CMSA

Twisted D-branes and TQFTs valued in Calabi-Yau categories
2026-05-04 15:00 - 16:00 (America/New_York) | 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.

Workshop on Calabi-Yau metrics and optimal transport
2026-05-18 09:00 - 2026-05-22 17:00 | CMSA 20 Garden Street Cambridge, Massachusetts 02138 United States
Workshop on Calabi-Yau metrics and optimal transport
Dates: May 18–22, 2026
Location: Harvard CMSA, 20 Garden Street, Cambridge MA
Recent advances in the study of Calabi-Yau metrics have revealed an interesting connection with optimal transport, and the regularity theory for optimal transport is expected to play an increasingly important role in the study of Kähler geometry. The goal of this workshop is to bring together the optimal transport and complex geometry communities to investigate problems arising from these exciting developments.
Register to attend in-person
Register for Zoom Webinar

Minicourse Speakers

Robert McCann, University of Toronto
Yang Li, Cambridge University

Workshop Speakers

Rolf Andreasson, Chalmers University, Sweden
Benjy Firester, MIT
Jakob Hultgren, Umea University, Sweden
Young-Heon Kim, University of British Columbia
Nam Le, Indiana University
Jiakun Liu, University of Sydney
Arghya Rakshit, University of Toronto
Gabor Szekelyhidi, Northwestern University
Yueqiao Wu, Johns Hopkins University

Organizers:

Tristan Collins, University of Toronto
Mattias Jonsson, University of Michigan
Connor Mooney, University of California, Irvine
Freid Tong, University of Toronto

Schedule (subject to change)
Monday, May 18, 2026
9:00–9:30 am
Breakfast
9:30–10:45 am
Tutorial: Yang Li, Cambridge University (via Zoom Webinar)
10:45–11:15 am
Break
11:15 am–12:30 pm
Tutorial: Robert McCann, University of Toronto
Title: A geometric approach to apriori estimates for optimal transport maps
Abstract: A key inequality which underpins the regularity theory of optimal transport for costs satisfying the Ma-Trudinger-Wang condition is the Pogorelov second derivative bound. This translates to an a priori interior modulus of the differential estimate for smooth optimal maps. We describe a new derivation of this estimate with Brendle, Leger and Rankin which relies in part on Kim, McCann, and Warren’s observation that the graph of an optimal map becomes a volume maximizing non-timelike submanifold when the product of the source and target domains is endowed with a suitable pseudo-Riemannian geometry that combines both the marginal densities and the cost. This unexpected links optimal transport to the plateau problem in geometry with split signature, and shows the key difficulty is showing the maximizing non-timelike submanifold is in fact (uniformly) spacelike. J. Reine Angew. Math. 817 (2024) 251-266 doi.org/10.1515/crelle-2024-0071 arXiv 2311.10208
12:30–2:00 pm
Lunch (catered)
2:00–3:15 pm
Talk: Nam Le, Indiana University
Title: Variational approach to degenerate Monge-Ampère equations with mixed measures and monotonicity
Abstract: In this talk, we will discuss the solvability and uniqueness for several degenerate Monge-Ampère equations including the Monge-Ampère eigenvalue problem in real Euclidean spaces that involve singular Borel measures. Our approach systematically analyzes the Monge-Ampère energy from the variational point of view and appropriately exploits monotonicity arguments. We will examine several essential tools: the mixed Monge-Ampère measure, Aleksandrov-Blocki-Jerison type maximum principles, convex envelope, comparison principles for subcritical equations, and integration by parts whose failure leads to symmetry breaking and nonuniqueness phenomena.
3:15–3:45 pm
Break
3:45–5:00 pm
Talk: Yueqiao Wu, Johns Hopkins University
Title: Valuative aspects of complete Calabi-Yau metrics of Euclidean volume growth
Abstract: The search of a complete Calabi-Yau metric on an affine variety X amounts to solving a complex Monge-Ampère equation subject to nice “boundary conditions” at infinity. In the case where X is the complement of an SNC anticanonical divisor on a Fano manifold, generalizing the work of Tian-Yau, Collins-Li showed that such boundary data can be extracted from solutions to certain real Monge-Ampère equations. If we require the metric to have Euclidean volume growth, however, it is understood that the boundary conditions should come from prescribing a Calabi-Yau asymptotic cone at infinity. This is the same as giving the algebro-geometric data of a valuation which induces a degeneration of X to a K-stable affine cone. In this talk, we will explain that such valuations in fact always come from Fano type compactifications of X, similar to the ones considered by Tian-Yau and Collins-Li. In addition, K-semistability of the affine cone can be characterized intrinsically by a valuative criterion on X. Based on joint work with Mattias Jonsson.

Tuesday, May 19, 2026
9:00–9:30 am
Breakfast
9:30–10:45 am
Tutorial: Robert McCann, University of Toronto
Title: Trading linearity for ellipticity: A low regularity Lorentzian splitting theorem
Abstract: While Einstein’s theory of gravity is formulated in a smooth setting, the celebrated singularity theorems of Hawking and Penrose describe many physical situations in which this smoothness must eventually breakdown. It is thus of great interest to study the theory in low regularity settings. In the lecture, we establish a low regularity splitting theorem by sacrificing linearity of the d’Alembertian to recover ellipticity. We exploit a negative homogeneity $p$-d’Alembert operator for this purpose. The same technique yields a simplified proof of Eschenberg (1988) Galloway (1989) and Newman’s (1990) confirmation of Yau’s (1982) conjecture, bringing all three Lorentzian splitting results into a framework closer to the Cheeger-Gromoll splitting theorem from Riemannian geometry. Based on joint work with Mathias Braun, Nicola Gigli, Argam Ohanyan, and Clemens Saemann: 1) arXiv 2501.00702 2) arXiv 2408.15968 3) arXiv 2410.12632 4) arXiv 2507.06836
10:45–11:15 am
Break
11:15 am–12:30 pm
Tutorial: Yang Li, Cambridge University (via Zoom Webinar)
12:30–2:00 pm
Lunch Break
2:00–3:15 pm
Talk: Young-Heon Kim, University of British Columbia
Title: Trajectory Inference via Multi-marginal Schrödinger Bridges
Abstract: Trajectory inference arises in important scientific problems. In particular, biological development can be interpreted as a curve in the space of gene-expression distributions, and the goal is to infer this trajectory from observed data. There has been progress by using optimal transport (OT) as a way to interpolate between distributions. More recently, Schrödinger bridges, a stochastic generalization of OT, have been considered. In this talk, we discuss stability of such OT-based methods. This is joint work with Geoffrey Schiebinger and Rentian Yao.
3:15–3:45 pm
Break
3:45–5:00 pm
tba
6:30 pm
Dinner

Wednesday, May 20, 2026
9:00–9:30 am
Breakfast
9:30–10:45 am
Tutorial: Yang Li, Cambridge University (via Zoom Webinar)
10:45–11:15 am
Break
11:15 am–12:30 pm
Tutorial: Robert McCann, University of Toronto
Title: The monopolist’s free boundary problem in the plane: an excursion into the economic value of private information
Abstract: The principal-agent problem is an important paradigm in economic theory for studying the value of private information: the nonlinear pricing problem faced by a monopolist is one example; others include optimal taxation and auction design. For multidimensional spaces of consumers (i.e. agents) and products, Rochet and Chone (1998) reformulated this problem as a concave maximization over the set of convex functions, by assuming agent preferences are bilinear in the product and agent parameters. This optimization corresponds mathematically to a convexity-constrained obstacle problem. The solution is divided into multiple regions, according to the rank of the Hessian of the optimizer.
If the monopolists costs grow quadratically with the product type we show that a partially smooth free boundary delineates the region where it becomes efficient to customize products for individual buyers. We give the first complete solution of the problem on square domains, and discover new transitions from unbunched to targeted and from targeted to blunt bunching as market conditions become more and more favorable to the seller.
Based on works with Kelvin Shuangjian Zhang, Cale Rankin, and Lucas O’Brien in various combinations:
1) Math. Models Methods Appl. Sci. 34 (2024) 2351-2394; 2) J. Convex Anal. (Rockafellar 90 Issue), 32 (2) (2025) 579-584; 3) arXiv 2303.04937; 4) arxiv 2412.15505; 5) arXiv 2603.14100.

Thursday, May 21, 2026
9:00–9:30 am
Breakfast
9:30–10:45 am
Talk: Gabor Szekelyhidi, Northwestern University
Title: Nondegenerate Neck Pinches along the 2d Lagrangian mean curvature flow
Abstract: The Thomas-Yau-Joyce conjecture predicts that the mean curvature flow can be used to decompose Lagrangian submanifolds in Calabi-Yau manifolds into special Lagrangian building blocks. The basic mechanism for this decomposition is given by neck pinches. I will discuss work on the behavior of such neck-pinch singularities, in particular the class of nondegenerate neck pinches, which satisfy certain properties conjectured by Joyce. The construction also relates to work of Neves on finite time singularity formation.
10:45–11:15 am
Break
11:15 am–12:30 pm
Talk: Rolf Andreasson, Chalmers University, Sweden
Title: Optimal transport between boundaries of dual reflexive polytope
Abstract: I will present an optimal transport problem between the boundaries of a pair of reflexive polytopes. Under a certain structural condition on its solution, this problem is related the study of metric degenerations of families of Calabi–Yau hypersurfaces in the corresponding toric Fano variety. A better understanding of such solutions and their regularity would shed light on several aspects of the degeneration and conjectural Gromov–Hausdorff limit, and I will present some open directions of research. This is based on joint work with Jakob Hultgren, Mattias Jonsson, Enrica Mazzon and Nicholas McCleerey.
12:30–2:00 pm
Lunch Break
2:00–3:15 pm
Talk: Jakob Hultgren, Umea University, Sweden
Title: Affine mondoromy, cost functions and real Monge-Ampère equations
Abstract: Recent results of Blum-Liu and Y. Li show that the metric SYZ conjecture holds. The solution hinges on the existence of valuatively independent bases for spaces of sections of the polarising bundle. These bases induce a cost function, providing a link between the non-Archimedean Monge-Ampère equation and optimal transport. The resulting SYZ-fibration is constructed on a large but non-explicit set. In order to better understand this set, more information about the cost function is arguably needed. We propose a cost function explicitly computable from the monodromy of an affine structure on the essential skeleton. In the case of the Fermat family of cubic curves, this cost function (as opposed to the one attained from the ambient projective space) can be shown to agree with the one attained from a valuatively independent basis. We conjecture that this equality of cost functions holds in general, and demonstrate in examples how the explicit cost function can be used to directly produce solutions to real Monge-Ampère equations on the essential skeleton. Joint work with Sohaib Khalid.
3:15–3:45 pm
Break
3:45–5:00 pm
Talk: Benjy Firester, MIT
Title: Free boundary Monge-Ampere equations with applications to optimal transport and Calabi-Yau geometry
Abstract: I will present a variational framework to solve a general class of free-boundary Monge-Ampère equations. This approach combines the classical first and second boundary value problems by imposing both the boundary data and the gradient image of the solution. I will explore applications to the Monge-Ampère eigenvalue problem, convex reconstruction theorems, and geometric problems including a hemispherical Minkowski problem, Calabi-Yau metrics, and free boundary toric Kähler–Einstein/Kähler-Ricci soliton metrics. I will also discuss the connection to the boundary regularity of optimal transport.

Friday, May 22, 2026
9:00–9:30 am
Breakfast
9:30–10:45 am
Talk: Jiakun Liu, University of Sydney
Title: Free boundary problems in optimal transportation
Abstract: In this talk, I will present some recent results on the regularity of free boundaries in optimal transportation, including higher-order regularity, global regularity, and a model case involving multiple targets. These results are based on a series of joint works with Shibing Chen, Xianduo Wang, and Xu-Jia Wang.
10:45–11:15 am
Break
11:15 am–12:30 pm
Talk: Arghya Rakshit, University of Toronto
Title: Solutions to the Monge–Ampère equation with singular structures
Abstract: We construct examples of solutions to the Monge–Ampère equation with point masses exhibiting polyhedral singular structures. We further analyze the stability of these singular sets under small perturbations of the data. In addition, we construct solutions whose Monge–Ampère measure contains a singular component supported on lower-dimensional sets and we study the regularity of such solutions.

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.

Big Data Conference 2026
2026-09-03 09:00 - 2026-09-04 17:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Big Data Conference 2026
Dates: Sep. 3–4, 2026
Location: Harvard University CMSA, 20 Garden Street, Cambridge & via Zoom
The Big Data Conference features speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics.
Register to attend in person
Register for Zoom Webinar

Details TBA

The Geometry of Machine Learning 2026
2026-09-08 09:00 - 2026-09-11 17:00 | CMSA 20 Garden Street Cambridge, Massachusetts 02138 United States
The Geometry of Machine Learning 2026
Dates: September 8–11, 2026
Location: Harvard CMSA, Room G10, 20 Garden Street, Cambridge MA 02138
Organizers: Michael R. Douglas (CMSA) and Mike Freedman (CMSA)

Details TBA

Support provided by Logical Intelligence.

Lagrangian Floer theory and Applications Program
2026-09-15 09:00 - 2026-11-21 17:00 | CMSA 20 Garden Street Cambridge, Massachusetts 02138 United States
Lagrangian Floer theory and Applications Program
Dates: September 15-November 21, 2026
Location: CMSA G10, 20 Garden St., Cambridge MA 02138
This thematic program will focus on recent developments in Lagrangian Floer theory and applications. These i
nclude the development of family Floer theory, degeneration techniques, Floer homotopy theory in the Lagrangian case, Floer theory in prime characteristic, and applications to problems in singularity theory, geometry and dynamics.
A one-week workshop will be held near the start of the program (September 28 – October 2, 2026), with the same title as the thematic program.
Organizers: Denis Auroux (Harvard), Jonny Evans (Lancaster), and Chris Woodward (Rutgers)

To express interest in attending the workshop or program, and to apply for funding if available, please fill out the form.
Funding from the National Science Foundation may be available for US-based graduate students and postdoctoral fellows.

image: Water Sky Garden, Vancouver
Date: 31 January 2010, 12:57:46
Source: Studio Echelman
Author: Peter Vanderwarker, Studio Echelman

CMSA/Tsinghua Math-Science Literature Lecture: Robert Gompf
2026-09-16 09:00 - 10:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA/Tsinghua Math-Science Literature Lecture
Date: September 16, 2026
Time: 9:00 – 10:30 am ET
Location: CMSA G10, 20 Garden Street & via Zoom Webinar
Speaker: Robert E. Gompf, University of Texas, Austin

Beginning in Spring 2020, the CMSA began hosting a lecture series on literature in the mathematical sciences, with a focus on significant developments in mathematics that have influenced the discipline, and the lifetime accomplishments of significant scholars.

CMSA Q&A Seminar: Hugh Woodin, Harvard
2026-09-16 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

Workshop on Lagrangian Floer theory and applications
2026-09-28 08:00 - 2026-10-02 17:00 | CMSA 20 Garden Street Cambridge, Massachusetts 02138 United States
Workshop on Lagrangian Floer theory and applications
Dates: September 28 – October 2, 2026
Location: CMSA G10, 20 Garden St., Cambridge MA 02138
This workshop is part of the Lagrangian Floer theory and applications Program

Organizers: Denis Auroux (Harvard), Jonny Evans (Lancaster), and Chris Woodward (Rutgers)

details tba

Northeast Conference on Categorical Methods
2026-11-06 09:00 - 2026-11-07 17:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Northeast Conference on Categorical Methods

This conference is intended to bring together researchers in all areas of mathematics and mathematical physics whose work involves the use of methods from categorical algebra, abstract homotopy theory, and higher category theory. Our goal is to showcase new, exciting research and offer an avenue for researchers from the Northeast US to discuss their work and collaborate with people in this ever-growing community.
Organized by Dan Freed, Harvard Math & CMSA; Owen Gwilliam, UMass Amherst; and Lorenzo Riva, Harvard CMSA

Stable Homotopy Theory and Arithmetic Geometry
2027-02-15 08:00 - 2027-05-15 17:00 | CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Stable Homotopy Theory and Arithmetic Geometry
Dates: Feb 15–May 15, 2027
Location: Harvard CMSA, 20 Garden St, Cambridge MA
This program will focus on interactions between stable homotopy theory and arithmetic geometry. In recent years, ideas from homotopy theory have begun to play an important role in areas such as p-adic cohomology, prismatic methods, and aspects of the Langlands program, while techniques from arithmetic geometry have led to new insights and computations in chromatic homotopy theory. Despite this growing overlap, researchers in the two areas often use different languages and tools. A central goal of the program is to make these ideas more accessible across fields and to encourage collaborations around shared problems.
The program will run from February 15 to May 15 and will be built around research and informal collaboration. It will begin with a short introductory bootcamp, followed by two focused workshops (one near the start and one toward the end), a weekly seminar with broadly accessible talks, and a weekly open-problem session. Most of the time will be left open for discussion and joint work among participants, aiming to spark new projects and longer-term connections between the two communities.
The program will include:
(1) a bootcamp during the week Feb. 22–26, consisting of introductory lectures on both subjects;
(2) two research workshops—one during Mar. 1–5 and one during May 3–7—highlighting current developments, especially those at the interface of the two areas;
(3) a weekly seminar featuring talks of broad relevance to participants; and
(4) a weekly open-problem seminar aimed at proposing and developing collaborative research directions, both for the duration of the program and beyond.
Register Online

Organizers: Tomer Schlank (Harvard), Jared Weinstein (Boston University), Mark Kisin (Harvard), Jeremy Hahn (MIT), Lucas Mann (Münster)
