Exotic R^4's are unclassifiable
2026-03-27 15:00 - 17:15 (America/New_York) | Virtual
Freedman Seminar
Speaker: Robert Gompf, UT Austin
Title: Exotic R^4’s are unclassifiable
Abstract: We will use descriptive set theory to show that there is a precise sense in which exotic R^4’s are unclassifiable. For other open manifolds, we can reach a much higher level of unclassifiability. This is work in progress with Aristotelis Panagiotopoulos.

K-theoretic stable envelopes, quantum loop groups and wall-crossings
2026-03-30 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Tianqin Zhu, Columbia University
Title: K-theoretic stable envelopes, quantum loop groups and wall-crossings
Abstract: The stable envelope is an important tool in both geometric representation theory and the enumerative geometry. One of the most important application is that it generates the geometric quantum loop group via the FRT formalism. In this talk, we will show that the geometric quantum loop group is isomorphic to the Drinfeld double given by the preprojective K-theoretic Hall algebra and the nilpotent K-theoretic Hall algebra. Moreover we will show a more refined result that the wall-crossing for the K-theoretic stable envelope is controlled by the universal R-matrix for the slope subalgebra of the Drinfeld double, which leads to the isomorphism between the wall subalgebra in geometric quantum loop groups and the slope subalgebras in the Drinfeld double. If time permits, I will talk about the recent progress of such isomorphism in the case of the critcial stable envelopes in both critical K-theory and critical cohomology. This is based on the work 2511.02161

1-shifted Yangians from 1-shifted Lie bialgebras
2026-03-31 16:15 - 18:00 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Joint Math/CMSA Geometry and Quantum Theory Seminar
Speaker: Vasily Krylov, Harvard
Title: 1-shifted Yangians from 1-shifted Lie bialgebras
Abstract: In the previous talk, Keyou explained that the fusion of line defects in 3d holomorphic–topological field theories is expected to be governed by so-called DG-shifted Yangians. Following arXiv:2503.08770, I will present examples of such DG-shifted Yangians arising from 1-shifted Lie bialgebras. We will discuss both the classical and DG-shifted settings from a purely mathematical perspective.

CMSA Q&A Seminar: Lauren Williams, Harvard
2026-04-01 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q&A Seminar
Speaker: Lauren Williams, Harvard
Topic: The First Proof Project

Failures of Holographic Emergence
2026-04-03 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Elliott Gesteau, CMSA
Title: Failures of Holographic Emergence
Abstract: Recent developments have taught us that some semiclassical spacetimes, in particular those containing closed universe components, cannot emerge from a holographic correspondence. In this talk, I will explain how one can get to this conclusion by using either quantum information theory or properties of the large N limit of AdS/CFT, and propose a criterion for detecting failures of spacetime emergence.

Twistorial constructions of higher genus integrability
2026-04-06 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Seraphim Jarov, Perimeter Institute
Title: Twistorial constructions of higher genus integrability
Abstract: I will present a new method to engineer integrable models in 4d with higher genus spectral parameters. The method has a twistorial origin – by working on a branched covering of twistor space, I show how one can derive deformations of holomorphic BF theory on twistor space which descend to elliptic and hyperelliptic models on R^4 via the Penrose transform. I show how one can bootstrap the Penrose transformed actions using symmetry and integrability to find deformations of self-dual Yang-Mills theory. I will also discuss some novel deformations of a BF type description of Hitchin’s equations. This is based on my paper: 2509.12486

Facets of link homology
2026-04-06 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Mikhail Khovanov, Johns Hopkins University
Title: Facets of link homology
Abstract: We will review some link homology theories of algebraic origin and their connections to representation theory and geometry.

A Mumford form on infinite Grassmannians
2026-04-07 16:15 - 18:00 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Joint Math/CMSA Geometry and Quantum Theory Seminar
Speaker: Oswaldo Vázquez (Harvard)
Title: A Mumford form on infinite Grassmannians
Abstract: The Polyakov measure in bosonic string theory can be expressed in terms of the Mumford form, which is a trivializing section of a product of determinant line bundles over the moduli space of genus g curves. We will discuss the work in https://arxiv.org/abs/2412.18570, which reviews how the moduli space can be embedded in an infinite dimensional Grassmannian as a Virasoro orbit and generalizes the Mumford form to other such orbits. In particular, this “universal Mumford form” can be described in terms of coordinates in the Grassmannian, which are amenable to computation and thus could have implications to the evaluation of amplitudes.

Multiplicities of graded families of ideals on Noetherian local rings
2026-04-09 16:00 - 17:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Algebra Seminar
Speaker: Dale Cutkosky, University of Missouri
Title: Multiplicities of graded families of ideals on Noetherian local rings
Abstract: Let $R$ be an arbitrary $d$-dimensional Noetherian local ring with maximal ideal $m_R$. In this talk, we give a generalization of the multiplicity $e(I)$ of an $m_R$-primary ideal $I$ of $R$ to a multiplicity $e(mathcal I)$ of a graded family of $m_R$-primary ideals $mathcal I$ in $R$. This multiplicity gives the classical multiplicity $e(I)$ if $mathcal I={I^n}$ is the $I$-adic filtration, and agrees with the volume, $lim_{nrightarrow infty}d!frac{ell(R/I_n) }{n^d}$ for $R$ such that $dim N(hat R)>d$, the required condition for the volume of graded families of $m_R$-primary ideals to exist as a limit. We will show that many of the classical theorems for the multiplicity of an ideal generalize to this multiplicity, including mixed multiplicities, the Rees theorem and the Minkowski inequality and equality. We give proofs which are independent of the theory of volumes and Okounkov bodies for all of our results, with the one exception being the proof of the Minkowski equality. We do this by interpreting the multiplicity of graded families of $m_R$-primary ideals as an intersection product on the family of $R$-schemes which are obtained by blowing up $m_R$-primary ideals in $R$.

Quantum topology from dynamics
2026-04-10 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Sunghyuk Park, CMSA
Title: Quantum topology from dynamics
Abstract: Dynamics studies the long-term behavior of systems that evolve over time, such as the famous Lorenz system.
Quantum topology, by contrast, studies knots and low-dimensional manifolds through invariants that are usually constructed using representation-theoretic tools. In this talk, I will explain how quantum invariants of knots and 3-manifolds can be recovered from the dynamics of certain three-dimensional flows. Time permitting, I will also explain how this new bridge arises from ideas in topological string theory.

Abelian gauge fields and duality
2026-04-14 16:15 - 18:00 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Joint Math/CMSA Geometry and Quantum Theory Seminar
Speaker: Dan Freed, Harvard Math & CMSA
Title: Abelian gauge fields and duality
Abstract: Motivated by the new paper arXiv:2603.19161, I will give a general talk about abelian gauge fields, including duality. I will start with classical Maxwell theory, then discuss various “finite” examples, the typical p-form abelian gauge field, and some exotic examples such as Ramond–Ramond fields and the B-field in superstring theory. I will then get to the new paper and, time permitting, will suggest a very general framework that covers all examples.

Swampland and our Universe
2026-04-15 08:00 - 2026-04-16 17:00 | CMSA 20 Garden Street Cambridge, Massachusetts 02138 United States
Swampland and our Universe
Dates: April 15–16, 2026
Location: Harvard CMSA, Room G10, 20 Garden Street, Cambridge MA
The swampland program has inspired a range of new ideas in both cosmology and neutrino physics. This workshop brings together experts in neutrino physics, dark energy, dark matter, early-universe cosmology, and string theory to share insights on these developments and to discuss current and future experimental tests.
Speakers

Ignatios Antoniadis, IAS, Princeton
Alek Bedroya, Princeton
Mike Boylan-Kolchin, UT Austin
M.C. Gonzalez-Garcia, YITP Stony Brook & ICREA U. Barcelona
Mustapha Ishak-Boushaki, UT Dallas
Marc Kamionkowski, Johns Hopkins
Miguel Montero, Institute of Theoretical Physics, Madrid
Georges Obied, U Chicago
Matt Reece, Harvard
Tracy Slatyer, MIT

Organizers: Luis Anchordoqui (CUNY Lehman College), Sonia Paban (Harvard Physics), and Cumrun Vafa (Harvard Physics)

Videos are available on the CMSA Youtube Swampland Playlist
Schedule
(download pdf)
Wednesday, Apr. 15, 2026
8:00–9:00 am
Breakfast
9:00–10:00 am
Marc Kamionkowski, Johns Hopkins: Dark-matter dynamics and new physics
Abstract: Galactic halos that are spherical, stationary, and composed of collisionless dark matter are easy to describe mathematically. If dark matter decays or interacts or there is some departure from equilibrium or time evolution of the system, all bets are off. In this case costly N-body simulations are required. If, however, one retains the assumption of spherical symmetry, these systems can be evolved numerically with a far simpler algorithm that is easily coded run in a matter of minutes on a laptop, rather than a day on a supercomputer. I will describe this approach and illustrate with simulations of self-interacting dark matter, decaying dark matter (with and without anisotropic velocity distributions, supermassive-black-hole growth, tidal stripping, mixed SIDM/CDM models. Come prepared with your own non-standard dark-matter model; we’ll see if we can simulate it during the talk!
10:00–10:30 am
Coffee Break
10:30–11:30 am
Tracy Slatyer, MIT: What (more) the CMB can teach us about dark matter
Abstract: Observations of the cosmic microwave background have already provided critical evidence for dark matter, but can also stringently constrain a range of dark matter properties. I will outline CMB constraints on dark matter properties based on purely gravitational effects, and then discuss in more detail how both CMB anisotropies and the blackbody spectrum can be used to test dark matter interactions with the Standard Model.
11:30 am–1:00 pm
Lunch Break (catered)
1:00–2:00 pm
Alek Bedroya, Princeton: How Quantum Gravity Constrains Physics on the Largest Length Scales
Abstract: I will review the hierarchy of energy scales in quantum gravity, from the Hubble scale in the IR to the quantum-gravity cutoff and the Planck scale in the UV, and emphasize the nontrivial UV/IR relations that connect them. I will discuss conjectures constraining scalar potentials and explain how they are related to the behavior of the other energy scales, together with bottom-up arguments based on general principles of quantum gravity such as holography. In particular, I will explain how well-motivated holographic assumptions lead to strong restrictions on scalar potentials, ruling out parametrically prolonged accelerated expansion for positive potentials and obstructing parametric scale separation for negative potentials associated with AdS vacua. Title: How Quantum Gravity Constrains Physics on the Largest Length Scales
Abstract: I will review the hierarchy of energy scales in quantum gravity, from the Hubble scale in the IR to the quantum-gravity cutoff and the Planck scale in the UV, and emphasize the nontrivial UV/IR relations that connect them. I will discuss conjectures constraining scalar potentials and explain how they are related to the behavior of the other energy scales, together with bottom-up arguments based on general principles of quantum gravity such as holography. In particular, I will explain how well-motivated holographic assumptions lead to strong restrictions on scalar potentials, ruling out parametrically prolonged accelerated expansion for positive potentials and obstructing parametric scale separation for negative potentials associated with AdS vacua.
2:00–2:30 pm
Coffee Break
2:30–3:30 pm
Mustapha Ishak-Boushaki, UT Dallas: Persistent and serious challenge to the ΛCDM throne: Evidence for dynamical dark energy rising from combinations of different types of datasets
Abstract: We derive multiple constraints on dark energy and compare dynamical dark energy models with a time-varying equation of state (w0waCDM) versus a cosmological constant model (LCDM). We use Baryon Acoustic Oscillation (BAO) from DESI and DES, Cosmic Microwave Background from Planck with and without lensing from Planck and ACT (noted CMBL and CMB, respectively), supernovae(SN), and cross-correlations between galaxy positions and galaxy lensing from DES. We use pairs or triplets of datasets where we exclude one type of dataset each time and categorize them as “NO SN”, “NO CMB” and “NO BAO” combinations. In all cases, we find that the combinations favor the w0waCDM model over LCDM, with significance ranging from 2.0 to 3.0-sigma. The persistence of this pattern across various dataset combinations even when any of the datasets is excluded supports an overall validation of this trending result regardless of any specific dataset. Next, we use larger combinations of these datasets after verifying their mutual consistency within the w0waCDM model. We find combinations that give robust significance levels, with DESI+DESY6BAO+CMBL+SN giving 3.4-sigma. In sum, while we need to remain cautious, the trend and pattern of these results beyond any single type of dataset and their associated systematics presents a compelling overall portrait not in favor of the LCDM and constitutes a serious challenge to the model’s reign. A few other cosmological results will be provided.
3:30–4:00 pm
Coffee Break
4:00–5:00 pm
Georges Obied, U Chicago: The Dark Dimension and its interplay with DESI data
Abstract: In this talk, I will discuss the motivation for considering an extra mesoscopic Dark Dimension of length l ~ 1 – 10 microns, taking into account theoretical and observational arguments. I will then talk about cosmological aspects of the Dark Dimension. In particular this scenario leads, by the universal coupling of the Standard Model sector to bulk gravitons, to massive spin 2 KK excitations of the graviton in the Dark Dimension (the “dark gravitons”) as an unavoidable dark matter candidate. Observations allow such an extra dimension of size in the micron range. Finally, I will discuss how this scenario can naturally accommodate features recently observed by the DESI survey such as an effective dark energy equation of state that is smaller than -1.

Thursday, Apr. 16, 2026
8:00–8:30 am
Breakfast
8:30–9:30 am
MC Gonzalez-Garcia, YITP Stony Brook & ICREA U. Barcelona: Massive Neutrinos in 2026: What we know, what we do not know (yet?), and what we do not understand
Abstract: In this talk I will present an update of the current understanding (and some not understanding) of the neutrino masses and the lepton mixing and some other minimal SM extensions as derived from direct scrutiny of the results of neutrino flavour oscillation experiments, some other laboratory probes, and the cosmos.
9:30–10:00 am
Coffee Break
10:00–11:00 am
Miguel Montero, IFT, Madrid: Neutrinos and B-L symmetry in the Dark Dimension scenario
Abstract: The Dark Dimension proposes the existe of a micrometer-sized large extra dimension, whose size is tied to the observed small vacuum energy. I will review the scenario, and then discuss how to embed the B-L global symmetry of the SM, focusing on one possibility which leads to an explanation of the observed coincidence between neutrino mass scale and the vacuum energy scale, while leading to 3 light species of right-handed neutrinos. I will also briefly discuss potential opportunities for detection of the resulting neutrino oscillations.
11:00–11:30 am
Coffee Break
11:30 am–12:30 pm
Ignatios Antoniadis, IAS, Princeton: Searching for the dark dimension in neutrino experiments
Abstract: Micron size extra dimensions offer a possibility to explain the smallness of neutrino masses if the right-handed neutrino propagates in the higher dimensional bulk. I will discuss the theoretical framework and the experimental signatures of this proposal in present and future experiments of KATRIN prototype, aiming to measure the magnitude of neutrino masses and to search for extra sterile-type species.
12:30–1:30 pm
Lunch Break (catered)
1:30–2:30 pm
Mike Boylan-Kolchin, UT Austin: Galaxies as Tracers of the Matter Density Field
Abstract: Galaxy formation is often (rightly) thought of as involving a complex interplay of messy astrophysical processes, but it also traces the nonlinear evolution of the matter density in the Universe. Remarkably, it appears that properties of this nonlinear field are intimately connected to properties of the initial linear fluctuations and some basic physics of dark matter interactions. I will explore some of these connections, with applications that include the surprisingly fast evolution of early galaxy formation as revealed by JWST and properties of the lowest-mass dark matter clumps capable of hosting galaxies in the local Universe.
2:30–3:00 pm
Coffee Break
3:00–4:00 pm
Matt Reece, Harvard: Axions from String Theory, and String Theory from Axions
Abstract: String theory compactifications contain the right ingredients to produce axion fields that might solve the Strong CP problem or contribute to dark matter or dynamical dark energy in our universe. After briefly reviewing some of these ingredients, I will frame the inverse question: suppose that an axion is discovered, and its decay constant is measured in an experiment. Could this help us to locate ourselves in the string landscape? In particular, I will discuss how an axion could give us clues about the fundamental string scale and the scale of supersymmetry breaking.

Millennium Prize Problems Lecture - Peter Sarnak: Riemann Hypothesis
2026-04-15 17:00 - 18:00 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
Date: April 15, 2026
Time: 5:00–6:00 pm
Location: Harvard Science Center Hall C, 1 Oxford St., Cambridge MA
Speaker: Peter Sarnak, Institute for Advanced Study
Title: The Riemann Hypothesis
Abstract: After reviewing the hypothesis as put forth by Riemann we discuss its generalizations and analogues. We highlight a few of their implications and workarounds, and probing their truths.
Read more about the Riemann Hypothesis at the Clay Math website.
Organizers: Martin Bridson, Clay Mathematics Institute | Dan Freed, Harvard University and CMSA | Mike Hopkins, Harvard University

Millennium Prize Problems Lecture Series

Interpolation for points in $mathbb{P}^N, Ngeq 2$
2026-04-16 16:00 - 17:00 | CMSA Room G02, 20 Garden Street, Cambridge, MA, 02138
Algebra Seminar
Speaker: Dipendranath Mahato, Tulane University
Title: Interpolation for points in $mathbb{P}^N, Ngeq 2$
Abstract: Interpolation problems study hypersurfaces in projective space passing through prescribed sets of points. Classically, one asks how many independent conditions a collection of points imposes on hypersurfaces of a fixed degree, a question that can be studied algebraically via homogeneous ideals and their Hilbert functions. In this talk, I will begin with the classical interpolation problem for reduced points and introduce the algebraic framework used to study it. I will then move to fat point schemes, where points are assigned multiplicities and hypersurfaces are required to vanish to higher order. In this setting, interpolation problems naturally lead to symbolic powers of ideals and containment relations between symbolic and ordinary powers. I will conclude by discussing open questions, including potential connections between interpolation problems and combinatorial structures such as matroids.

Higgs and Coulomb branches: Geometry and Representation Theory
2026-04-17 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Vasily Krylov
Title: Higgs and Coulomb branches: Geometry and Representation Theory
Abstract: Higgs and Coulomb branches of quiver gauge theories form two important families of Poisson varieties that are expected to be exchanged under so-called 3D mirror symmetry. Quantized Coulomb branches are associative algebras deforming the algebras of functions on Coulomb branches. They are closely related to many important representation-theoretic structures, such as Yangians, quantum groups, and Hecke algebras. In this talk, I will discuss how 3D mirror symmetry, together with other insights motivated by physics, yields very explicit answers to purely representation-theoretic questions about representations of some of these quantum groups. Talk is based on joint works with Dinkins, Karpov, Klyuev, and Lance.

Zigzags, adjoints, and bordisms
2026-04-20 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Lorenzo Riva (Harvard CMSA)
Title: Zigzags, adjoints, and bordisms
Abstract: We will learn how to freely add adjoints to a category using a combinatorial procedure which involves drawing zigzags of squares. Peculiarly, we can use these to draw some bordisms. This is joint work with Martina Rovelli.

Introduction to A-infty categories
2026-04-21 16:15 - 18:00 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Joint Math/CMSA Geometry and Quantum Theory Seminar
Speaker: Ahsan Khan, Harvard CMSA
Title: Introduction to A-infty categories

Abstract: I will give a pedagogical account of A-infty categories and the various places they show up in mathematical physics.

CMSA/Tsinghua Math-Science Literature Lecture: Nicolai Reshetikhin (Tsinghua): Asymptotic representation theory
2026-04-22 09:00 - 10:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA/Tsinghua Math-Science Literature Lecture
Date: April 22, 2026
Time: 9:00 – 10:30 am ET
Location: via Zoom Webinar
Speaker: Nicolai Reshetikhin, Yau Mathematical Sciences Center, Tsinghua University
Title: Asymptotic representation theory
Abstract: Loosely speaking asymptotic representation theory studies representations of “large” groups or algebras. One of the first results in this direction is the study of Plancherel measures on the symmetric group $S_N$ in the limit $Nto infty$ by Vershik and Kerov and Logan and Shepp. The first part of the talk will be an overview of results on statistics of irreducible representations in large tensor products. Then we focus on more modern results on statistics of tilting and projective modules in large tensor products and on how some problems in asymptotic representation theory are related to dimer models in statistical mechanics.

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.

Boundedness for K-trivial varieties with fibrations
2026-04-23 13:30 - 14:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Differential Geometry and Physics Seminar
Speaker: François Greer, MSU
Title: Boundedness for K-trivial varieties with fibrations
Abstract: According to the Beauville-Bogomolov decomposition theorem, any smooth K-trivial variety admits a finite cover by a product of (1) abelian varieties, (2) strict Calabi-Yau varieties, and (3) irreducible holomorphic symplectic varieties (IHSV). In a fixed dimension, all abelian varieties are diffeomorphic, and indeed deformation equivalent through non-algebraic complex tori. The corresponding question remains largely open for cases (2) and (3). If we assume that a variety of class (2) or (3) admits a non-trivial fibration structure, then much more can be shown. In particular, fibered Calabi-Yau threefolds have bounded moduli problem, and IHSV of a fixed dimension with a Lagrangian fibration have bounded moduli. This is based on joint work with Engel, Filipazzi, Mauri, and Svaldi.

Sixth Annual Yip Lecture | Regina Barzilay, MIT: Can machine learning methods design drugs?
2026-04-23 16:00 - 17:00
Sixth Annual Yip Lecture
Date: April 23, 2026
Time: 4:00–5:00 pm ET
Location: Harvard Science Center Hall A & via Zoom Webinar
Speaker: Regina Barzilay, MIT
Title: Can ML methods design drugs?
Abstract: Today, life sciences are driven by prohibitively expensive wet lab experimentations, which limit the pace and scope of discovery. This talk focuses on AI algorithms that enable in-silico modeling of biological processes. Specifically, I will focus on algorithms for molecular and cellular modeling. I will highlight several successful examples where these algorithms have already transformed drug discovery. In the second part of the talk, I want to focus on problems where current methods fail to deliver as expected, motivating the need for algorithmic innovations.
Bio: Regina Barzilay is a School of Engineering Distinguished Professor for AI and Health in the Department of Electrical Engineering and Computer Science (EECS) at MIT. Since 2018, she has been the AI faculty lead for the MIT Jameel Clinic and a member of MIT CSAIL.
She is a member of three national academies, including the National Academy of Engineering, the National Academy of Medicine, and the American Academy of Arts & Sciences.
She is also a recipient of various awards, including a 2017 MacArthur fellowship “Genius Grant.” In 2020, she was awarded the Squirrel AI Award for Artificial Intelligence for the Benefit of Humanity. More recently, she has been recognized in the 2025 TIME100 AI List and awarded with the IEEE Frances E. Allen Medal for her development of innovative machine learning algorithms that have significantly advanced human language technology and transformed medical diagnostics and drug discovery.
She completed her PhD in Computer Science from Columbia University, and spent a year as a postdoc at Cornell University. Barzilay received her undergraduate degree from Ben-Gurion University of the Negev, Israel.
The Yip Lecture takes place thanks to the support of Dr. Shing-Yiu Yip.

The Intermingling of Symmetry and Parametrization in Matrix Product States
2026-04-24 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Daniel Spiegel
Title: The Intermingling of Symmetry and Parametrization in Matrix Product States
Abstract: In the study of quantum spin systems, it is by now well-known that interesting phases of quantum matter can arise from gapped ground states when the system is invariant under a symmetry group G or when the system varies continuously with a parameter in a topological space X. In these cases, phases are characterized by indices taking values in group cohomology of G or the cohomology of X, respectively. The situation where one has both a symmetry and a parametrization is much less studied but can lead to interesting phases even when both the aforementioned indices are trivial. In this talk, I will discuss work in progress on a simple construction for general index for symmetry protected parametrized systems of matrix product states and will show some illustrative examples.

Compression Is All You Need: Modeling Mathematics
2026-04-24 14:00 - 16:30 | Virtual
Freedman Seminar
Speaker: Mike Freedman, Harvard CMSA
Title: Compression Is All You Need: Modeling Mathematics
Abstract: The talk will exposit a recent eponymous arXiv posting with coauthors Vitaly Aksenov, Eve Bodnia, and Mike Mulligan. The approach is to think like a physicist and model a seemingly complex bit of reality: mathematics, by a simple toy model where exact computations can be carried out and then compared with observation. The models are finitely generated monoids and the data is derived from MathLib a large Lean-based repository. The hierarchical nature of definitions and lemmas in math is modeled by adding redundant generators to the monoids – think of the powers of 10 within the natural numbers which support place notation. Place notation confers an exponential compression of how we describe numbers; exploration of MathLib shows that this theme persists to (human) mathematics writ large. We hope that the observables we describe will help our agents navigate to interesting mathematical destinations.

Mathematics and Biology II: Mathematics and Science of Behavior
2026-04-27 09:00 - 2026-04-30 17:00 | CMSA 20 Garden Street Cambridge, Massachusetts 02138 United States
Mathematics and Biology II: Mathematics and Science of Behavior
Dates: April 27–30, 2026
Location: Harvard CMSA, Room G10, 20 Garden Street, Cambridge MA
Youtube Playlist

This meeting will explore the emerging mathematics and science of embodied cognition—the idea that behavior arises not solely from the brain but through the dynamic interaction of brain, body, and environment. Understanding how animals sense, move, decide, and coordinate, from individual sensorimotor loops to collective dynamics, demands mathematical frameworks that integrate geometry, dynamics, stochastic processes, control theory, and multiscale physics. The meeting will bring together experimentalists studying behavior across species with theorists and engineers building mathematical models and bio-inspired machines, to identify shared principles of adaptive behavior.

Co-organizers: L. Mahadevan (Harvard), Francesco Mori (Harvard CMSA), Venkatesh Murthy (Harvard)
Speakers

Pulkit Agrawal, MIT
Kristin Branson, HHMI
Antonio C. Costa, Sorbonne University/Paris Brain Institute
Noah Cowan, Johns Hopkins University
Robert Datta, Harvard Medical School
Ben de Bivort, Harvard University
Ofer Feinerman, Weizmann Institute of Science
Deborah Gordon, Stanford University
Albert Kao, UMass Boston
Ann Kennedy, Scripps Research Institute
Hungtang Ko, Tufts University
George Lauder, Harvard University
Bence Ölveczky, Harvard University
Kirstin Petersen, Cornell University
Pavan Ramdya, EPFL
Elizabeth Tibbetts, University of Michigan
Robert Wood, Harvard University

Schedule (pdf)
Monday, Apr. 27, 2026
9:00–9:30 am: Breakfast
9:30–10:15 am: Deborah Gordon, Stanford University
Title: The dynamics of collective behavior in changing environments
Abstract: Collective behavior operates without central control, using interactions among participants adjust to changing conditions. There is enormous diversity in the dynamics of collective behavior, including in the rate of response to conditions, in feedback regimes that set whether interactions stimulate or inhibit activity, and the extent of centralization or modularity of information flow. An ecological perspective suggests how this diversity of collective behavior reflects the dynamics of the environment, including its stability, the ratio of resources spent to resources gained, and the distribution of resources in time and space.
As examples, I will discuss field studies and modelling of the regulation of foraging behavior in two species of ants, Harvester ant colonies in the desert regulate foraging to manage high costs, in water loss, to obtain scattered and stable resources. They use a centralized system, with the default to remain inactive unless stimulated, that is slow to adjust foraging activity. In contrast, the turtle ant colonies form trail networks in the canopy of the tropical forest, in unstable conditions where activity costs are low, to find and collect ephemeral and patchy resources. They use a highly modular system, with the default to sustain activity unless inhibited, that can rapidly adjust trail networks to changing resources and conditions.
10:15–10:30 am: Discussion
10:30–11:00 am: Tea Break
11:00–11:45 am: Hungtang Ko, Tufts University
Title: Collective mechanical intelligence: how fluid environments mediate self-organization of swarms
Abstract: Biological collectives across scales self-organize within fluid environments. The mechanical coupling between swarming agents and fluid fields provides opportunities for both passive self-assembly and active, fluid-mediated communication. However, while sporadic evidence of collective mechanical intelligence exists, its underlying mechanisms remain elusive. In this talk, I will focus on two key systems: fire ant rafts and fish schools. Using a combination of experiments and mathematical models, I will show that fire ant rafts leverage passive interfacial forces for self-assembly and self-stabilization. Furthermore, I will demonstrate how schools of giant danio utilize mechanically intelligent formations in 3D, and discuss how swarm robotics may provide the key to future research in collective mechanical intelligence.
11:45 am–12:00 pm: Discussion
12:00–1:30 pm: Catered Lunch
1:30–2:15 pm: Albert Kao, UMass Boston
Title: The limits and potential of collective wisdom
Abstract: Over the past several years, many studies have demonstrated, both in theory and in experiments, the ability of groups to make better decisions than individuals — a phenomenon known as collective wisdom. However, the task types and experimental paradigms used vary considerably, making comparisons across studies, and consequently a unified theory of collective wisdom, difficult. Here, I derive a measure called the effective group size which allows for such comparisons. I use this measure to demonstrate several limitations to collective wisdom, including when groups are large, when there are correlations in opinions in the group, and when information is passed down in chains. In addition, collective wisdom is fragile in the face of an individual who has a disproportionate amount of power, even if far from being a dictator.
2:15–2:30 pm: Discussion
2:30–3:15 pm: Ann Kennedy, Scripps Research Institute
Title: Neural mechanisms that gate the expression of motivated behaviors
Abstract: In order to survive and reproduce, animals must set and weigh off goals in a way that is adaptive and responsive to the context of the environment. Intense evolutionary pressure has wired these algorithms of survival into the connectivity and gene expression patterns of the brain. In this talk, I will present our lab’s recent work on the structure of animal behavior and its neural correlates, showing how theory and modeling can uncover the computational mechanisms by which the brain sets survival goals and weighs off competing survival needs. I will first show how at the macroscopic level, models of behavior as a feedback control system can help uncover control principles by which pressing survival needs can override less urgent drives. Next, I will present new work exploring how macroscopic drives are translated into moment-to-moment behavioral choices.

3:15–4:30 pm: Discussion
4:30–5:30 pm: CMSA Colloquium: Ofer Feinerman, Weizmann Institute of Science
Title: Enacted collective cognition: Brainless problem-solving in weaver ants
Abstract: Unlike most ants, weaver ants construct their nests by pulling together leaves. Because individual ants are small relative to the leaves, they assemble their bodies into temporary tools that bend the leaves into a hollow structure, later stabilized with larval silk. Remarkably, they achieve functional nests across a wide range of leaf shapes and configurations, suggesting that this distributed system is capable of solving complex, open-ended problems.
To understand how this is possible, we performed laboratory experiments using controlled leaf configurations. In simple cases, we show that ants can rely on a zipping heuristic that produces closed nests, and we use differential geometry to demonstrate how flexible leaves are transformed into rigid structures. Crucially, this zipping behavior forms a feedback loop in which ants continuously read and modify the evolving structure. In this sense, the nest itself functions as a shared physical information system.
This suggests that cognition in this system is not located within individual ants, but is enacted through the co-dynamics of the colony and the structure it builds. We present preliminary experiments with more complex leaf configurations, showing that this process can solve increasingly challenging construction problems. Together, these results point to a distributed, brainless, and enactive form of cognition.

Tuesday, April 28, 2026
9:00–9:30 am: Breakfast
9:30–10:15 am: Ben de Bivort, Harvard University
Title: Bayesian Inference on biophysical models of connectomes
Abstract: Recent progress in connectomics has opened new frontiers for understanding the underlying principles of neural circuits. By leveraging high-resolution maps of synaptic connections, computational models can simulate neural dynamics with unprecedented detail. However, it remains challenging to parsimoniously integrate circuit activity data with connectomic information to make biological in- sights. We propose a Bayesian framework as a principled method for bringing to bear existing data, enabling uncertainty quantification for inferring parameters of interest, as well as for predicted circuit outputs. To demonstrate this approach, we implement a simple spiking neuron model using leaky- integrate-and-fire dynamics in the Drosophila olfactory circuit, incorporating available firing rate data. We evaluate how models with varying levels of biological detail fit experimental data and examine how training on different subsets of data influences model predictions.
10:15–10:30 am: Discussion
10:30–11:00 am: Trainee talk: Yasuko Isoe, Harvard University
Title: Divergent spatiotemporal integration of whole-field visual motion in medaka and zebrafish larvae
Abstract: Cross-species comparisons offer powerful leverage for identifying conserved and divergent neural computations underlying innate behavior. Visual motion integration is a fundamental operation that stabilizes an animal’s position relative to its environment, yet how its underlying algorithms vary across closely related vertebrate brains remains poorly understood. We investigated how zebrafish (Danio rerio) and medaka (Oryzias latipes) larvae implement visual motion integration using both free-swimming behavioral assays and head-fixed, tail-free preparations, the latter allowing us to confirm and extend our findings under precise stimulus control. Using whole-field motion stimuli, we found that the two species employ distinct spatiotemporal filtering strategies. Medaka pool motion signals over larger visual fields and weight peripheral inputs more strongly, whereas zebrafish rely more on motion signals directly beneath the body. Temporally, zebrafish respond robustly to brief stimuli, while medaka require longer stimulus durations and sustain motion-driven activity well after stimulus offset. Decomposition of turning behavior revealed separable control modules for large and small corrective maneuvers, with species differences arising primarily from prolonged temporal integration in medaka. Together, our results demonstrate how alterations in basic computational motifs — spatiotemporal pooling, gain, and persistence — can generate divergent visuomotor strategies across closely related vertebrate brains, offering a window into the evolutionary diversification of sensorimotor computation.
11:00–11:30 am: Trainee Talk: Siddharth Jayakumar, Harvard University
Title: Mice follow scent trails using predictive policies
Abstract: Animals must extract reliable information from noisy sensory signals. In olfaction, this is especially challenging, since cues are sparse and must be actively sampled. We asked how mice navigate odor trails under these conditions. Using an “infinite” paper treadmill, we find that mice rapidly learn to track trails with high precision. Disrupting bilateral sampling introduces systematic, lateralized errors, consistent with a comparison of signals across the two sides. Individual inhalations near the trail trigger rapid corrective movements.
Interestingly, we find that mice do not follow trails purely reactively: deviations in tracking at unexpected trail bends reflected recent history, indicating the use of short-term memory. We have begun to investigate the neural substrates of this behavior, focusing on how sensory signals and predictive information are represented in the brain. Broadly, our results suggest that odor-guided navigation depends on combining immediate sensory input with a short-term internal estimate, enabling reliable tracking despite sparse cues.
11:30 am–12:00 pm: Discussion
12:00–1:30 pm: Catered Lunch
1:30–2:15 pm: Noah Cowan, Johns Hopkins University
Title: Toward a Control Theory for Active Sensing
Abstract: Active sensing is often defined as “movement for the purpose of sensing.” Here, I take a different perspective—that active sensing in biological systems is not a distinct class of behaviors, but rather a set of movement phenomena that arise from a control objective. Biological sensors adapt to persistent stimuli, acting like high-pass filters that tend to block “DC.” Such “change-detecting” sensors can support efficient coding with a high dynamic range, and in engineering, bio-inspired event cameras are similar: they transmit information only when a pixel changes and, as such, are extremely fast and make efficient use of bandwidth for the right applications. However, such “AC” sensors pose technical challenges for control. Specifically, event-like biological sensors can cause a nonlinear system (1) to lose local linear observability, and (2) to become impossible to stabilize about an equilibrium point (Biswas, Sontag, Cowan, Eur J Control, 2025). Active sensing behaviors must emerge for stable control, even in the somewhat paradoxical setting where the task-level goal is to remain stationary. Here, I will discuss my lab’s progress in analyzing how animals use active sensing behaviors to format sensory information, enhancing observability and control. I will also present our efforts to formalize controller synthesis with event-like sensors.
2:15–2:30 pm: Discussion
2:30–3:15 pm: Robert Datta, Harvard Medical School
Title: Unveiling structure in natural behavior
Abstract: Ethologists describing animals in the wild have long appreciated that naturalistic, self-motivated behavior is built from modules that are linked together over time into predictable sequences. Many such sequences are built to extract information from the environment.
And yet, it remains unclear how the brain regulates the selection of individual behavioral modules for expression at any given moment, or how it dynamically composes these modules into the fluid behaviors observed when animals act of their own volition, and in the absence of experimental restraint, task structure or explicit reward. Here we use novel methods for characterizing spontaneous mouse behavior to reveal mechanisms used by the brain to create the architecture of self-guided behavior.
3:15–4:30 pm: Discussion

Wednesday, April 29, 2026
9:00–9:30 am: Breakfast
9:30–10:15 am: Kristin Branson, HHMI
Title: How can generative AI help us understand animal behavior?
Abstract: Understanding animal behavior at an algorithmic level — what animals attend to, how they form internal world models, goals, and plans, and how state maps to action — remains a central challenge in neuroethology. Large-scale behavioral experiments now produce trajectory datasets of extraordinary scale and complexity, but existing approaches necessarily compress this complexity to just a few dimensions. We argue that generative AI offers a path toward rich, query-able models of the data. We adapt transformer-based sequence modeling to multi-agent animal keypoint trajectories, treating behavior forecasting as analogous to next-token prediction. Our agent-based network inputs biologically-motivated sensory representations and outputs the distribution of future pose velocities. We show that the model captures statistical properties of the behavioral distribution. We have built a Python library that encapsulates the complexity of transforms relating raw keypoints and model inputs and outputs to make these tools extensible by the NeuroAI community and accessible to theorists and experimentalists. Finally, we argue that mechanistic interpretability methods allow us to query trained models through the natural framework of artificial neuroethology experiments.
10:15–10:30 am: Discussion
10:30–11:00 am: Tea Break
11:00–11:30 am: Trainee talk: Golnar Gharooni Fard, Harvard University
Title: The Geometry and Dynamics of Embodied Cognition: From Collective Architecture to Interspecies Navigation
Abstract: Biological behavior is fundamentally an emergent property of the coupling between an agent’s physical form, its environment, and local interaction rules. In this talk, I explore the mathematical principles of this “embodied cognition” across two distinct scales: the stigmergic spatial memory of honeybee collectives and the real-time dynamic coordination of human-bird mutualism. I’ll start by discussing static embodied intelligence through the lens of honeycomb construction. Using 3D-printed foundations to introduce controlled geometric frustration (including misalignment angles and lattice shifts) I demonstrate how honeybee collectives resolve structural mismatches through the adaptive placement of topological defects. I will show how these complex behavioral responses can be modeled as a physics-based potential minimization problem, proving that the hive’s “intelligence” is a distributed response to local geometric cues. In the second part, I transition to “dynamic” coordination by examining the mutualistic search for honeybee nests between humans and honeyguide birds in Africa. Unlike the persistent memory of the wax comb, this interspecies cooperation requires real-time processing of noisy, stochastic signals. I present a data-driven model of this interaction as a coupled tracking problem. By analyzing the interplay between human engagement and a leaky integrator memory constant, I identify the sweet spots of temporal integration required to successfully filter bird behavior and maintain goal-oriented navigation. Together, these two projects demonstrate that a data-driven physics-inspired modeling framework, can uncover the fundamental rules of agent-environment coupling that drive adaptive behavior across biological scales.
11:30 am–12:00 pm: Trainee talk: Wenyi Zhang, Harvard University
Title: Mechanisms of Setpoint Control in Drosophila Navigation System
Abstract: Navigation provides a powerful system for studying how animals balance behavioral persistence with flexibility. During navigation, fruit flies often default to fast straight walking (or “menotaxis”) in a barren environment, maintaining a stable heading setpoint over a long period of time. Conversely, when the local environment is enriched with sensory stimuli, flies often explore the environment with more frequent heading changes, either through directed steering driven by a sequence of updating setpoints, or through undirected turning driven by temporarily lifting the setpoint control. Although this framework suggests a central role for the setpoint in guiding navigation, the neural mechanisms for flexible setpoint control remain unclear.
Here we identified h∆A, a central complex cell type involved in setpoint control. In an aversive heat paradigm, hΔA played an important role in the fly’s sensory-driven deviation from the menotactic goal direction. We characterized hΔA population activity and found that it carries two separable activity components: a bump-like signal that encodes a slowly varying travel-direction-related setpoint, and a spatially uniform signal associated with turning. We further identified modulatory inputs to hΔA that shape h∆A activity. Together, these results support a model in which short- and long-timescale setpoints compete for steering control, and suggest a circuit mechanism by which flies balance directional persistence with flexible reorientation under changing sensory conditions.
12:00–1:30 pm: Catered Lunch
1:30–2:15 pm: Bence Ölveczky, Harvard University
Title: Using neuro-biomechanical simulations to probe neural control of learned skills
Abstract: The goal of my lab is to decipher the circuit logic by which the brain learns and controls motor skills. The standard mechanistic approach is to dissect the underlying circuits brain area-by-brain area, inferring function by relating recordings and perturbations within each to behavior. This runs into fundamental problems in highly recurrent systems, where activity in any one node is shaped by the dynamics of the whole, a problem compounded by the fact that the circuits we probe control a complex biomechanical body and not measurable features of behavior. I will discuss these challenges and present results suggesting that neuro-biomechanical simulation, leveraging advances in physics simulation and AI, can offer a powerful alternative window into the neural circuits underlying learned skills.
2:15–2:30 pm: Discussion
2:30–3:15 pm: Pavan Ramdya, EPFL
Title: Object manipulation and affordance learning in Drosophila
Abstract: Many animals must manipulate objects to perform tasks like pushing away debris when navigating over complex, natural terrain. For previously unseen objects, efficient manipulation requires that their affordances–the possible actions one can perform upon them–first be learned through experience. However, the behavioral and neural mechanisms underlying the learning of object affordances remain largely unknown. To address this gap, we show that adult Drosophila melanogaster flies can learn to push novel spherical objects without being given any explicit reward. To do this, flies appear to learn the ball’s pushability affordance: pushing is delayed when animals are first exposed to an immobile ball, and manipulating one ball accelerates pushing of a second one in a new context. Behavioral quantification of a large-scale neural silencing screen reveals that specific visual projection neurons and olfactory sensory neurons regulate initial reactions to the object while dopaminergic neurons and the mushroom bodies, a center for learning and memory in insects, are critical for generalizing object affordances. These findings open the door to a mechanistic understanding of object manipulation and affordance learning.
3:15–4:30 pm: Discussion

Thursday, April 30, 2026
9:00–9:30 am: Breakfast
9:30–10:15 am: Pulkit Agrawal, MIT
Title: What Robots Are Missing: Force Intelligence and Lifelong Learning
Abstract: Modern robots can plan sophisticated motions, yet they remain slow, brittle, and unreliable on tasks humans find effortless. The missing piece is not better planning, but better force reasoning: knowing when, where, and how much force to apply under uncertainty and across diverse tasks. Force intelligence, I argue, is a unifying principle for scalable robotics—bridging dexterous manipulation and whole-body control. However, even a force-aware robot that cannot learn from its own experience will remain brittle. Today’s systems are effectively frozen after training, unable to adapt once deployed. Real-world autonomy instead demands learning in deployment: the ability to improve continuously from interactions, failures, and successes. In this talk, I will present our lab’s recent work on lifelong learning and outline a future path for how combining it with force-centric design could enable reliable, useful robots in the real world.
10:15–10:30 am: Discussion
10:30–11:00 am: Tea Break
11:00–11:45 am: Antonio C. Costa, Sorbonne University/Paris Brain Institute
Title: Unraveling the structure of behavioral variation: a dynamical approach to naturalistic data
Abstract: Animal behavior varies widely, both within the same individual over time and between individuals. While often overlooked, this variation reflects hidden control variables and mechanisms that were shaped by evolution. For example, variation in behavioral traits can help populations withstand environmental change, while atypical motor patterns in neurological disorders may offer clues for personalized therapies. Comparing such complex behaviors is difficult. When dynamics are nonlinear and unfold over multiple timescales, standard metrics based on summary statistics often miss meaningful differences. To address this, we introduce a framework that encodes multiscale dynamics to compare behavior from data. By modeling nonlinear dynamics probabilistically (using transfer operators inferred from time-series data), we define a distance metric that captures behavioral differences across timescales. Tailored to finite, noisy datasets, our approach identifies principal axes of variation and enables rigorous clustering of individual trajectories. We demonstrate this framework in various biological systems, including bacterial chemotaxis and larval zebrafish locomotion, where the inferred axes of behavioral variation reflect underlying physiological variables and developmental histories.
11:45 am–12:00 pm: Discussion
12:00–1:30 pm: Catered Lunch
1:30–2:15 pm: Elizabeth Tibbetts, University of Michigan
Title: What paper wasps can teach us about the evolution of animal minds
Abstract: Why do animals differ in their cognitive abilities? Some animals fail at apparently simple tasks, while others have a remarkable capacity to collect, retain, and use information from the environment to guide their behavior. Although paper wasps brains are smaller than a grain of rice, Tibbetts will show that wasps can perform seemingly complex behaviors like individual face recognition, transitive inference, social eavesdropping, and concept learning. She will also describe experiments that take advantage of natural variation in behavior within and among wasp species to test how social interactions shape the development and evolution of cognitive abilities.
2:15–2:30 pm: Discussion
2:30–3:15 pm: Robert Wood, Harvard University
Title: The Mechanical Side of Artificial Intelligence
Abstract: Artificial Intelligence research typically focuses on perception, learning, and control methods to enable autonomous agents, including robots, to make and act on decisions in real-world scenarios. However, even the most capable AI without a well-designed physical structure is of minimal use for canonical robotics tasks. Our research is focused on the design, mechanics, materials, and manufacturing of novel robot platforms that make perception, control, or action easier or more robust for natural, unstructured, and often unpredictable environments. Key principles in this pursuit include bioinspired designs, smart materials for novel sensors and actuators, and the development of multi-scale, multi-material manufacturing methods. This talk will illustrate this philosophy by highlighting the creation of three classes of robots with unique hardware challenges: bioinspired microrobots, soft-bodied robots for manipulation, and robots for interacting with delicate marine life.
3:15–4:00 pm: Discussion
4:00–5:00 pm: George Lauder, Harvard University
Title: Fish schooling behavior from kinematics to hydrodynamics to energetics
Abstract: Do fish moving in a school reduce their energetic costs compared to swimming alone? If so, how does collective motion reduce the energy needed to move? Only within the last two years have experimental studies directly demonstrated that fish swimming in a group have lower energy expenditure than solitary locomotion. Most studies of how fish move in a collective have focused on understanding the potential benefits of swimming in fixed relative positions. But recent experiments on fish schooling behavior have revealed that fish within the school are nearly constantly rearranging their relative positions. In this talk I will show how fish in a school can save energy even if they do not maintain fixed positions. Analyses of water flow patterns within fish schools have been used to resolve this “paradox” and show that fish movement within a school creates hydrodynamic shelters with zones of reduced flow velocity that nearby fish can take advantage of.

Higher current algebras and chiral algebras
2026-04-27 15:00 - 16:00 | CMSA G102, 20 Garden Street, Cambridge, MA, 02138
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Charles Young (University of Hertfordshire)
Title: Higher current algebras and chiral algebras
Abstract: Vertex algebras capture physicists’ notion of OPEs in chiral CFTs, in complex dimension one. For various motivations, one would like to have analogs of vertex algebras in higher dimensions. Chiral algebras, in the sense of Beilinson-Drinfeld and Francis-Gaitsgory, provide a natural framework here, because they re-express the vertex algebra axioms (which are rather sui generis, and therefore hard to generalize) as something more recognizable (a chiral algebra is a Lie algebra, of a sort).
I will review this, and then go on to introduce a certain concrete model of the unit chiral algebra in higher dimensions. In higher dimensions one is forced to work up to coherent homotopy in some fashion; in this model it turns out to be in the mildest fashion one could hope for: namely, one moves from Lie algebras to their homotopy analogs, L-infinity algebras, and from chiral algebras to homotopy chiral algebras in a sense introduced by Malikov-Schechtman.
The main tool in the talk will be a strict cdga model — the polysimplicial model — of derived global sections of the structure sheaf on configuration space. The hope is that this model will prove well-adapted to doing concrete calculations, and in that direction, I will gesture towards a homotopy version of the usual Arnold/Orlik-Solomon relations for broken circuits.
This is joint work with Zhengping Gui and Laura Felder and is based largely on the preprint 2506.09728

Enacted collective cognition: Brainless problem-solving in weaver ants
2026-04-27 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Ofer Feinerman, Weizmann Institute of Science
Title: Enacted collective cognition: Brainless problem-solving in weaver ants
Abstract: Unlike most ants, weaver ants construct their nests by pulling together leaves. Because individual ants are small relative to the leaves, they assemble their bodies into temporary tools that bend the leaves into a hollow structure, later stabilized with larval silk. Remarkably, they achieve functional nests across a wide range of leaf shapes and configurations, suggesting that this distributed system is capable of solving complex, open-ended problems.
To understand how this is possible, we performed laboratory experiments using controlled leaf configurations. In simple cases, we show that ants can rely on a zipping heuristic that produces closed nests, and we use differential geometry to demonstrate how flexible leaves are transformed into rigid structures. Crucially, this zipping behavior forms a feedback loop in which ants continuously read and modify the evolving structure. In this sense, the nest itself functions as a shared physical information system.
This suggests that cognition in this system is not located within individual ants, but is enacted through the co-dynamics of the colony and the structure it builds. We present preliminary experiments with more complex leaf configurations, showing that this process can solve increasingly challenging construction problems. Together, these results point to a distributed, brainless, and enactive form of cognition.

The classifying space of a Morse flow category
2026-04-28 16:15 - 18:00 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Joint Math/CMSA Geometry and Quantum Theory Seminar
Speaker: Lorenzo Riva, Harvard CMSA
Title: The classifying space of a Morse flow category

Abstract: Following a paper of Calle and Liu we show that, under suitable tameness assumptions, the classifying space of the Morse category associated to a manifold M with a Morse function recovers the homotopy type of M, thereby addressing a gap in a preprint of Cohen-Jones-Segal. We also give a counterexample when those assumptions are not satisfied.

Transcendental Epsilon Multiplicity via Divisor Volumes
2026-04-30 16:00 - 17:00 | CMSA Room G02, 20 Garden Street, Cambridge, MA, 02138
Algebra Seminar
Speaker: Sudipta Das, Tata Institute of Fundamental Research
Title: Transcendental Epsilon Multiplicity via Divisor Volumes
Abstract: In this talk, our goal is to establish a structural bridge between asymptotic commutative algebra and transcendence theory to show that there exists an ideal in a Noetherian local ring whose epsilon multiplicity is transcendental. By equating the local-cohomological definition of epsilon multiplicity to a global divisorial volume integral on a projective bundle, we apply Baker’s theorem on linear forms in logarithms to prove that the resulting arithmetic invariant falls strictly outside the field of algebraic numbers. This talk is based on collaborative work with Vinh Pham and Stephen Landsittel.

note room change to G02

Lifting F-split surfaces to the Witt vectors
2026-05-01 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Iacopo Brivio, CMSA
Title: Lifting F-split surfaces to the Witt vectors

Abstract: Algebraic varieties in positive characteristic are ill behaved compared to characteristic zero ones. Several important tools available over the complex numbers, such as the Hodge decomposition theorem, are either not available or straight-away false. There are two important classes of positive characteristic varieties which have better behavior: Witt liftable varieties and Frobenius split varieties. A folklore conjecture predicts that the latter class is contained in the former. In a joint work with Bernasconi, Kawakami and Witaszek we proved that this is the case for surfaces. I will give an overview of this result as well as some applications thereof.

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