CMSA

The geometry of pure spinor superfield formalism
2025-02-20 10:00 - 11:00 (America/New_York) | Virtual
Mathematical Physics and Algebraic Geometry Seminar
Speaker: Simone Noja (Heidelberg University)
Title: The geometry of pure spinor superfield formalism
Abstract: In this talk I will present a mathematical perspective on the pure spinor superfield formalism. In particular, I will discuss how field multiplets in supersymmetric theories can be constructed mathematically from geometric data associated with certain algebraic varieties—namely, the nilpotence variety of the (super)symmetry algebra of the theory. After discussing key examples, I will, time permitting, outline a possible generalization of the formalism within the framework of derived geometry.

CMSA Q&A Seminar: Phillip Matchett Wood
2025-02-19 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q&A Seminar
Speaker: Phillip Matchett Wood, Harvard University
Topic: Info session on the CMSA/Mathematics Summer REU Program (Research Experience for Undergraduates)

Algebras of "symmetries" in QFT and applications to solitons (1)
2025-02-18 16:15 - 18:15 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speaker: Dan Freed, Harvard CMSA and Math
Title: Algebras of “symmetries” in QFT and applications to solitons (1)
https://arxiv.org/abs/2403.08883

General Relativity Seminar
2025-02-18 11:00 - 12:00 | Virtual
General Relativity Seminar
Speaker: Maximilian Ofner, University of Vienna
Title: Stability and Instability of Relativistic Fluids in Slowly Expanding Spacetimes
Abstract: Homogeneous and isotropic solutions to the relativistic Euler equations are known to be unstable on a Minkowski background. However, for FLRW models with a fast expansion rate, relativistic fluids stabilize. This scenario suggests a transition between stable and unstable behavior, somewhere along a family of spacetimes parametrized by their expansion rate. In this talk we will discuss this phase transition for various equations of state, focusing on the regime of linear and decelerated expansion. This is based on recent analytical results, complemented by numerical analysis.

Jack polynomials and enumeration of non-orientable maps
2025-02-14 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Houcine Ben Dali, Harvard CMSA
Title: Jack polynomials and enumeration of non-orientable maps
Abstract: A map is a graph embedded on a surface, which may be orientable or not. The representation theory of the symmetric group can be used to write the generating series of maps on orientable surfaces using Schur symmetric functions.
Several conjectures suggest that Jack polynomials—a one-parameter deformation of Schur functions—are related to the enumeration of non-orientable maps counted with a “non-orientability” weight. In this talk, I will discuss some of these conjectures and present recent progress in this direction.

2025 Ding Shum Lecture: Irit Dinur, IAS: Expanders from local to global
2025-02-13 16:00 - 17:00 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
On February 13, 2025 the CMSA hosted the sixth annual Ding Shum Lecture, given by Irit Dinur, Institute for Advanced Study.
Location: Harvard Science Center Hall A & via Zoom Webinar
Speaker: Irit Dinur, Institute for Advanced Study

Title: Expanders from local to global
Abstract: Imagine a network—like a social network, a transportation system, or even a biological system—where every part of the network is robustly connected to the rest. Expander graphs are the mathematical idealization of such networks. They are structures where any small group of points (nodes) has many connections to the rest of the graph, ensuring that no part is isolated and information (or influence) spreads efficiently throughout.
We will begin by surveying expander graphs, their discovery and construction, and some fascinating applications such as error-correcting codes, pseudorandomness, and probabilistically checkable proofs (PCPs), highlighting their role as a foundation for many breakthroughs in theoretical computer science. Then, we will shift focus to an exciting new kind of expanders called high dimensional expanders (HDXs). While expanders are well-understood and widely applied, HDXs remain enigmatic, with potential that we are only starting to uncover. We will talk about a fascinating local to global feature that HDXs have, and some applications.

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

The Structure of the Flux Landscape
2025-02-13 10:00 - 11:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Mathematical Physics and Algebraic Geometry Seminar
Speaker: Damian Van de Heisteeg, Harvard CMSA
Title: The Structure of the Flux Landscape
Abstract: Identifying flux vacua in string theory with stabilized complex structure moduli presents a significant challenge, necessitating the minimization of a scalar potential complicated by infinitely many exponential corrections. In order to obtain exact results we connect three central topics: transcendentality or algebraicity of coupling functions, emergent symmetries, and the distribution of vacua. We demonstrate these ideas on an explicit example where we determine the landscape of exact flux vacua with a vanishing superpotential. We examine the implications of the tadpole bound, which intriguingly confines flux vacua to real values of the moduli, providing a potential avenue for addressing the strong CP problem.

Discovering Data Structures: Nearest Neighbor Search and Beyond
2025-02-12 14:00 - 15:00 | Virtual
New Technologies in Mathematics Seminar
Speaker: Omar Salemohamed, Mila
Title: Discovering Data Structures: Nearest Neighbor Search and Beyond
Abstract: As neural networks learn increasingly sophisticated tasks—from image recognition to mastering the game of Go—we ask: can deep learning discover data structures entirely from scratch? We introduce a general framework for data structure discovery, which adapts to the underlying data distribution and provides fine-grained control over query and space complexity. For nearest neighbor (NN) search, our model (re)discovers classic algorithms like binary search in one dimension and learns structures reminiscent of k-d trees and locality-sensitive hashing in higher dimensions. Additionally, the model learns useful representations of high-dimensional data such as images and exploits them to design effective data structures. Beyond NN search, we believe the framework could be a powerful tool for data structure discovery for other problems and adapt our framework to the problem of estimating frequencies over a data stream. To encourage future work in this direction, we conclude with a discussion on some of the opportunities and remaining challenges of learning data structures end-to-end.

CMSA Q&A Seminar: Javier Gomez-Serrano
2025-02-12 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q&A Seminar
Speaker: Javier Gomez-Serrano, Brown University
Topic: Please tell us about the Millennium prize problem for Navier-Stokes and segue from that into ML?

Discussion of Integrating quantum groups over surfaces
2025-02-11 16:15 - 18:15 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speaker: Ben Gammage, Harvard University
Title: Discussion of Integrating quantum groups over surfaces
https://arxiv.org/abs/1501.04652

On the past maximal development of near-FLRW data for the Einstein scalar-field Vlasov system
2025-02-11 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar
Speaker: Liam Urban (University of Vienna)

Title: On the past maximal development of near-FLRW data for the Einstein scalar-field Vlasov system
Abstract: In recent years, the formation of Big Bang singularities has been increasingly well understood in presence of scalar-field matter, which suppresses the geometric oscillations that one generically expects otherwise. From a cosmological perspective, however, one would like to understand whether this feature persists when coupled to further models that more closely resemble the matter content in our universe.
In this talk, I will discuss the past nonlinear stability of FLRW solutions to the Einstein scalar-field Vlasov system in three and four spacetime dimensions without symmetry assumptions. The latter is based on joint work with David Fajman. In both works, near-FLRW solutions are
shown to be asymptotically velocity term dominated toward the past, resulting in a quiescent Big Bang singularity with stable Kretschmann scalar blow-up. The Vlasov distribution, however, becomes highly anisotropic towards the Big Bang singularity, concentrating in preferred momentum directions associated with eigendirections of the shear. To ensure that the scalar field sufficiently mitigates this behaviour, one crucially exploits a scaling hierarchy between horizontal and vertical derivatives in the expansion normalized Vlasov equation. In four
spacetime dimensions, this analysis is paired with a Bel-Robinson energy formalism to control the spacetime and scalar field evolution, while one finds a significantly more direct proof in three dimensions since the spatial Riemann curvature is pure trace.
As a corollary, one also obtains that the Strong Cosmic Censorship conjecture holds for four-dimensional polarized $U(1)$-symmetric solutions to the Einstein vacuum equations with spatial topology $MtimesS^1$ and isotropic quotient.

AI in math and theoretical physics: Status and prospects
2025-02-10 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Michael Douglas, Harvard CMSA
Title: AI in math and theoretical physics: status and prospects
Abstract: AI is making great progress and has the potential to change how we work in unprecedented ways. In this talk I will survey a few recent works which illustrate the state of the art, some from my own research, some developed at the CMSA’s recent program on Mathematics and Machine Learning. I will then report on current developments in AI and speculate on how they will affect our work in the next few years.

On 5d conformal matter
2025-02-10 11:00 - 12:00 | Virtual
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Mario De Marco (UL Brussels)
Title: On 5d conformal matter
Abstract: SCFTs with 8 supercharges lie at the sweet spot of the classification program of susy scale-invariant theories: with this amount of susy, the classification is in principle achievable, despite being non-trivial. In this talk, I will present the geometric approach to the classification of 5d SCFTs, based on geometric engineering on non-compact Calabi-Yau manifolds. The strategy is to imagine a 5d SCFT as a non-Lagrangian generalization of a quiver, and to build this generalised quiver by gauging together indecomposable blocks, called “5d conformal matter theories”. In this talk, I will start with a recap of the geometric construction of [2311.04984]. I will then present some forthcoming results, concerning the (p,q) web realization of 5d conformal matter theories, their reduction to 4d, their magnetic quiver, and the discovery of exotic “trifundamental” and “quadrifundamental” 5d indecomposable blocks (with flavor group at least SO(4k+2)^3 or SO(4k)^4).
In collaboration with M. Del Zotto, M. Graffeo, J. Grimminger, and A. Sangiovanni.

Joint BHI/CMSA Foundation Seminar: Quantum Effects Inside Black Holes
2025-02-10 09:30 - 10:30 | Black Hole Initiative, 20 Garden Street, Cambridge MA, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Joint BHI/CMSA Foundation Seminar
Location: BHI seminar room
Speaker: Noa Zilberman (Princeton University)
Title: Quantum Effects Inside Black Holes
Abstract: Astrophysical black holes are known to be rotating. Within classical General Relativity, the simplest spacetime solution (the Kerr solution) describing a rotating black hole reveals a traversable passage through an inner horizon – which in turn may lead to another external universe. But does this remain the case when taking quantum effects into account?
Answering this question, along others, requires one to understand the manner in which quantum energy fluxes affect the internal geometry of a black hole. It has been widely anticipated, yet inconclusive (till this work), that such effects would diverge at the inner horizon of a spinning black hole. This divergence, if indeed takes place, may drastically affect the internal black hole geometry, potentially preventing the inner horizon traversability. Clarifying this issue requires the computation of the quantum energy fluxes in black hole interiors. However, this has been a serious challenge for decades.
Using a combination of old and new methods, we have managed to compute the quantum energy fluxes at the inner horizon of a spinning black hole, in a vacuum state corresponding to an evaporating black hole. We found that these fluxes are either positive or negative, depending on the black hole spin (and polar angle). The sign of these fluxes may be crucial to the nature of their backreaction on the geometry (as should be dictated by the semiclassical Einstein equation).
In this seminar, we shall briefly describe the basic framework of semiclassical general relativity and the renormalization procedure, and then present our novel results for the quantum fluxes at the inner horizon of a rotating black hole, briefly mentioning possible implications for the inner horizon traversability.

Is every knot isotopic to the unknot?
2025-02-07 14:00 - 15:45 | Virtual
Freedman CMSA Seminar
*via Zoom*
Speaker: Sergey Melikhov, Steklov Math Institute
Title: Is every knot isotopic to the unknot?
Abstract: The following problem was stated by D. Rolfsen in his 1974 paper; according to R. Daverman it was being discussed since the mid-60s. Is every knot in $S^3$ isotopic (=homotopic through embeddings) to a PL knot — or, equivalently, to the unknot? In particular, is the Bing sling isotopic to a PL knot? We show that the Bing sling $B$ is not isotopic to any PL knot by an isotopy which extends to an isotopy of any 2-component link obtained from $B$ by adding a disjoint component $Q$ such that $lk(B,Q)=1$. Moreover, the assertion remains true if the additional component is allowed to self-intersect, and even to get replaced by a new one at any time instant $t$, as long as it remains disjoint from the original component $K_t$ and represents the same conjugacy class as the old one in $G/[G’,G”]$, where $G=pi_1(S^3setminus K_t)$. The are examples showing that the latter result cannot be improved in certain ways. I plan to present a sketch of the proof, modulo some ingredients. The details can be found in arXiv:2406.09365 and the main ingredients in arXiv:2406.09331 and arXiv:math/0312007v3.

Quantum algebras and R-matrices from the equivariant affine Grassmannians
2025-02-06 10:00 - 11:00 | Virtual
Mathematical Physics and Algebraic Geometry Seminar
Speaker: Wenjun Niu, Perimeter Institute
Title: Quantum algebras and R-matrices from the equivariant affine Grassmannians
Abstract: In this talk, I will explain my joint work with R. Abedin, in which we construct, for each Lie algebra g, a Hopf algebra and a spectral R-matrix satisfying quantum Yang-Baxter equation. This Hopf algebra is a quantization of the Lie bi-algebra structure on T^*g[t] defined by Yang’s r-matrix, and therefore we call it the Yangian of T^*g. The construction is based on the category of coherent sheaves on the equivariant affine Grassmannian associated to the formal group of g, and is motivated by the study of the category of line defects in a 4 dimensional holomorphic-topological field theory.

CMSA Q&A Seminar: Subir Sachdev
2025-02-05 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q&A Seminar

Speaker: Subir Sachdev, Harvard University
Topic: What is a quantum critical region?

Blob homology
2025-02-04 16:15 - 18:15 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speaker: Sunghyuk Park, Harvard CMSA
Title: Blob homology

The mass angular momentum inequality
2025-02-04 11:00 - 12:00 | Virtual
General Relativity Seminar
Speaker: Gilbert Weinstein, Ariel University
Title: The mass angular momentum inequality
Abstract: We show that either there is a counterexample to black hole uniqueness, in the form of a regular axisymmetric stationary vacuum spacetime with an asymptotically flat end and multiple degenerate horizons which is ‘ADM stable’, or the following statement holds. Complete, simply connected, maximal initial data sets for the Einstein equations with multiple ends that are either asymptotically flat or asymptotically cylindrical, admit an ADM mass lower bound given by the square root of total angular momentum, under the assumption of nonnegative energy density and axisymmetry. Moreover, equality is achieved bound only for a constant time slice of an extreme Kerr spacetime. The proof is based on a novel flow of singular harmonic maps with hyperbolic plane target, under which the renormalized harmonic energy is monotonically nonincreasing. Relevant properties of the flow are achieved through a refined asymptotic analysis of solutions to the linearized harmonic map equations.

Rational approximation and the AAA algorithm
2025-02-03 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Nick Trefethen, Harvard University
Title: Rational approximation and the AAA algorithm
Approximation by rational functions used to be mainly a theoretical subject, but with the introduction of the AAA algorithm in 2018, it became computationally practical and indeed easy. The implications for what we can do numerically are enormous. This talk will outline the algorithm and demonstrate its application to a collection of problems. We can also use it to demonstrate the potential theory that underlies the theory of rational approximation, a topic that goes back to Joseph Walsh here at Harvard a century ago.

Topological to Gravitational Leptogenesis, via Ultra Unification
2025-02-03 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Juven Wang (LIMS, Royal Institution)
Title: Topological to Gravitational Leptogenesis, via Ultra Unification
Abstract: We propose a new mechanism for leptogenesis, named Topological Leptogenesis, in which dark matter consists of topological order, so gapped anyon excitations decay to generate the Standard Model lepton asymmetry. Topological Leptogenesis is in contrast with the Majorana Leptogenesis and Gravitational Leptogenesis. In the standard Majorana Leptogenesis, the baryon asymmetry of the present universe is attributed to the leptogenesis from the sterile right-handed neutrino with heavy Majorana fermion mass decaying into the Standard Model leptons in the very early universe, while the electroweak sphaleron causes baryogenesis at a later time. Gravitational leptogenesis can be regarded as an intermediate step between Majorana particle leptogenesis and topological non-particle leptogenesis. Topological Leptogenesis is derived out of Ultra Unification constructed from a mod 16 nonperturbative global anomaly cancellation that adds a symmetry-extended anomalous gapped topological quantum field theory (TQFT) to the Standard Model. Thus (1) the Beyond-the-Standard-Model (BSM) Dark Matter partly consists of Topological Order with low energy TQFT, while there are anyon string excitations above the energy gap. (2) The 5th force is a Topological Discrete Gauge Force of (B-L) that mediates between the Standard Model particles, the BSM Topological Order, and gapped anyon string non-particle excitations.
Based on https://arxiv.org/abs/2501.00607, https://arxiv.org/abs/2012.15860, https://arxiv.org/abs/2302.14862 and https://arxiv.org/abs/2411.05786.

Smooth projective fibrations over the projective line and their sections
2025-01-31 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Iacopo Brivio
Title: Smooth projective fibrations over the projective line and their sections
Abstract: Suppose $fcolon Xto mathbf{CP}^1$ is a smooth projective fibration, is it then true that $f$ has a section? This deceptively simple result was established by Seidel and McDuff using deep methods of symplectic geometry. Alex Pieloch recently generalized this to morphisms with at most one singular fibers and furthermore showed that $X$ uniruled, that is covered by images of $mathbf{P}^1$. In my talk I will explain how to recover Pieloch’s result from the Good Minimal Model Conjecture.

CMSA/MATH Welcome Back Gathering
2025-01-30 16:00 - 17:30 | CMSA 20 Garden Street Cambridge, Massachusetts 02138 United States
Thursday, Jan. 30, 2025
4:00 pm
All CMSA and Math affiliates are invited.

Stochastic Process and Noncommutative Geometry
2025-01-30 10:00 - 11:00 | Hybrid
Mathematical Physics and Algebraic Geometry Seminar
Speaker: Zichang Wang (Tsinghua University)
Title: Stochastic Process and Noncommutative Geometry
Abstract: We explain a stochastic approach to topological field theory and present a case study of quantum mechanical model and its relation to noncommutative geometry. For detail reference, see https://arxiv.org/abs/2501.12360

Review of the excision property in factorization homology
2025-01-28 16:15 - 18:15 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speaker: Keyou Zeng, Harvard CMSA
Title: Review of the excision property in factorization homology

A homotopy of 2d SCFTs and an implication for Topological Modular Forms
2025-01-27 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Vivek Saxena (YITP Stony Brook and NHETC Rutgers)
Title: A homotopy of 2d SCFTs and an implication for Topological Modular Forms
Abstract: The Segal-Stolz-Teichner conjecture states that there exists an isomorphism between deformation classes of two-dimensional N=(0,1) superconformal field theories (SCFTs) and generalized cohomology classes known as Topological Modular Forms (TMFs). Such 2d N=(0,1) SCFTs arise naturally in physics as worldsheet theories of (possibly compactified) heterotic strings. Recently, this connection was used to prove the absence of global anomalies in heterotic string theories and make predictions about topological terms in their low-energy effective actions, among other things.
In this talk, after giving a brief overview of these ideas, I will describe a physics ”proof” (using methods from 2d CFT) of a mathematical conjecture of Tachikawa and Yamashita about TMF classes in degree 31. Specifically, by examining the two worldsheet theories corresponding to two T-dual nine-dimensional spacetime non-supersymmetric heterotic string theories (namely the $(E_8)_1 times (E_8)_1$ theory and the $(E_8)_2$ theory), I will argue that the $(E_8)_2$ theory corresponds to the unique nontrivial torsion element $[(E_8)_2]$ of TMF$^{31}$ with zero mod-2 elliptic genus.

Joint BHI/CMSA Foundation Seminar: Quantum Criticality in Black Hole Dynamics
2025-01-27 09:30 - 10:30 | Black Hole Initiative, 20 Garden Street, Cambridge MA, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Joint BHI/CMSA Foundation Seminar
Location: BHI Seminar Room
Speaker: Uri Kol, Harvard CMSA

Title: Quantum Criticality in Black Hole Dynamics
Abstract: Black hole perturbation theory captures a few important effects in the dynamics of binary mergers, such as tidal deformations and the decay of ringdown modes, as well as the physics of the photon ring. However, deriving qualitative results that lead to robust predictions in this theory remains a challenging problem, despite a rich scientific history.
Motivated by the immense experimental progress made in the field over the past decade, in this talk I will describe a new critical phenomenon emerging in the theory of perturbations around Kerr black holes. A critical point is identified at zero black hole temperature, giving rise to a wide regime at finite temperatures which is dominated by critical perturbations. As in quantum many-body systems, the physics in the critical regime is described exclusively by a set of critical exponents, therefore leading to robust predictions that are unique to the Kerr metric.

CMSA Q&A Seminar: Edgar Shaghoulian
2025-01-22 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q&A Seminar
Speaker: Edgar Shaghoulian, UC Santa Cruz
Topic: What are the main questions in quantum gravity today?

Workshop on Symmetries and Gravity
2025-01-21 09:00 - 2025-01-24 17:00 | CMSA 20 Garden Street Cambridge, Massachusetts 02138 United States
Workshop on Symmetries and Gravity
Dates: January 21-24, 2025
Location: Harvard CMSA, 20 Garden Street, Cambridge, MA 02138
Organizers: Ibrahima Bah (Johns Hopkins University), Patrick Jefferson (Johns Hopkins University), Yiming Chen (Stanford University)
Description: There is a widespread belief, that has its origins in work from the 70s, that a theory of quantum gravity cannot admit global symmetries. Traditionally, this was seen only as a qualitative statement about ordinary symmetries, but there have since been a number of developments that have both widened its scope and sharpened its implications. Recent work has greatly broadened the definition of global symmetries, and characterizes them in terms of topological operators in quantum systems. Concurrently, insights from quantum gravity have suggested ways to quantify the extent of global symmetry violation. Additionally, advances in the swampland program, along with amplitudes and bootstrap techniques, have shown ways to turn high-energy statements into constraints on low-energy effective field theories. In string theory, there are more concrete statements on charge violation in gravity, with proofs in limited context. In general, however, “no global symmetries in quantum gravity” continues to be an open conjecture with broad implications on the nature of quantum gravity and low-energy effective field theory. The main goal of the meeting is to bring together experts in the various arenas of research above, to reassess and develop new strategies for making progress on this long-standing open problem. Some objectives include understanding the violation of various generalized and categorical symmetries in gravity more cohesively, and putting concrete bounds on global charge-violating amplitudes at low energies.
Partially funded by the Simons Collaboration on Global Categorical Symmetries.

Confirmed Participants

Tom Banks, Rutgers
Federico Bonetti, Durham University
Christian Copetti, Oxford
Hector Parra De Freitas, Harvard
Damian van de Heisteeg, Harvard CMSA
Matilda Delgado, IFT
Michele Del-Zotto, Uppsala University
Muldrow Etheredge, UMass Amherst
Iñaki Garcia-Etxebarria, Durham University
Eduardo Garcia-Valdecasas, SISSA, Trieste
Naomi Gendler, Harvard
Kelian Haring, CERN
Daniel Harlow, MIT
Jonathan Heckman, University of Pennsylvania
Ben Heidenreich, UMass Amherst
Aidan Herderschee, IAS
Max Huebner, Uppsala University
Jesús Huertas, Instituto de Física Teórica
Theo Johnson-Freyd, Dalhousie University
Ho Tat Lam, MIT
Adam Levine, MIT
Yue-Zhou Li, Princeton
Jacob McNamara, Caltech
Ruben Minasian, Institute of Theoretical Physics Saclay
Amineh Mohseni, Harvard
Miguel Montero, IFT
Gregory Moore, Rutgers
Leonardo Rastelli, Stony Brook
Matt Reece, Harvard University
Grant Remmen, New York University
Diego Rodriguez-Gomez, University of Oviedo
Konstantinos Roumpedakis, Johns Hopkins
Tom Rudelius, Durham University
Vivek Saxena, Stony Brook and Rutgers
Edgar Shaghoulian, UC Santa Cruz
Shu-Heng Shao, Stony Brook and MIT
Adar Sharon, Simons Center for Geometry and Physics, Stony Brook
Irene Valenzuela, IFT and CERN
Thomas Waddleton, Johns Hopkins
Hao Xu, University of Göttingen
Xingyang Yu, Virginia Tech

Schedule
Tuesday, Jan. 21, 2025
9:00 – 9:30 am
Breakfast
9:30 – 11:00 am
Review
Leonardo Rastelli, Stony Brook University
Youtube Video
11:00 – 11:15 am
Break
11:15 am– 12:00 pm
Kelian Haring, CERN
Title: S-matrix bootstrap and black hole production
Abstract: I will review the expected effects of black hole production in scattering amplitudes. I will consider both symmetry-breaking and elastic amplitudes. I will argue that, in the elastic case, this input can be computationally useful. Then, I will discuss an example of a symmetry-breaking Wilson coefficient as a concrete target for the bootstrap.
Youtube Video
12:00 – 1:45 pm
Lunch Break
1:45 – 2:30 pm
Ho Tat Lam, MIT
Title: Global Aspects of Exactly Marginal Current-Current Deformations
Abstract: Conformal field theories connected by exactly marginal deformations form conformal manifolds. In two dimensions, a large class of conformal manifolds is generated by bilinears of currents, known as current-current deformations. In this talk, we will revisit these deformations and prove that a dense set of points on the conformal manifolds are related to the seed theory through discrete gauging. This perspective enables us to connect the topology of the conformal manifolds with the anomalies of the currents and to show that enhanced invertible symmetries reorganized into non-invertible symmetries away from the symmetry enhanced points. We will also discuss how current-current deformation can be understood from the recently proposed continuous abelian symmetry topological field theory.
Youtube Video
2:30 – 3:15 pm
Tom Banks, Rutgers University
Title: Symmetries in the Hilbert Bundle Formulation of Quantum Gravity
Abstract: Results of Jacobson, Carlip and Solodukhin from the 1990s, as extended by Banks and Zurek in 2021, point to a solution of Einstein’s equations as a hydrodynamic approximation to a quantum gravitational system, which determines the density matrix assigned to each subsystem corresponding to a hydrodynamic causal diamond in terms of the Virasoro generator of a cut off 1 + 1 dimensional CFT. The full quantum system can be viewed as a Hilbert bundle over the space of timelike geodesics on the hydrodynamic background. Isometries of the background generically map one fiber of the bundle to another and don’t act on a fixed Hilbert space. Time evolution along each geodesic is given by an analog of “one sided modular flow in QFT”, which in this context is a sequence of unitary embeddings of smaller diamond Hilbert spaces into larger ones. A full unitary map on the entire Hilbert space of a fiber requires a “Quantum Principle of Relativity” equating the entanglement spectrum of the density matrix of the largest diamond in the overlap between diamonds on different geodesics. In principle, this implies asymptotic symmetries for spacetimes which have them. For the case of asymptotically AdS space, this can be worked out in a hand waving way by using the Tensor Network Renormalization Group of Evenbly and Vidal. For asymptotically flat space we probably require a better non-perturbative definition of the space of asymptotic states to understand the action of the Poincare group. For de Sitter space there is no sense in which the de Sitter group acts on any set of asymptotic observables. Ironically, there IS an approximate de Sitter invariance of at least low point inflationary correlation functions, but I will not have time to discuss that.
Youtube Video
3:15 – 3:45 pm
Break
3:45 – 4:30 pm
Christian Copetti, Oxford University
Title: Non-Invertible Symmetries, Generalized Gauging and Factorization
Abstract: We analyze a toy model for low dimensional holography, in which the dual theory is an ensemble over 2d RCFTs. This simple model lacks factorization on multi-boundary geometries and at the same time has a (generalized) bulk global symmetry. We show that both problems are solved if the path integral prescription is modified by a generalized gauging operation, which can also be interpreted as the insertion of (topological) EOW branes.
Youtube Video
4:30 – 5:00 pm
Free Discussion
Wednesday, Jan. 22, 2025
9:00 – 9:30 am
Breakfast
9:30 – 11:00 am
Review
Daniel Harlow, MIT
Youtube Video
11:00 – 11:15 am
Break
11:15 am– 12:00 pm
Jacob McNamara, Caltech
Title: Conserved Charges of Closed Universes
Abstract: In quantum gravity, while our standard notions of symmetry operator become hard to define, the notion of conserved charge continues to make sense. After a general discussion of conserved charges in quantum gravity, I will present a new kinematic invariant of a gravitational path integral that refines the cobordism groups of quantum gravity: the (higher) category of closed universe charges. By categorifying an argument of Coleman, Giddings, and Strominger, I will argue that conserved charges in quantum gravity of any form degree arise only due to a categorical version of ensemble holography.
Youtube Video
12:00 – 1:45 pm
Lunch Break
1:45 – 2:30 pm
Federico Bonetti, Durham University
Title: Aspects of Categorical Symmetries for Branes
Youtube Video
2:30 – 3:15 pm
Konstantinos Roumpedakis, Johns Hopkins University
Title: Symmetry Operators and Gravity
Abstract: It is widely believed that there are no conserved charges in a theory of gravity, based on arguments involving black holes. Moreover, the modern approach to study global symmetries is the language of topological operators. In this talk, I will revisit the absence of global symmetries in a theory of gravity from the perspective of topological operators. More specifically, I will argue that topological operators for continuous symmetries written in terms of currents need regularization, which effectively gives them a small but finite width. The regulated operator is a finite tension object which fluctuates. In the zero-width limit these fluctuations freeze, recovering the properties of a topological operator. When gravity is turned on, the zero-width limit becomes ill-defined, thereby prohibiting the existence of topological operators. This talk is based on work in collaboration with Ibrahima Bah, Patrick Jefferson, and Thomas Waddleton.
Youtube Video
3:15 – 3:45 pm
Break
3:45 – 4:30 pm
Iñaki Garcia-Etxebarria, Durham University
Title: Some aspects of symmetry descent
Abstract: SymTFTs allow us to encode the symmetry structure of Quantum Field Theories in a convenient way. For those QFTs that arise in geometric engineering, or holography, we expect to be able to derive the SymTFT from the geometric data of the string background. This talk will describe some recent progress in this direction, together with S. Hosseini and with F. Gagliano.
Youtube Video
4:30 – 5:00 pm
Free Discussion
6:00 pm
Dinner at Changsho Restaurant
Thursday, Jan. 23, 2025
9:00 – 9:30 am
Breakfast
9:30 – 11:00 am
Review
Irene Valenzuela, IFT and CERN
Title: Breaking of Symmetries in Gravity
Abstract: Global symmetries are expected to be broken (or gauged) in quantum gravity. However, we can still learn a lot from understanding the mechanisms by which quantum gravity avoids them and quantifying their breaking. Remarkably, several Swampland constraints can be reinterpreted as consequences of breaking global symmetries. I will first focus on quantifying the minimal symmetry violation of axionic shift symmetries, and show how the bottom-up expectation based on black holes seems to hold in string theory examples. I will then discuss how this symmetry violation changes as we move in the moduli space, implying a drop-off of the quantum gravity cut-off when the symmetry is approximate. Finally, I will discuss the fate of non-invertible symmetries in string theory, and how they are typically broken at loop level. Nevertheless, these approximate non-invertible symmetries are still useful to fill in the gaps in the worldsheet proofs of some Swampland conjectures.
11:00 – 11:15 am
Break
11:15 am– 12:00 pm
Tom Rudelius, Durham University
Title: A Symmetry-Centric Perspective on the Geometry of the Landscape and the Swampland
Abstract: As famously observed by Ooguri and Vafa nearly twenty years ago, scalar field moduli spaces in quantum gravity appear to exhibit various universal features. For instance, they seem to be infinite in diameter, have trivial fundamental group, and feature towers of massive particles that become light in their asymptotic limits. In this talk, I will explain how these features can be reformulated in more modern language using generalized notions of global symmetries. Such symmetries are ubiquitous in non-gravitational quantum field theories, but it is widely believed that they must be either gauged or broken in quantum gravity. We will see that the observations of Ooguri and Vafa can be understood as consequences of such gauging or breaking.
12:00 – 1:45 pm
Lunch Break
1:45 – 2:30 pm
Miguel Montero, IFT
Title: Parity symmetry breaking and the membrane Weak Gravity Conjecture
Abstract: Symmetries are expected to be broken or gauged in any consistent theory of quantum gravity, and this also applies to spacetime symmetries such as parity. I will argue that, in the context of 4d N=1 AdS vacua of string theory, the Weak Gravity Conjecture for membranes case only holds if the vacuum has an exact (i.e. gauged) parity symmetry of Pin+ type. I will give top-down examples of M-theory vacua illustrating this, and show that in the DGKT scenario (a putative massive IIA vacuum with scale separation, whose full consistency is the subject of some debate in the literature) there is no parity symmetry, and the membrane WGC is violated. Thus, there is either a pathology in DGKT, or the membrane WGC is wrong. Both possibilities would have interesting consequences, and I will outline ongoing work to figure out which one is it.
2:30 – 3:15 pm
Matilda Delgado, IFT
Title: Dualities, Defects and Duality Defects
Abstract: I will outline how duality symmetries in quantum gravity theories naturally predict the existence of defects associated with duality transformations. While some of these objects are well-understood and extensively studied, others remain enigmatic; I will discuss this with examples. I will conclude by discussing the potential role of dualities in characterising the UV defects predicted by cobordism conjecture (and more generally by the no global symmetries conjecture). Based on: [2412.03640]
3:15 – 3:45 pm
Break
3:45 – 4:30 pm
Max Hübner, Uppsala University
Title: Metric Isometries, Holography, and Continuous Symmetry Operators
Abstract: In the AdS/CFT correspondence, a topological symmetry operator of the boundary CFT is dual to a dynamical brane in the gravitational AdS bulk. Said differently, this predicts a dynamical brane for every global symmetry of the boundary CFT. We analyze this correspondence for continuous symmetries which arise from a consistent truncation of isometries on the “internal” factor X of AdS × X. We discuss how this perspective can be used to both derive properties of the topological symmetry operators and non-topological properties of their bulk duals.
4:30 – 5:00 pm
Free Discussion

Friday, Jan. 24, 2025
9:00 – 9:30 am
Breakfast
9:30 – 10:15 am
Jonathan Heckman, University of Pennsylvania
Title: Cobordism Utopia
Abstract: On general grounds one expects that global symmetries are absent in quantum gravity. We discuss some aspects of this issue, focusing on the recently proposed Swampland Cobordism Conjecture, and related conjectures connected with completeness of the spectrum of states charged under symmetries. In particular, the U-dualities of M-theory provide an excellent arena both for testing aspects of these conjectures, as well as predicting the existence of new dynamical objects. We also comment on how this approach connects to related top down and holographic approaches to constructing and studying gauging and breaking symmetries in quantum gravity. Based on joint work to appear with Braeger, Debray, Dierigl, and Montero.
10:15 – 11:00 am
Naomi Gendler, Harvard University
11:00 – 11:15 am
Break
11:15 am – 12:00 pm
Diego Rodriguez-Gomez, University of Oviedo
Title: Non-BPS branes as holographic symmetry operators
Abstract: We propose a holographic description of the operators implementing continuous global symmetries that are dual to superstring gauge fields in terms of non-BPS D- branes, and consider some possible further extensions.
12:00 – 12:45 pm
Greg Moore, Rutgers University
Title: Summing Over Bordisms In 2d TQFT: Déjà Vu
Abstract: This is basically a rerun of a talk I gave on zoom for the CMSA on March 16, 2022. I will review the contents of a paper I wrote with Anindya Banerjee 2201.00903, but including a few minor updates. I will describe a construction in Topological Field Theory (TFT) which was motivated by developments in the quantum gravity community. The goal is to provide an interpretation of a model discussed by D. Marolf and H. Maxfield 2002.08950 aimed at fitting their model within the functorial framework of Quantum Field Theory (QFT). Given a TFT one can consider – formally – the sum over all bordisms between fixed ingoing and outgoing spatial slices (with appropriate weight factors for the bordisms) of the amplitudes associated to the bordism by the TFT. This construction leads to convergent sums in dleq 2 dimensions, at least for for generic parameters of the TFT. I will describe a curious splitting property satisfied by the total amplitude. I view the splitting property as an alternative to ensemble-type interpretations. There will be a cameo appearance of a very interesting paper by Daniel Friedan 2306.00019 which purports to give an axiomatic framework for Euclidean Quantum Gravity (EQG) analogous to the functorial formalism of QFT. I will also note, in passing, that these extremely simple, low-dimensional, baby baby baby models of EQG admit global symmetries and continuous parameters.
1:00 pm
Farewell Lunch

Tyurin degenerations, Relative Lagrangian foliations and categorification of DT invariants
2024-12-19 10:00 - 11:00 | Virtual
Mathematical Physics and Algebraic Geometry Seminar
Speaker: Artan Sheshmani (BIMSA)
Title: Tyurin degenerations, Relative Lagrangian foliations and categorification of DT invariants
Abstract: We discuss construction of a derived Lagrangian intersection theory of moduli spaces of perfect complexes, with support on divisors on compact Calabi-Yau threefolds. Our goal is to compute deformation invariants associated to a fixed linear system of divisors in CY3. We apply a Tyurin degeneration of the CY3 into a normal-crossing singular variety composed of Fano threefolds meeting along their anti-canonical divisor. We show that the moduli space over the Fano 4 fold given by total space of degeneration family satisfies a relative Lagrangian foliation structure which leads to realizing the moduli space as derived critical locus of a global (-1)-shifted potential function. We construct a flat Gauss-Manin connection to relate the periodic cyclic homology induced by matrix factorization category of such function to the derived Lagrangian intersection of the corresponding “Fano moduli spaces”. The later provides one with categorification of DT invariants over the special fiber (of degenerating family). The alternating sum of dimensions of the categorical DT invariants of the special fiber induces numerical DT invariants. If there is time, we show how in terms of “non-derived” virtual intersection theory, these numerical DT invariants relate to counts of D4-D2-D0 branes which are expected to have modularity property by the S-duality conjecture. This talk is based on joint work with Ludmil Katzarkov, Maxim Kontsevich, recent work with Jacob Krykzca, and former work with Vladimir Baranovsky.
