Abelian duality via derived geometry
2026-05-18 15:00 - 16:00 (America/New_York) | 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.

Introduction to First Proof: A conversation
2026-06-03 13:00 - 14:00 | Virtual
Introduction to First Proof: A conversation
Date: June 3, 2026
Time: 1:00–2:00 pm
Location: via Webinar
Harvard CMSA Director Dan Freed will lead a dialogue with First Proof Editors Mohammed Abouzaid (Stanford), Nikhil Srivastava (UC Berkeley), Rachel Ward (UT Austin), and Lauren Williams (Harvard) to explore the origins and goals of First Proof, sample some of their current work, and discuss their future plans. This hour-long conversation will give a window into the fast-moving and deep interaction of Mathematics and AI.

First Proof, Second Batch: Results
2026-06-10 13:00 - 14:00 | Virtual
First Proof, Second Batch: Results
Date: June 10, 2026
Time: 1:00–2:00 pm ET
Location: via Webinar
The First Proof Editors present the results of their Second Batch benchmark testing on AI systems.
First Proof Editors

Mohammed Abouzaid (Stanford)
Nikhil Srivastava (UC Berkeley)
Rachel Ward (UT Austin)
Lauren Williams (Harvard)

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

Confirmed Speakers

SueYeon Chung, Harvard
Bailey Flanigan, MIT
Sergey Ovchinnikov, MIT
Adit Radhakrishnan, MIT
Andrew Sutherland, MIT
Chris Wiggins, Columbia
Rex Ying, Yale
Wei Zhou, Harvard

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
Register to attend in person
Register for Zoom Webinar

Confirmed Speakers:

Nada Amin, Harvard
Randall Balestriero, Brown
Michael Brenner, Harvard and Google
Bennet Chow, UCSD
Surya Ganguli, Stanford
Boris Hanin, Princeton
Roi Holtzman, Oxford
Dimitry Krotov, IAS
Slava Krushkal, Virginia
Mike Mulligan, UCR, Logical Intelligence
Gabriele Poesia, Stanford
Mathew Vanherreweghe, Logical Intelligence
Sean Welleck, CMU (via Zoom)
Mattiew Wyart, JHU

Organizers: Michael R. Douglas (CMSA) and Mike Freedman (CMSA)

Details TBA

Support provided by Logical Intelligence.

AI for the Working Mathematician
2026-09-09 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
AI for the Working Mathematician
Speaker: Daniel Litt, University of Toronto
Title: TBA

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 include 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

Ahlfors Lectures: Mohammed Abouzaid
2026-09-16 - 2026-09-17 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
Ahlfors Lectures
Dates: September 16 & 17, 2026
Time: 4:00–5:00 pm
Speaker: Mohammed Abouzaid (Stanford)
Register to attend in person or online at: https://www.math.harvard.edu/event/ahlfors-lecture-series-mohammed-abouzaid/

September 16, 2026
Title: Framed bordism and nearby Lagrangians
Abstract: The problem of understanding Lagrangian embeddings in symplectic manifolds remains a mystery. The simplest class of symplectic manifolds are the cotangent bundles of smooth manifolds, which is the setting for the most prominent open problem in the subject: Arnold’s nearby Lagrangian conjecture which asserts the connectedness of the space of Lagrangians for which the relative class of the symplectic form vanishes. In particular, the conjecture asserts that all such submanifolds are diffeomorphic. In view of recent work with Alvarez-Gavela, Courte, and Kragh, as well as work of Procelli and Smith, I will use the question as a motivation for joint work with Andrew Blumberg on a bordism-theoretic approach to define bordism-valued refinements of Floer homology.

September 17, 2026
Title: Complex bordism and Hamiltonian fibrations
Abstract: As a consequence of his theory of weights, Deligne proved that smooth complex projective varieties, carrying a smooth morphism to the projective line, have rational cohomology groups that are isomorphic to the tensor product of the cohomology of the fibre with that of the base. In joint work with McLean and Smith, we should that the result not only holds for symplectic manifolds, but is in fact a consequence of an analogous result that holds for complex cobordism. The proof identifies bordism of “stably complex derived orbifolds” as the correct framework in which to formulate these results, and I will discuss joint work with Shaoyun Bai to understand these bordism groups.
The Ahlfors Lecture Series is presented by the Harvard University Math Department in memory of Professor Lars Ahlfors.

CMSA/Tsinghua Math-Science Literature Lecture: Robert Gompf: On classifying smoothings of R^4–from the beginning to the present
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

Please register to attend
In-person registration

Zoom Webinar registration

Speaker: Robert E. Gompf, University of Texas, Austin
Title: On classifying smoothings of R^4–from the beginning to the present
Abstract: The field of 4-manifold topology was born around 1981 with two independent revolutionary breakthroughs, by Fields medalists Michael Freedman and Simon Donaldson. Freedman showed that topological 4-manifolds obeyed the well-developed theory of higher-dimensional manifolds, while Donaldson used nonlinear analysis (gauge theory) to show that smooth 4-manifolds are quite different from their high-dimensional counterparts. The clash between the two theories makes 4-manifold topology uniquely intricate within manifold theory. One of the most startling consequences is that unlike in other dimensions, Euclidean 4-space R^4 admits exotic smoothings. Equivalently, there are smooth 4-manifolds that are homeomorphic, but not diffeomorphic, to R^4. We will trace the classification theory of these manifolds from their discovery to the most recent development (joint with Aristotelis Panagiotopoulos) that they cannot be classified by any countable family of numerical invariants.

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 Special Seminar: Thanasis Fokas, University of Cambridge
2026-09-22 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Special Seminar
Speaker: Thanasis Fokas, University of Cambridge

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

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

Invited Speakers

Mohammed Abouzaid, Stanford University
Octav Cornea, University of Montréal
Tobias Ekholm, Uppsala University
Sheel Ganatra, USC
Andrew Hanlon, University of Oregon
Yanki Lekili, Imperial College London
Mark Mclean, Stonybrook
Georgios Dimitroglou Rizell, Uppsala University
Paul Seidel, MIT
Egor Shelukhin, University of Montréal
Vivek Shende, Berkeley/Syddansk
Siu-Cheong Lau, Boston University

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

AI for the Working Mathematician
2026-10-09 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
AI for the Working Mathematician
Speaker: Jordan Ellenberg, University of Wisconsin-Madison
Title: TBA

Math Science Lectures in Honor of Raoul Bott | Daniel Litt, U Toronto
2026-10-19 16:00 - 17:00 | Massachusetts
TITLE TBA
Dates: October 19 & 21, 2026
Time: 4:00–5:00 pm ET
Location: Science Center Lecture Hall A and via Webinar
In-person registration
Webinar Registration

Speaker: Daniel Litt, University of Toronto & Benedict H. Gross Distinguished Visitor, Harvard Mathematics Department
Lecture 1: Monday, October 19, 2026, followed by a reception in the Math Dept Austine & Chilton McDonnell Common Room, 4th floor

Lecture 2: Wednesday, October 21, 2026

Harvard Mathematics Professor Raoul Bott (1923 – 2005), was a Hungarian-American mathematician known for numerous foundational contributions to geometry in its broad sense. He is best known for his Bott periodicity theorem, the Morse–Bott functions which he used in this context, and the Borel–Bott–Weil theorem.

Math Science Lectures in Honor of Raoul Bott | Daniel Litt, Benedict H. Gross Distinguished Visitor, Harvard Mathematics Department
2026-10-21 16:00 - 17:00 | Massachusetts
TITLE TBA
Dates: October 19 & 21, 2026
Time: 4:00–5:00 pm ET
Location: Science Center Lecture Hall A and via Webinar
In-person registration
Webinar Registration

Speaker: Daniel Litt, Benedict H. Gross Distinguished Visitor, Harvard Mathematics Department
Lecture 1: Monday, October 19, 2026, followed by a reception in the Math Dept Austine & Chilton McDonnell Common Room, 4th floor

Lecture 2: Wednesday, October 21, 2026

Harvard Mathematics Professor Raoul Bott (1923 – 2005), was a Hungarian-American mathematician known for numerous foundational contributions to geometry in its broad sense. He is best known for his Bott periodicity theorem, the Morse–Bott functions which he used in this context, and the Borel–Bott–Weil theorem.

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
Dates: November 6–​7, 2026
Location: CMSA G10, 20 Garden St., Cambridge MA 02138

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.

There will be time for 4 short talks by early-career mathematicians.

REGISTRATION FORM (link)

Invited Speakers

Andrew Blumberg, Columbia University
Soren Galatius, Columbia University
Tony Pantev, University of Pennsylvania
Nick Rozenblyum, University of Toronto
Tomer Schlank, University of Chicago/Harvard University
Brian Williams, Boston University
Inna Zakharevich, Cornell University

Organized by Dan Freed, Harvard Math & CMSA; Owen Gwilliam, UMass Amherst; and Lorenzo Riva, Harvard CMSA

Differential Geometry and Physics Seminar
2026-12-03 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Differential Geometry and Physics Seminar
Speaker: Paul Feehan, Rutgers University
Title: TBA

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)

Stable Homotopy Theory and Arithmetic Geometry Boot Camp
2027-02-22 09:00 - 2027-02-26 17:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Stable Homotopy Theory and Arithmetic Geometry Boot Camp
Dates: February 22-26, 2027

Stable Homotopy Theory and Arithmetic Geometry Workshop I
2027-03-01 09:00 - 2027-03-05 17:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Stable Homotopy Theory and Arithmetic Geometry Workshop I
Dates: March 1–5, 2027

Seventh Annual Yip Lecture | L. Mahadevan, Harvard
2027-03-03 16:00 - 17:00 | Massachusetts
Sixth Annual Yip Lecture
Date: Wednesday, March 3, 2027
Time: 4:00–5:00 pm
Location: Harvard Science Center Hall D & via Zoom Webinar
Speaker: L. Mahadevan, Harvard

The Yip Lecture takes place thanks to the support of Dr. Shing-Yiu Yip.

2027 Ding Shum Lecture: Avi Wigderson, IAS
2027-03-31 16:00 - 17:00 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
2026 Ding Shum Lecture
Date: Wednedsay, March 31, 2027
Time: 4:00 pm
Location: Harvard Science Center Hall D & via Zoom Webinar
A reception will follow the talk in the Mathematics Department Austine & Chilton McDonnell Common Room, 4th floor, Science Center.
Speaker: Avi Wigderson, IAS

This event is made possible by the generous funding of Ding Lei and Harry Shum.

Stable Homotopy Theory and Arithmetic Geometry Workshop II
2027-05-03 09:00 - 2027-05-07 17:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Stable Homotopy Theory and Arithmetic Geometry Workshop II
Dates: May 3–7, 2027

CMSA Quantum Field Theory Program
2027-08-30 09:00 - 2028-05-05 17:00 | Hybrid – G10
CMSA Quantum Field Theory Program
Dates: August 30, 2027 – May 5, 2028
Location: Harvard CMSA, 20 Garden Street, Cambridge MA
Quantum field theory (QFT) has long been a subject with a large influence on mathematics, yet there is still no unified mathematical framework that encompasses all viewpoints. Constructive QFT and Algebraic QFT—typified by the Wightman and Haag-Kastler axiom systems, respectively—have many achievements in relativistic and Euclidean QFT, but they do not include Wick-rotated theories on compact manifolds and so miss many of the geometric, topological, and algebraic developments of the past several decades. These developments include supersymmetric QFT and applications to geometry and topology, generalized symmetries in QFT, and a robust mathematical theory of topological QFTs. The more recent Segal and Costello-Gwilliam axiom systems do accommodate some of these developments, but they are largely disjoint from the analytic progress. Techniques from probability theory and stochastic PDE have been used to advance traditional constructive and algebraic QFT; they have also been applied to obtain rigorous results in two-dimensional conformal field theory and Euclidean lattice gauge theories. There has also been recent progress in quantum lattice systems, revealing surprising new bridges between operator algebras and topology.
This special year at CMSA aims to shape the direction of the field by bringing the analytic and geometric threads of mathematical QFT into closer contact. The program will gather a diverse group of mathematicians together with physicists who enjoy close interactions with mathematicians. The year will be organized around the four focus areas listed below. There will be several short courses and one weeklong workshop for each of these focus areas. All lectures will be hybrid.
FOCUS AREAS
First Semester

Axiomatic approaches to QFT
Symmetry, anomalies, and topology

Second Semester

Probabilistic methods in QFT
Supersymmetry, geometry, and moduli spaces

SIGN UP
We welcome long-term visitors as well as short-term visitors and online participants. If you would like to participate in the program, other than the workshops, please click here: Visitor Form
If you would like to be on a mailing list for information and announcements about this special year, please click here: Subscribe to the CMSA QFT Program Mailing List

Organizers:

Sourav Chatterjee (Stanford University)
Clay Cordova (University of Chicago)
Dan Freed (Harvard University)
Anton Kapustin (Caltech)
Constantin Teleman (University of California, Berkeley)
