CMSA

On the p-curvature of quantum connections of CY threefolds
2026-02-09 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: Shaoyun Bai (MIT)
Title: On the p-curvature of quantum connections of CY threefolds
Abstract: The small quantum connection of Calabi-Yau varieties has integral coefficients, thus admits reduction mod a prime number p. A fundamental invariant associated with flat connections over characteristic p is the p-curvature, which lies at the heart of study of algebraic differential equations. I will explain how to identify the p-curvature of quantum connection of any compact Calabi-Yau threefold with the quantum Steenrod operation, thereby providing a modular description of the p-curvature in this setting. I will also discuss the role of BPS invariants and the mirror symmetry context. This is based on joint work with Jae Hee Lee.

Phase Transition to Chaos in Complex Ecosystems with Non-reciprocal Interactions
2026-02-09 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Pankaj Metha, Boston University
Title: Phase Transition to Chaos in Complex Ecosystems with Non-reciprocal Interactions
Abstract: Nonreciprocal interactions between microscopic constituents can profoundly shape the large-scale properties of complex systems. In this pedagogical chalk talk, I will discuss recent work from our group on phase transitions and chaos in high-dimensional ecosystems with non-reciprocal interactions. Our approach builds on a generalization of MacArthur’s consumer-resource model that incorporates asymmetric interactions between species and resources. I will highlight rich connections between this problem and the mathematics of disordered systems (cavity method and DMFT), random matrix theory, and constrained optimization.

CMSA Q&A Seminar: James Eldred Pascoe, Drexel University
2026-02-11 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q&A Seminar
Speaker: James Eldred Pascoe, Drexel University
Title: (What is) The tracial fundamental group and free universal monodromy?
Abstract: We introduce the tracial fundamental group to classify the analytic continuation of functions that are locally behave like the trace of natural matrix valued functions. While globally defined natural matrix-valued functions (known as free noncommutative functions, which roughly locally are defined by noncommutative power series) satisfy universal monodromy, we show that these tracial free functions exhibit a rigid but nontrivial structure governed by the aforementioned group. We prove that the tracial fundamental group is always a torsion-free, divisible abelian group, standing in sharp contrast to the non-abelian fundamental groups of classical domains.

ReLU and Softplus neural nets as zero-sum, turn-based, stopping games
2026-02-11 14:00 - 15:00 | Virtual
New Technologies in Mathematics Seminar
Speaker: Yiannis Vlassopoulos, Athena Research Center
Title: ReLU and Softplus neural nets as zero-sum, turn-based, stopping games
Abstract: Neural networks are for the most part treated as black boxes. In an effort to begin elucidating the mathematical structure they encode, we will explain how ReLU neural nets can be interpreted as zero-sum turn-based, stopping games. The game runs in the opposite direction to the net. The input to the net is the terminal reward of the game, the output of the net is the value of the game at its initial states. The bias at each neuron is used to define the reward and the weights are used to define state-transition probabilities. One player –Max– is trying to maximize reward and the other –Min-, to minimize it. Every neuron gives rise to two game states, one where Max plays and one where Min plays. In fact running the ReLU net is equivalent to the Shapley-Bellman backward recursion for the value of the game. As a corollary of this construction we get a path integral expression for the output of the net, given input. Moreover using the fact that the Shapley operator is monotonic (with respect to the coordinate-wise order) we get bounds for the output of the net, given bounds for the input. Adding an entropic regularization to the ReLU net game allows us to interpret Softplus neural nets as games in an analogous fashion.
This is joint work with Stéphane Gaubert.

Gromov-Hausdorff limits of collapsing Calabi-Yau fibrations
2026-02-12 13:30 - 14:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Differential Geometry and Physics Seminar
Speaker: Gabor Szekelyhidi, Northwestern University
Title: Gromov-Hausdorff limits of collapsing Calabi-Yau fibrations
Abstract: A well studied problem is the metric behavior of Calabi-Yau metrics on a fibration in a family of Kahler classes that collapses the fibers. I will discuss recent progress showing that the Gromov-Hausdorff limit can be identified with the base of the fibration, generalizing results of Gross-Tosatti-Zhang, Song-Tian-Zhang and Li-Tosatti. A new ingredient is to exploit the RCD property of the Gromov-Hausdorff limit.

A leisurely stroll through the theory of adjunctions
2026-02-13 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Lorenzo Riva, Harvard CMSA
Title: A leisurely stroll through the theory of adjunctions
Abstract: Adjoint functors (and, more generally, adjunctions in a 2-category) are ubiquitous in algebra and topology. In this talk I will give an overview of the basics of adjunctions, with the ultimate goal being understanding the statement of the cobordism hypothesis. Time permitting, I will talk about some recent work on a combinatorial construction yielding free adjunctions.

Geometric structures on gauge theoretic moduli spaces
2026-02-17 16:15 - 18:00 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speaker: Saman Habibi Esfahani (CMSA)
Title: Geometric structures on gauge theoretic moduli spaces
Abstract: Motivated by Witten’s study of instantons on S3 x S1, we survey some classical and recent results, programs, and conjectures on geometric structures, such as symplectic and hyperkahler, on moduli spaces of instantons and monopoles on various manifolds, from a mathematical perspective. This talk serves as background for Max’s talk on 2/24.

CMSA Q&A Seminar: Dan Freed, Harvard
2026-02-18 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q&A Seminar
Speaker: Dan Freed, Harvard
Topic: How does one navigate the job market as a postdoc in 2026?

Topics in the Relation of Four-Manifold Invariants and Supersymmetric Field Theory
2026-02-19 13:30 - 14:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Differential Geometry and Physics Seminar
Speaker: Greg Moore, Rutgers University
Title: Topics in the Relation of Four-Manifold Invariants and Supersymmetric Field Theory
Abstract: We will begin with a review of topological twisting as a choice of background fields. We then review the standard paradigm for the formulation of Donaldson invariants as correlation functions in twisted supersymmetric N=2 d=4 quantum field theory, together with the quantum field theory (QFT) derivation of the relation of the Donaldson invariants to Seiberg-Witten invariants. We then consider what can be said using other twisted QFTs. We present some new results on the four-manifold invariants derived from N=2 supersymmetric QCD. We then move on to 5d theories and the “K-theoretic Donaldson invariants” and comment briefly on the 6d theories and the “elliptic Donaldson invariants.” In the unlikely event that time permits we finish with the extension to families of four-manifolds, where the coupling to a suitably twisted and truncated superconformal gravity is expected to produce invariants valued in the cohomology of the classifying space of the diffeomorphism group of the four-manifold.

Constructing oriented TQFTs from twisted pivotal tensor categories
2026-02-19 15:30 - 16:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Geometry and Quantum Theory Seminar
Speaker: William Stewart
Title: Constructing oriented TQFTs from twisted pivotal tensor categories
Abstract: The cobordism hypothesis classifies n-dimensional oriented TQFTs in terms of SO(n) homotopy fixed point data. An SO(2) homotopy fixed point structure on a finite tensor category gives rise to a twisted pivotal structure (a more general notion than a pivotal structure). In this talk, I will illustrate how the usual skein theory (also called string nets) of a pivotal tensor category can be generalized to the twisted pivotal setting, yielding new 2d oriented TQFTs. This is joint work with Ben Haioun and Filippos Sytilidis.

Theory of Task-Adapted Dynamics in Large Recurrent Neural Networks
2026-02-20 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Blake Bordelon, CMSA
Title: Theory of Task-Adapted Dynamics in Large Recurrent Neural Networks
Abstract: Recurrent neural networks (RNNs) encode expressive and flexible dynamical systems which can adapt to perform tasks by modifying the internal connections between neurons. In this work we analyze the structure of the dynamical systems encoded in RNNs after being trained to perform a learning task. We derive a mean field theory of the dynamics of RNNs before and after learning. Our theory predicts heterogeneous activity and tuning of single neurons, but precise, deterministic predictions for population level autocorrelation and outputs of the network. Further, our theory enables us to interpolate between different operating regimes for RNN learning including (1) reservoir computing regime where internal adaptations do not adapt to data as the model outputs fit the provided data and (2) a feature-learning where the internal dynamics of the network change significantly due to task learning and reflect temporal properties of the learning task. These different regimes exhibit different levels of chaotic activity, oscillatory behaviors, and length generalization properties as feature learning enables maintenance of temporal patterns over longer periods than the supervision period. We apply this theory to a biologically grounded motor learning task where a recurrent population is trained to output EMG signals from macaque motor units during an oriented reaching task. We find that many levels of feature-learning strength give rise to high quality fits of the EMG data, resulting in a family of solutions that are compatible with the neural data. Based on work with David Clark, Jacob Zavatone Veth, and Cengiz Pehlevan.

Bi-HKT Manifolds, Sigma Models, Large N=4 and their String Constructions
2026-02-24 16:15 - 18:00 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speakers: Max Hübner, CMSA
Title: Bi-HKT Manifolds, Sigma Models, Large N=4 and their String Constructions
Abstract: We continue our review of Witten’s paper “Instantons and the Large N=4 Algebra”. We discuss the realization of large N=4 supersymmetry in the context of supersymmetric sigma-models, and discuss and motivate string theoretic duals to these sigma models. This talk aims to supply physical insight building on Saman’s talk from last week 2/17.

Scaling Stochastic Momentum from Theory to LLMs
2026-02-25 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
New Technologies in Mathematics Seminar
Speaker: Courtney Paquette, McGill University
Title: Scaling Stochastic Momentum from Theory to LLMs
Abstract: Given the massive scale of modern ML models, we now often get only a single shot to train them effectively. This limits our ability to sweep architectures and hyperparameters, making it essential to understand how learning algorithms scale so insights from small models transfer to large ones.
In this talk, I present a framework for analyzing scaling laws of stochastic momentum methods using a power-law random features model, leveraging tools from high-dimensional probability and random matrix theory. We show that standard SGD with momentum does not improve scaling exponents, while dimension-adapted Nesterov acceleration (DANA)—which explicitly adapts momentum to model size and data/target complexity—achieves strictly better loss and compute scaling. DANA does this by rescaling its momentum parameters with dimension, effectively matching the optimizer’s memory to the problem geometry.
Motivated by these theoretical insights, I introduce logarithmic-time scheduling for large language models and propose ADANA, an AdamW-like optimizer with growing memory and explicit damping. Across transformer scales (45M to 2.6B parameters), ADANA yields up to 40% compute savings over tuned AdamW, with gains that improve at scale.
Based on joint work with Damien Ferbach, Elliot Paquette, Katie Everett, and Gauthier Gidel.

Higher Symmetries, Eta Invariants and Anomaly Theories
2026-02-26 13:30 - 14:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Differential Geometry and Physics Seminar
Speaker: Mirjam Cvetic, University of Pennsylvania
Title: Higher Symmetries, Eta Invariants and Anomaly Theories
Abstract: In recent years, much progress has been made in understanding the extra-dimensional origin of higher symmetry structures of many quantum field theories (QFTs) obtained via geometric engineering. Among others, our understanding of anomaly structures in QFTs has been significantly improved. Key in these considerations is the asymptotic boundary of the internal dimensions which geometrizes many topological QFT features. Within this context we present explicit results for anomaly coefficients in five-dimensional supersymmetric QFTs that are engineered in M-theory on Calabi-Yau three-folds, and show that eta-invariants of the asymptotic boundary of the engineered geometry are key to determine 1-form self-anomaly coefficients. The results both for orbifolds with isolated and non-isolated orbifold singularities are presented.

Gauge theory, from low dimensions to higher dimensions and back
2026-02-27 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Saman Habibi Esfahani, CMSA
Title: Gauge theory, from low dimensions to higher dimensions and back
Abstract: Almost thirty years ago, Donaldson and Thomas proposed extending powerful ideas from gauge theory, which had transformed the study of three- and four-dimensional manifolds, to higher dimensions, with the goal of defining new invariants of special holonomy manifolds. In this talk, I will outline the main ideas behind this program, mention some recent progress, and describe the key obstacles that remain, most notably non-compactness phenomena that make the analysis difficult.

Inverse problems in soft and active matter
2026-03-02 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: L. Mahadevan, Harvard
Title: Inverse problems in soft and active matter
Abstract: How can one grow a face or a flower from a flat sheet? Fold a sheet into an origami pattern? Control phase separation? Transport a drop of active matter? Steer an ant swarm? I will discuss potential answers to some of these inverse problems that unites ideas from optimal control and optimal transport for the steering of particles and fields.

Solitonic Symmetry: Cohomology with TFT Coefficients
2026-03-03 16:15 - 18:00 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speaker: Sanjay Raman, Harvard
Title: Solitonic Symmetry: Cohomology with TFT Coefficients
Abstract: We review the formalism of https://arxiv.org/pdf/2307.00939, which develops the theory of solitonic symmetry in quantum field theory. The algebraic structure of solitonic symmetry is determined by the fusion of topological functionals in a given path-integral formulation of topological field theory, and acts generically on topological defects determined by homotopy classes of maps to a “space of fields.” We will argue that the structure of solitonic symmetry in a theory with field space (Y) assembles into what looks like the cohomology of (Y) with coefficients in TFTs. We study this formalism in examples and show in particular that the maximal invertible solitonic subsymmetry reduces to the expected result.

Fukaya categories and higher representation theory
2026-03-05 13:30 - 14:30 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
Differential Geometry and Physics Seminar
Speaker: Vivek Shende (Syddansk Universitet & UC Berkeley)
Title: Fukaya categories and higher representation theory
Abstract: I will explain how Lagrangian Floer homology in certain monopole moduli spaces recovers the Khovanov homology and its relatives, by a description strikingly similar to the Oszvath-Szabo Heegard-Floer theory. I will also explain how the ‘sectorial descent’ of Fukaya categories can be used to construct Rouquier’s promised monoidal structure on the category of representations of the categorified “positive part” of the quantum group. This is joint work with Mina Aganagic, Elise LePage, and Peng Zhou.
Note: Location change to Harvard Science Center Room 300H

Freedman Seminar: Mattie Ji, Penn and Jeongwan Haah, Stanford
2026-03-06 15:00 - 17:15 | Hybrid
Freedman Seminar
Speakers: Mattie Ji (Penn) and Jeongwan Haah (Stanford)
Mattie Ji Title: Quantum Cellular Automata via Algebraic K-Theory
Abstract: Algebraic K-theory, on a very high level, is the study of how to break apart and assemble objects linearly, which makes the field amenable to classification questions. In this work, we apply this methodology to study the classification of quantum cellular automata (QCA). Over an arbitrary commutative ring R and a general class of metric spaces X, we construct a space of QCA that depends only on the large-scale (coarse) geometry of X. We explain how QCA classification groups (QCA modulo circuits) either arise naturally as or are refined by this space in most cases of interest.
Motivated by negative K-theory, we also show the classification of QCA on Euclidean lattices is given by an $Omega$-spectrum indexed by the dimension. As a corollary, we also obtain a non-connective delooping of the K-theory of Azumaya R-algebras, whose negative homotopy groups are the QCA classification groups. When R is the complex numbers, our method can be adapted to yield an $Omega$-spectrum for QCA of $C^*$-algebras with unitary circuits. This talk is based on joint work with Bowen Yang.

Jeongwan Haah Title: Fermionic QCA in 2d are trivial
Abstract: We consider bounded spread automorphisms of Z/2-graded algebra (fermionic QCA) on the two-dimensional lattice and prove that every fQCA is a unitary circuit followed by fermionic shifts when stabilized by Majorana modes. This is an analog of a theorem by Freedman and Hastings for the case of ungraded algebras. The overall argument follows a similar line in that we show invertible subalgebras in 1d is trivial, but the stabilization is used crucially. By an existing argument, this triviality of fQCA in 2d implies that the 3d (bosonic) QCA that disentangles the Walker-Wang model with three-fermion theory is nontrivial. The latter was known to be nontrivial against Clifford gates but remained conjectural against more general unitary gates. To my knowledge, this gives the only example ungraded QCA that is proved to be nontrivial against general unitary circuits and shifts, and the only example ungraded invertible subalgebra that is not isomorphic to any tensor product algebra. I will explain elements new to the fermionic setting and give an overview of the nontriviality argument. (Based on an upcoming work with Jeffrey Kwan and David Long)

The categorical 't Hooft expansion
2026-03-09 15:00 - 16:00 | Virtual
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Davide Gaiotto (Perimeter Institute)
Title: The categorical ‘t Hooft expansion
Abstract: The ‘t Hooft expansion is the key structure underlying dualities between gauge theories of large matrices and string theories. I will review categorical aspects of the ‘t Hooft expansion, matching the formal deformation space of certain “fundamental modifications” of the gauge theory to the formal deformation space of a category of boundary conditions (“D-branes”) for a 2d dg-TFT, to be identified with the world-volume theory for the string theory. I will illustrate this by reviewing the holographic description of matrix models.

TQFTs do not detect the Milnor sphere
2026-03-10 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: TQFTs do not detect the Milnor sphere
Abstract: I will talk about the recent paper of Gripaios and Randall-Williams with that title, where they prove that a functorial TQFT (i.e. a symmetric monoidal functor from the n-dimensional bordism category into a suitably nice target category) assigns the same value to homotopy spheres that bound a parallelizable manifold, extending some no-go theorems of Reutter and Schommer-Pries.

Strongly adapted contact geometry of Anosov 3-flows
2026-03-12 13:30 - 14:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Differential Geometry and Physics Seminar
Speaker: Surena Hozoori (Brandeis)
Title: Strongly adapted contact geometry of Anosov 3-flows
Abstract: We will discuss some recent developments in the contact geometric theory of Anosov 3-flows, whose roots go back to the works of Mitsumatsu and Eliashberg-Thurston in the mid 1990s. In particular, we provide a contact geometric characterization of Anosov 3-flows based on interactions with Reeb dynamics, as well as investigate the basic properties of the resulting geometries. Time permitting, we will discuss how these results allow one to re-approach some classical questions in Anosov dynamics.

Finite N indices from branes and negative branes
2026-03-16 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Kasia Budzik (Harvard University)
Title: Finite N indices from branes and negative branes
Abstract: Finite-N effects in large-N gauge theories, such as trace relations, are expected to be holographically dual to non-perturbative phenomena in string theory, such as Giant Graviton branes. A convenient setting to study these effects are supersymmetric indices of U(N) gauge theories. The finite-N indices can be reproduced by a series of corrections to the infinite-N result, known as the Giant Graviton expansion.
In this talk I will present a generalization of the Molien-Weyl formula computing generating functions of invariants of supergroups U(N|M), which arise as gauge groups of brane/negative brane systems in string theory. The formula leads to a new expansion relating finite-N and infinite-N indices of U(N) gauge theories. I will comment on its relation to Murthy’s Giant Graviton expansion and suggest a physical interpretation in terms of branes and negative branes. This talk is based on arXiv:2509.20451 and work in progress with Davide Gaiotto.

Dynamic reasoning
2026-03-18 14:00 - 15:00 | Virtual
New Technologies in Mathematics Seminar
Speaker: Emmanuel Abbé, EPFL, Institute of Mathematics and School of Computer and Communication Sciences & Apple
Title: Dynamic reasoning
Abstract: In the current AI landscape, reasoning is frequently equated with the generation of intermediate “thinking traces”. However, these traces are merely a mechanism, not the ultimate objective.
Relying solely on the presence of a trace can be deceptive, as models often learn to mimic the format of reasoning while effectively overfitting to specific training distributions.
To build more robust and versatile reasoners, we shift our focus to more specific structural properties of the thinking process, in particular compositionality (inductive CoT, AdaBack) and abstraction (AbstRaL).

Moduli of subcanonical points
2026-03-19 16:00 - 17:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Algebra Seminar
Speaker: Dawei Chen, Boston College
Title: Moduli of subcanonical points
Abstract: Subcanonical points are special Weierstrass points on smooth algebraic curves whose semigroups are symmetric. In this talk, I will explain the rich geometry of the moduli space of subcanonical points, with a focus on its connected components, birational geometry, topology, and the deformation theory of related monomial singularities.

Line operators in holomorphic QFT
2026-03-24 16:15 - 18:00 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Joint Math/CMSA Geometry and Quantum Theory Seminar
Speaker: Keyou Zeng (CMSA)
Title: Line operators in holomorphic QFT
Abstract: We will discuss the recent work (arxiv:2508.11749), which defines the so called dg shifted Yangian. I will discuss their origin from the study of 3d holomorphic topological field theories, a variant of 3d TQFT. A dg shifted Yangian is supposed to control the fusion of line defect in the corresponding 3d HT theories. I will illustrate these discussions in examples.

Gauge theory on Hyperkähler manifolds
2026-03-26 13:30 - 14:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Differential Geometry and Physics Seminar
Speaker. Emily Autumn Windes (New Uzbekistan University)
Title: Gauge theory on Hyperkähler manifolds
Abstract: In this talk, I describe various distinguished classes of connections on Hyperkähler manifolds and their dimensional reductions. Then, I describe a construction of new examples of Sp(2)-instantons, primitive HYM connections, and Spin(7)-instantons with symmetry on the manifold T*CP2. This talk is based on joint work with Jesse Madnick and Izar Alonso.

The Beilinson-Bloch conjecture for some non-isotrivial varieties over global function fields
2026-03-26 16:00 - 17:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Algebra Seminar
Speaker: Matt Broe, Boston University
Title: The Beilinson-Bloch conjecture for some non-isotrivial varieties over global function fields
Abstract: The Beilinson-Bloch conjecture is a generalization of the Birch and Swinnerton-Dyer conjecture, which relates the ranks of Chow groups of smooth projective varieties over global fields to the order of vanishing of L-functions. We prove the conjecture for certain classes of non-isotrivial varieties over Fq(t), including some cubic threefolds and fivefolds. We deduce the Birch and Swinnerton-Dyer conjecture for their intermediate Jacobians, and use it to establish new cases of the Tate conjecture over finite fields.

Exotic R^4's are unclassifiable
2026-03-27 15:00 - 17:15 | 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
