cellular automata, but with much richer structure. I will describe a classification of the Clifford subclass of QCAs using methods from algebraic L-theory. The main result identifies the group of Clifford QCAs, up to natural equivalences, with L-theory homology of the underlying space. This gives a conceptual explanation of previously observed periodic patterns in lattice models and extends the picture to more general spaces. I will outline the ideas behind the construction and indicate how the framework connects topology, operator algebras, and quantum information. If time permits, I will also comment on what is known — and unknown — about the general (non-Clifford) case.

Categorical 't Hooft expansion and Chiral Algebras
2025-10-20 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Adrian López-Raven, Perimeter
Title: Categorical ‘t Hooft expansion and Chiral Algebras
Abstract: In https://arxiv.org/abs/2411.00760, we show how holographic dual B-model backgrounds can be systematically derived from the ‘t Hooft expansion of specific families of chiral algebras. The resulting holographic dual backgrounds are typically non-commutative and appear to be novel. In this talk I’ll review certain aspects of our construction. In particular, we’ll review how to build a category of D-branes for the String Theory dual, starting from the planar limit of the chiral algebra. Given its generality, I’ll emphasize the potential utility of the construction in the study of weak coupling holography for general theories with a large N limit.

CMSA Q&A Seminar: Thomas Grimm
2025-10-22 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q&A Seminar
Speaker: Thomas Grimm, Utrecht & CMSA
Topic: What is o-minimality and what is it good for?

The Carleson project: A collaborative formalization
2025-10-22 14:00 - 15:00 | Virtual
New Technologies in Mathematics Seminar
Speaker: María Inés de Frutos Fernández, Mathematical Institute, University of Bonn
Title: The Carleson project: A collaborative formalization
Abstract: A well-known result in Fourier analysis establishes that the partial Fourier sums of a smooth periodic function $f$ converge uniformly to $f$, but the situation is a lot more subtle for e.g. continuous functions. However, in 1966 Carleson proved that they do converge at almost all points for $L^2$ periodic functions on the real line. Carleson’s proof is famously hard to read, and there are no known easy proofs of this theorem. As a large collaborative project, we have formalized in Lean a generalization of Carleson’s theorem in the setting of doubling metric measure spaces (proven in 2023), and Carleson’s original result as a corollary. In this talk I will give an overview of the project, with a focus on how the collaboration was organized.

Character sheaves on the loop Lie algebra and its global implications
2025-10-23 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Algebra Seminar
Speaker: Zhiwei Yun, MIT
Title: Character sheaves on the loop Lie algebra and its global implications
Abstract: Motivated by Lusztig’s definition of character sheaves on a reductive Lie algebra, we propose a definition of character sheaves on the loop Lie algebra. The construction can be viewed as a p-adic analogue of the orbit method, and the resulting sheaves are closely related to characters of supercuspidal representations of J.K.Yu. Further, the construction suggests a definition of wildly ramified Hitchin moduli spaces suitable for the study of ramified geometric Langlands. This is joint work with Bao Chau Ngo.

On some new irrationality results
2025-10-23 16:00 - 17:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Differential Geometry and Physics Seminar
Speaker: Ron Donagi, UPenn
Title: On some new irrationality results
Abstract: An algebraic variety X is rational if a Zariski-open subset of X is isomorphic to a Zariski-open subset of projective space. A weaker property is unirationality: X is unirational if a Zariski-open subset of projective space maps onto a Zariski-open subset of X. These properties are equivalent in dimensions 1 and 2. In the seventies it was discovered that they are not equivalent in dimension 3, as several different approaches succeeded in proving irrationality of some unirational varieties. The theory of Hodge atoms, recently developed by Katzarkov, Kontsevich, Pantev and Yu, uses ideas from mirror symmetry and quantum cohomology to exhibit new birational invariants capable of proving irrationality of some 4-dimensional unirational varieties. We illustrate the power of this new technique by applying it to the 4 dimensional intersection of quadrics in P^7.

Analytic Spread of Binomial Edge Ideals
2025-10-24 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Stephen Landsittel, CMSA
Title: Analytic Spread of Binomial Edge Ideals
Abstract: To an ideal J in a polynomial ring R over a field K we associate its analytic spread ell(J), which is the dimension of the fiber cone F(J) of J. When J is graded and generated in a single degree d, then F(J) is a finite type K-algebra.
To a graph G we associate its binomial edge ideal: J_G:= (x_i y_j – x_jy_i | {i,j} is an edge of G).
In this talk we will discuss recent work where sharp bounds are given for ell(J_G) and we compute the exact value when G is a pseudoforest. We accomplish this by computing the transcendence degree trdeg_{K} F(J), of the fiber cone over K.

de Rham Theory in Derived Differential Geometry
2025-10-27 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Grigorii Taroian, U Toronto
Title: de Rham Theory in Derived Differential Geometry
Abstract: In the talk, I will describe recent progress in building a version of de Rham theory for derived manifolds and derived differentiable stacks.
Derived differential geometry is a nascent field applying techniques from derived algebraic geometry to the study of spaces with smooth structures. As such, it serves as a natural home for studying objects arising in BV formalism. For instance, concepts such as critical loci of action functionals or their quotients by gauge actions can be naturally interpreted as derived differentiable stacks.
In our work, we build a version of de Rham theory for these spaces and prove a version of the de Rham isomorphism. Due to the highly singular nature of all objects involved, developing such a theory is significantly more challenging than in the usual differential geometry, and thus, we construct our formalism with inspiration from algebraic geometry rather than classical differential topology. As a main application of the developed theory, we obtain a version of the comparison morphism between de Rham and constant sheaf cohomology arising from the corresponding map of stacks. This should enable further developments, with a view towards a fully-fledged theory of shifted symplectic structures for derived differentiable stacks.
The talk is based on a preprint of the same name, arXiv:2505.03978.

Rigidity, expansion and polytopes
2025-10-27 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Eran Nevo (Hebrew University of Jerusalem)
Title: Rigidity, expansion and polytopes
Abstract: Given a graph G and an embedding of its vertices in R^d, what continuous motions of the vertices preserve all edge lengths? Clearly all motions induced by an isometry of R^d do, these are the trivial motions; are there any others? If the answer is NO for all (equivalently, for one) generic embedding, G is called d-rigid.
What are the d-rigid graphs?
This problem has been extensively studied since the 70s, and is still widely open for d≥3. It is studied mainly from algebraic geometry and combinatorial points of view. Variants of it, especially in dimensions 2 and 3, are of importance also beyond mathematics, e.g. in structural engineering, computational biology and more.
I will focus on a quantitative version of rigidity via spectral analysis of the related stiffness matrix, including the construction of “rigidity expanders”, generalizing expander graphs. Higher dimensional notions of rigidity and of stiffness matrices, and their relation to the study of polytopes, will be addressed too.

Geometry and Quantum Theory Seminar
2025-10-28 16:15 - 18:30 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speakers: (1) Elliott Gesteau, CMSA (60 min) and (2) Sanjay Raman, Harvard (30 min)
(1) Title: Holography for closed universes
Abstract: Recent advances in holography and black hole physics have prompted a number of new puzzles related to the physics of closed universes, which can be argued to have a one-dimensional Hilbert space of states from various perspectives. In this talk I will review this new set of puzzles, with an emphasis of the mathematical questions that they seem to raise.

(2) Title: Non-supersymmetric branes, bordism, and fractional charges
Abstract: We dive a little deeper into the non-supersymmetric brane configurations studied in Kaidi-Tachikawa-Yonekura (2024). We study the gravitational analogues of the branes in the aforementioned paper, relating them to relative defects predicted by the Cobordism Conjecture, and we argue for the existence of objects carrying fractional heterotic string and M2-brane charge.

Affine Springer fibers and representations
2025-10-30 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Algebra Seminar
Speaker: Roman Bezrukavnikov, MIT
Title: Affine Springer fibers and representations
Abstract: Relating representation categories of interest, such of modules over the quantum group, to topology of loop spaces has been an important theme in representation theory for some decades. I will describe a result of this sort involving a geometric object that has not appeared in this context until now, an affine Springer fiber, and mention its applications. Based on a joint work with Pablo Boixeda Alvarez, Michael McBreen and Zhiwei Yun.

RCD structures on singular Kahler varieties
2025-10-30 16:00 - 17:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Differential Geometry and Physics Seminar
Speaker: Jian Song, Rutgers University
Title: RCD structures on singular Kahler varieties
Abstract: Let X be a 3-dimensional projective variety with klt singularities. We prove that every singular Kahler metric on X with bounded Nash entropy and Ricci curvature bounded below induces a unique compact RCD space homeomorphic to the projective variety X itself. In particular, singular Kahler- Einstein spaces of complex dimension 3 with bounded Nash entropy are compact RCD spaces topologically and holomorphically equivalent to the underlying projective variety. Such results establish connections among algebraic, geometric and analytic structures of klt singularities from birational geometry and provide abundant examples of RCD spaces from algebraic geometry via complex Monge-Ampere equations.

Skein remain the same
2025-10-31 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Sunghyuk Park, CMSA
Title: Skein remain the same
Abstract: The count of holomorphic curves in a Calabi-Yau 3-fold ending on a Lagrangian is famously not deformation invariant, but Ekholm and Shende have shown that it can be made invariant by counting in the skein. Given a 3-manifold M and a branched cover arising from the projection of a Lagrangian 3-manifold L in the cotangent bundle of M, we use the skein-valued curve count to construct a map from the skein of M to that of L. When M and L are products of surfaces and intervals, deforming L within the space of Lagrangians yields a skein-valued lift of the Kontsevich-Soibelman wall-crossing formula. After all, the skeins remain the same. Based on joint work (arXiv:2510.19041) with Tobias Ekholm, Pietro Longhi, and Vivek Shende.

A fully local extension of Chern-Simons theory
2025-11-04 16:15 - 18:30 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speaker: Dan Freed
Title: A fully local extension of Chern-Simons theory
Abstract: The Reshetikhin-Turaev-Witten invariants of 3-manifolds fit into a 3-dimensional topological field theory that also attaches invariants to 2-manifolds and 1-manifolds. It has long been asked to extend to invariants of 0-manifolds as well, a question that often takes the form: What does Chern-Simons theory attach to a point?. In joint work with Claudia Scheimbauer and Constantin Teleman we use the cobordism hypothesis to construct a fully local version of Chern-Simons theory. We also consider different versions with different tangential structures, as I will explain.

CMSA Q&A Seminar: Paul Seidel, MIT
2025-11-05 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q&A Seminar
Speaker: Paul Seidel, MIT
Topic: Fukaya categories of Landau-Ginzburg models

Discovery of unstable singularity with machine precision
2025-11-05 14:00 - 15:00 | CMSA 20 Garden Street Cambridge, Massachusetts 02138 United States
New Technologies in Mathematics Seminar
Speaker: Yongji Wang, NYU Courant Institute of Mathematical Sciences
Title: Discovery of unstable singularity with machine precision
Abstract: Whether singularities can form in fluids remains a foundational unanswered question in mathematics. This phenomenon occurs when solutions to governing equations, such as the 3D Euler equations, develop infinite gradients from smooth initial conditions. Historically, numerical approaches have primarily identified stable singularities. However, these are not expected to exist for key open problems, such as the boundary-free Euler and Navier-Stokes cases, namely the Millennium Prize problem. For these problems, the true challenge lies in finding unstable singularities, which are exceptionally elusive, as any tiny perturbation can divert the system from its blow-up trajectory.
In this talk, I will present a new computational framework which has led to the first systematic discovery of new families of unstable singularities in various fluid equations. Our approach merges curated machine learning architectures with a multi-stage training scheme and a high-precision Gauss-Newton optimizer, creating a powerful tool for navigating the complex landscape of nonlinear PDEs. Beyond discovering these singularities, the precision of this method is another key breakthrough, achieving unprecedented accuracies on the order of $O(10^{-13})$—a level constrained only by the round-off errors of the GPU hardware. This level of precision meets the stringent requirements for rigorous mathematical validation of the discovered solution via computer-assisted proofs, offering a new pathway to resolving long-standing challenges in mathematical physics.

Dimension Reduction and Adiabatic Limits of Generalized ASD Instantons
2025-11-06 16:00 - 17:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Differential Geometry and Physics Seminar
Speaker: Dylan Galt, Harvard
Title: Dimension Reduction and Adiabatic Limits of Generalized ASD Instantons
Abstract: I will begin by explaining a dimension reduction result for Tian’s generalized ASD instantons over product manifolds, which generalizes work of Yuanqi Wang on codimension-one reduction and includes the cases of G2 and Spin(7) instantons as well as degree zero Hermitian-Yang-Mills connections. The proof is inspired by a simple observation about the Yang-Mills energy and suggests a natural adiabatic picture for these generalized ASD connections. I will describe ongoing work towards establishing such an adiabatic scheme, emphasizing some of the complications that arise in the general case and explaining what can be said for G2 instantons. Everything I will talk about is joint work with my collaborator Langte Ma.

Classification of 2D Stabilizer States
2025-11-07 12:00 - 13:00 | 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.
