pp Waves: Quasinormal Modes & Hidden Symmetries of Black Holes
2024-11-12 11:00 - 12:00 (America/New_York) | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar
Speaker: Ahmed Seta, Harvard University
Title: pp Waves: Quasinormal Modes & Hidden Symmetries of Black Holes
Abstract: The spectrum of quasinormal modes of 4D flat space black holes is not analytically tractable, but there are two asymptotic limits where the QNM spectrum is under control: weak damping and strong damping. In this talk, I will explain how these asymptotic QNMs are controlled by dynamical symmetries of the wave equation in certain kinematic limits. These two asymptotic limits are, in turn, captured by the two classes of bound null geodesics in the black hole geometry: the photon ring and the horizon. I will also discuss the Penrose limit: a scaling limit into the geometry experienced by these geodesics, which results in a plane-wave spacetime where the dynamical symmetries get enhanced into isometries.

Frontier of Formal Theorem Proving with Large Language Models: Insights from the DeepSeek-Prover Series
2024-11-13 10:00 - 23:00 | Virtual
New Technologies in Mathematics Seminar
Speaker: Huajian Xin, DeepSeek
Title: Frontier of Formal Theorem Proving with Large Language Models: Insights from the DeepSeek-Prover Series
Abstract: Recent advances in large language models have markedly influenced mathematical reasoning and automated theorem proving within artificial intelligence. Yet, despite their success in natural language tasks, these models face notable obstacles in formal theorem proving environments such as Lean and Isabelle, where exacting derivations must adhere to strict formal specifications. Even state-of-the-art models encounter difficulty generating accurate and complex formal proofs, revealing the unique blend of mathematical rigor required in this domain. In the DeepSeek-Prover series (V1 and V1.5), we have explored specialized methodologies aimed at addressing these challenges. This talk will delve into three foundational areas: the synthesis of training data through autoformalization, reinforcement learning that utilizes feedback from proof assistants, and test-time optimization using Monte Carlo tree search. I will also provide insights into current model capabilities, persistent challenges, and the future potential of large language models in automated theorem proving.

(Un)likely intersections
2024-11-14 10:00 - 11:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Mathematical Physics and Algebraic Geometry Seminar
Speaker: Tom Scanlon, UC Berkeley
Title: (Un)likely intersections

Abstract: The Zilber-Pink conjectures predicts that for an ambient special variety (such as an abelian variety or a Shimura variety), if is an irreducible algebraic subvariety which is not contained a proper special subvariety of (e.g. a proper algebraic subgroup in the abelian variety case or a variety of Hodge type in the case of Shimura varieties), then the union of the unlikely intersections as ranges over the special subvarieties of with is not Zariski dense in . While various instances of this conjecture have been proven, it remains open in most cases of interest. In this lecture, I will describe some of my work with Jonathan Pila in which we prove an effective function field version of this conjecture along with a counterpart to the Zilber-Pink conjecture proven with Sebastian Eterović: after accounting for some geometric obstructions, the likely intersections, i.e. the union of the intersections with special and , are dense in the Euclidean topology in . Our techniques for both results come from o-minimal complex analysis and differential algebra.

Quantum Criticality in Black Hole Scattering
2024-11-15 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Uri Kol
Title: Quantum Criticality in Black Hole Scattering
Abstract: Perturbation theory around rotating black holes captures a few important effects in the physics of gravitational waves emitted from binary mergers. Despite a long and rich history, developing a qualitative understanding of the system remains a challenging problem. In this talk I will describe an emergent critical phenomena arising in black hole perturbation theory, which is reminiscent of the structure found in quantum many-body systems. A critical point is identified at zero temperature, giving rise to a wide “quantum” critical region at finite temperatures that is dominated by critical fluctuations. In the critical region, the physics is exclusively described by a set of critical exponents, therefore leading to robust predictions.

Freedman CMSA Seminar
2024-11-15 14:30 - 17:30 | Virtual
Freedman CMSA Seminar
*Note: via Zoom only*

2:00-3:30 pm ET
Speaker: Michael Freedman, Harvard CMSA
Title: Some questions and theorems about closed 3 manifolds embedded in S^4
Abstract: Much is unknown about smooth embeddings of 3-manifolds in S^4; the Schoenflies problem (Is there only one smoothly embedded 3-sphere in S^4 up to isotopy?) is the best-known example. There has long been a hope that 3-manifold reasoning applied to level-sets will be helpful. I’ll mention some successes and failures of this method and revisit a classical theorem of Hantzsche in this light. (Hantzsche: If a 3-manifold embeds in S^4 its linking form is hyperbolic.)

3:30-4:00 pm ET
Break/Discussion

4:00-5:30 pm ET
Speaker: Slava Krushkal, University of Virginia
Title: A higher order torsion linking form for 3-manifolds
Abstract: This talk is based on a joint work with Mike Freedman defining a triple linking form for rational homology spheres, assuming that the classical torsion linking pairing of three classes pairwise vanishes. I will discuss its vanishing for 3-manifolds in S^4, and its relation to the Matsumoto triple intersection form on 4-manifolds.

Emergent Non-Invertible Symmetries —The Adjoint QCD Example
2024-11-18 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Shani Nadir Meynet (Uppsala)
Title: Emergent Non-Invertible Symmetries — The Adjoint QCD Example
Abstract: After reviewing some general properties of generalized symmetries and the renormalization group (RG) flow for quantum field theories (QFT), I’ll describe how the recently discovered non-invertible symmetries can be used to study theories at strong coupling. I’ll illustrate these facts using (3+1)-dimensional adjoint QCD with two flavors as an example. This theory can be obtained by mass deforming a pure N=2 super Yang-Mills theory. Relying on supersymmetric results, dynamical abelianization and monopole condensation, we are able to get to the description of an infrared (IR) phase as an abelian theory flowing to a CP1 sigma model. In this scenario, the IR phase has an emergent non-invertible symmetry, which is matched with the non-invertible symmetry of the IR CP1 phase. This result illustrates how an emergent non-invertible symmetry can be used to provide a bridge connecting gauge theories at strong coupling and their IR via dynamical abelianization.

The Einstein-Euler system with a physical vacuum boundary in spherical symmetry
2024-11-19 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar
Speaker: Marcelo Disconzi, Vanderbilt University
Title: The Einstein-Euler system with a physical vacuum boundary in spherical symmetry
Abstract: We establish local well-posedness for the Einstein-Euler system with a physical vacuum boundary in spherical symmetry. Our proof relies on a new way of thinking about Einstein’s equations in spherical symmetry that is well-adapted to the fluid’s characteristics on the free boundary. We also exploit the Einstein constraint equations in spherical symmetry in a new way, as a tool to understand the evolution problem. This is joint work with Jared Speck.

Factorization algebras in TQFT
2024-11-19 18:00 - 19:00 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speakers: Mayuko Yamashita, Kyoto University
Title: Factorization algebras in TQFT
Abstract: This is the first in the series of our working seminars on factorization algebras/homologies. This talk focuses on locally constant factorization algebras, which correspond to Topological QFTs. I first explain they are equivalent to algebras over E_n operads and their variants. Then I define the factorization homology and discuss basic properties and examples. If time allows, I also mention the connection with the cobordism hypothesis.

Thinking Like Transformers - A Practical Session
2024-11-20 10:00 - 23:00 | Virtual
New Technologies in Mathematics Seminar
Speaker: Gail Weiss, EPFL
Title: Thinking Like Transformers – A Practical Session
Abstract: With the help of the RASP programming language, we can better imagine how transformers—the powerful attention based sequence processing architecture—solve certain tasks. Some tasks, such as simply repeating or reversing an input sequence, have reasonably straightforward solutions, but many others are more difficult. To unlock a fuller intuition of what can and cannot be achieved with transformers, we must understand not just the RASP operations but also how to use them effectively.
In this session, I would like to discuss some useful tricks with you in more detail. How is the powerful selector_width operation yielded from the true RASP operations? How can a fixed-depth RASP program perform arbitrary length long-addition, despite the equally large number of potential carry operations such a computation entails? How might a transformer perform in-context reasoning? And are any of these solutions reasonable, i.e., realisable in practice? I will begin with a brief introduction of the base RASP operations to ground our discussion, and then walk us through several interesting task solutions. Following this, and armed with this deeper intuition of how transformers solve several tasks, we will conclude with a discussion of what this implies for how knowledge and computations must spread out in transformer layers and embeddings in practice.

CMSA Q&A Seminar: Anurag Anshu
2024-11-20 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q&A Seminar
Speaker: Anurag Anshu, Harvard University
Topic: What is quantum complexity theory?

A new construction of c = 1 conformal blocks
2024-11-20 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Mathematical Physics and Algebraic Geometry Seminar
Speaker: Qianyu Hao, University of Geneva
Title: A new construction of c = 1 conformal blocks

Abstract: The Virasoro conformal blocks are very interesting since they have many connections to other areas of math and physics. For example, when c = 1, they are related to tau functions of Painlevé equations. I will first explain what Virasoro conformal blocks are. Then I will describe a new way to construct Virasoro blocks at c = 1 on C by using the “abelian” Heisenberg conformal blocks on a branched double cover of C. The main new idea in our work is to use a spectral network. It is closely related to the idea of nonabelianization of the flat connections in the work of Gaiotto-Moore-Neitzke and Neitzke-Hollands. This nonabelianization construction enables us to compute the harder-to-get Virasoro blocks using the simpler abelian objects. This is based on a joint work with Andrew Neitzke.

Perturbative Factorization Algebras
2024-11-20 16:30 - 17:30 | Science Center Hall E, 1 Oxford Street, Cambridge, MA, 02138, United States
Geometry and Quantum Theory Seminar
Speaker: Ahsan Khan

Title: Perturbative Factorization Algebras

Abstract: In physics the starting point in studying a QFT is to write down an appropriate action functional. My talk will aim to sketch how this connects with the framework of factorization algebras.

CMSA/Tsinghua Math-Science Literature Lecture: Bjorn Poonen, MIT
2024-11-21 09:00 - 10:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA/Tsinghua Math-Science Literature Lecture
Date: November 21, 2024
Time: 9:00 – 10:30 am ET
Location: CMSA G10, 20 Garden Street, Cambridge MA & via Zoom
Speaker: Bjorn Poonen, MIT
Title: Ranks of elliptic curves
Abstract: Elliptic curves are simplest varieties whose rational points are not fully understood, and they are the simplest projective varieties with a nontrivial group structure. In 1922 Mordell proved that the group of rational points on an elliptic curve is finitely generated. We will survey what is known and what is believed about this group.

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.

Skein valued curve counts for the topological vertex and knot conormals
2024-11-21 10:30 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Mathematical Physics and Algebraic Geometry Seminar
Speaker: Tobias Ekholm, Uppsala University
Title: Skein valued curve counts for the topological vertex and knot conormals
Abstract: Combining the invariance of holomorphic curve counts in the skein module with a study of holomorphic curves at infinity of the vertex we find three simple skein operator polynomials that annihilates the (skein valued) topological vertex. We show that these operator polynomials together with natural initial conditions determine the partition function uniquely and then demonstrate that the original Aganagic-Klemm-Marino-Vafa formula for the topological vertex interpreted as a skein valued curve count satisfies the operator polynomials. This is joint work with Longhi and Shende. We end with a general discussion of similar ‘skein D-modules’ for knot conormals.

Identity crises phenomena in the large cardinal hierarchy
2024-11-22 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Alejandro Poveda
Title: Identity crises phenomena in the large cardinal hierarchy

Abstract: It is well-known that certain mathematical questions cannot be answered on the grounds of the standard foundation of mathematics. Large cardinal axioms constitute a series of postulates about the higher infinite which permit to classify these undecidable problems in a coherent hierarchy way. Specifically, large cardinals together with ZFC (the standard axiomatic of Mathematics) provide a complete classification of all mathematical theories according to the so-called consistency strength. One of the main tenets of modern set theory has been to investigate how the large-cardinal hierarchy is organized across the mathematical universe. To a large extent this hierarchy is nicely disposed and such a disposition is unambiguous (i.e., immune to the independence phenomenon).

In an unexpected turn of events, in the late 70’s Magidor discovered the identity crisis phenomena of the large cardinal hierarchy. Magidor proved that certain strata of the hierarchy are susceptible to be modified via Cohen’s method of forcing. Specifically, he showed that the first strongly compact cardinal can be either the first measurable cardinal or the first supercompact cardinal. It turns out that the first measurable is always much smaller than the first supercompact. These discrepancies on the identity of the first strongly compact cardinal were termed by Magidor the Identity Crisis Phenomenon.

In this talk I plan to provide an introduction to the world of large cardinals keeping an eye on the identity crises phenomena. Time permitting, I’ll present a few recent results answering questions by Magidor and discuss their connection with Woodin’s Ultimate-L Conjecture.

Foundation Seminar
2024-11-25 09:30 - 11:00 | Black Hole Initiative, 20 Garden Street, Cambridge MA, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Foundation Seminar (Joint Seminar with BHI)

Title: Searching for Dark Matter in the Sky
Abstract: Astrophysical and cosmological observations have allowed us to measure the abundance of dark matter and have provided important information on its properties. I will discuss past, present and future efforts to map the gravitational footprint of dark matter throughout the cosmos, and what such studies can (and cannot) tell us about dark matter’s fundamental nature. I will also review how even tiny non-gravitational interactions of dark and visible matter could lead to a range of “indirect detection” signals, and outline the status and prospects of searches for such signals, with a focus on the next decade or so.

Mathematical Structures of Scattering Amplitudes
2024-11-25 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Anastasia Volovich, Brown University
Title: Mathematical Structures of Scattering Amplitudes
Abstract: Planar N=4 Yang-Mills scattering amplitudes have been computed to very high loop order. They have many remarkable properties that have sparked interest from mathematicians working on combinatorics, algebraic geometry, and number theory. At the same time, several methods that have been developed for N=4 Yang-Mills can often be applied to more general quantum field theories, including QCD. I will overview some of these exciting developments.

Computability on $mathbb R$ and other continuum-size structures
2024-12-02 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Russell Miller, CUNY
Title: Computability on $mathbb R$ and other continuum-size structures
Abstract: We begin by recalling the notion of a computable function on the real numbers $mathbb R$, developed independently by Gregorczyk and Lacombe over sixty years ago. Using this notion, we note that the real numbers that are themselves computable form a countable subfield of $mathbb R$ with exactly the same first-order properties as $mathbb R$ itself. (Logicians would therefore call it an emph{elementary subfield}.) So, in a first-order sense, everything that happens in $mathbb R$ is already exemplified in this much nicer subfield. However, even when one knows that an existential statement holds for all parameters, it may be impossible (both in $mathbb R$ and in the subfield) to give a computable procedure for producing witnesses. Similar results hold in $mathbb C$.
We will then turn to a different continuum-sized structure: the absolute Galois group $operatorname{Gal}(mathbb Q)$ of the rational numbers. Once again the computable elements of this group form a subgroup, but now it is an open problem whether the group and the subgroup have the same first-order theory, let alone whether this is an elementary subgroup. (If they do have the same theory, this would put nice upper bounds on the complexity of the theory of $operatorname{Gal}(mathbb Q)$.) However, using joint work with Kundu, we can show that once again there is no computable procedure for producing witnesses to the truth of (true) existential statements, either in the full group or in the subgroup.

Mass for the large and for the small
2024-12-03 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar
Speaker: Tin Yau Tsang, Courant Institute, New York University
Title: Mass for the large and for the small

Abstract: Seeking a meaningful geometric (physical) invariant to describe a spacetime has sparked research in both mathematics and physics. In this talk, we will first see the fundamental progress made by Schoen-Yau and Witten on ADM (Arnowitt-Deser-Misner) mass. Then, we will see the progress on quasilocal masses in recent years. In particular, we would discuss the Hamiltonian formulation and the behaviour of quasilocal masses with the presence of apparent horizons.

Factorization Homology
2024-12-03 16:15 - 18:15 | Science Center Hall E, 1 Oxford Street, Cambridge, MA, 02138, United States
Geometry and Quantum Theory Seminar
Speakers: Sunghyuk Park and Vasily Krylov, Harvard CMSA
Title: Factorization Homology

Can Transformers Reason Logically? A Study in SAT-Solving
2024-12-04 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
New Technologies in Mathematics Seminar
Speaker: Leyan Pan, Georgia Tech
Title: Can Transformers Reason Logically? A Study in SAT-Solving
Abstract: Transformer-based LLMs have apparently demonstrated capabilities that resembles human reasoning. In our recent work, we investigated the Boolean reasoning abilities of decoder-only Transformers equipped with Chain-of-Thought, establishing that a Transformer model can decide all 3-SAT instances up to a bounded size (i.e., number of variables and clauses). In this talk, I will first review recent studies that formally examine the expressiveness of Transformer models. Next, I will explain how we establish an equivalence between Chain-of-Thought reasoning and algorithm, in our case, the DPLL SAT-solving algorithm. I will then discuss how to encode 3-SAT formulas and partial assignments as vectors so that the high-level operations in DPLL can be represented as vector operations and implemented using attention mechanisms within Transformers. Finally, I will present experimental results that support our theoretical predictions. I will also address why standard Transformers can only solve reasoning problems of bounded length, leading to failures in length-generalization, and discuss potential solutions to overcome this limitation.

Quantum Cellular Automata
2024-12-05 10:30 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Special Seminar
Speaker: Jeongwan Haah, Stanford University
Title: Quantum Cellular Automata
Abstract: A discrete time evolution on lattice systems that has a notion of lightcone is called a quantum cellular automaton. Lattice translation in 1D is a well-known example of QCA that is nontrivial in the sense that it is not a local Hamiltonian evolution. In higher dimensions, more subtle QCA are found in relation to certain topological phases of matter, but the scope of all QCA is far from being fully determined. I will report the status of our understanding on this subject, emphasizing the role of locally generated simple subalgebras.

On the Coulomb branch scaling dimensions of 4d N=2 SCFTs
2024-12-06 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Robert Moscrop
Title: On the Coulomb branch scaling dimensions of 4d N=2 SCFTs
Abstract: To each four dimensional N=2 superconformal field theory of rank-r, one can associate an r-tuple of numbers given by the scaling dimensions of a special set of protected operators whose VEVs parameterise the Coulomb branch. In this talk, I will demonstrate how the special geometry of the Coulomb branch heavily constrains not only the values of the scaling dimensions, but also the possible r-tuples of such numbers that can occur.

A simple model for universal quantum computation
2024-12-06 16:00 - 17:00 | Virtual
Freedman CMSA Seminar
Speaker: Michael Freedman
Title: A simple model for universal quantum computation
Abstract: I’ll present joint (unpublished) work with Charlie Marcus on a surprisingly simple – and potentially practical (?)– model for universal quantum computation whose only quantum primitive is the ability to measure a pair of adjacent electrons into either singlet (spin=0) or triplet (spin=1) sectors according to the Born rule. The electrons are located on quantum dots arranged in a triangular lattice whose edges are tiny strips of s-wave superconductor.

Quantum Effects Inside Black Holes
2024-12-10 09:30 - 11:00 | Black Hole Initiative, 20 Garden Street, Cambridge MA, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Joint CMSA/BHI Foundation Seminar
Location: BHI seminar room

Speaker: Noa Zilberman, Princeton
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.

The Einstein-Vlasov system in a large data regime
2024-12-10 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar
Speaker: Nikolaos Athanasiou, University of Crete, Greece
Title: The Einstein-Vlasov system in a large data regime
Abstract: In this talk, our object of study is the Einstein-Vlasov system with a massless Vlasov matter field. Complementing various important works obtaining the stability of Minkowski spacetime as a solution to this system, we look at the large data regime, motivated in turn by the signature for decay rates of various Ricci, curvature and matter components, first introduced by X. An. Our work provides a semi-global existence result and a trapped surface formation result for the Einstein-Vlasov system in the absence of spherical symmetry. Our proof is based on a double null gauge. Interestingly, we give a new way of obtaining estimates for the Vlasov matter, purely by commuting with various vector fields and without the need to use Jacobi fields.

The Quantum GIT conjecture
2024-12-12 10:00 - 11:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Mathematical Physics and Algebraic Geometry Seminar
Speaker: Daniel Pomerleano (UMass Boston)
Title: The Quantum GIT conjecture
Abstract: Let X be a Fano variety with G action. The quantum GIT conjecture predicts a formula for the quantum cohomology of “anti-canonical” GIT quotients X//G in terms of the equivariant quantum cohomology of X. The formula is motivated by ideas from 3- dimensional gauge theory (“Coulomb branches”) and provides a vast generalization of Batyrev’s formula for the quantum cohomology of a toric Fano variety. I will describe our ongoing work with C. Teleman proving this conjecture. Along the way, I will also discuss integral versions of certain classical facts in the theory of Hamiltonian G-manifolds which are of independent interest.

Nonlinear Bosonization of (Non-)Fermi Liquids
2024-12-13 10:00 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Yi-Hsien Du (MIT)
Title: Nonlinear Bosonization of (Non-)Fermi Liquids
Abstract: Fermi liquid theory is a cornerstone of condensed matter physics. I will show how to formulate Fermi liquid theory as an effective field theory. In this approach, the space of low-energy states of a Fermi liquid is identified with a coadjoint orbit of the group of canonical transformations. The method naturally leads to a nonlinear bosonized description of the Fermi liquid with nonlinear corrections fixed by the geometry of the Fermi surface. I will present that the resulting local effective field theory captures both linear and nonlinear effects in Landau’s Fermi liquid theory. The approach can be extended to encompass non-Fermi liquids, which correspond to strongly interacting fixed points obtained by deforming Fermi liquids with relevant interactions. I will also discuss how Berry curvature can be captured in the effective field theory approach.

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.

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
