Quantum Field Theory and Physical Mathematics
2025-03-03 15:00 - 16:00 (America/New_York) | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Kai Xu, Harvard
Title: Finite Landscape of 6d N=(1,0) Supergravity
Abstract: We present a bottom-up argument showing that the number of massless fields in six-dimensional quantum gravitational theories with eight supercharges is uniformly bounded. Specifically, we show that the number of tensor multiplets is bounded by T≤193, and the rank of the gauge group is restricted to r(V)≤480. Given that F-theory compactifications on elliptic CY 3-folds are a subset, this provides a bound on the Hodge numbers of elliptic CY 3-folds: h1,1(CY3)≤491, h1,1(Base)≤194 which are saturated by special elliptic CY 3-folds. This establishes that our bounds are sharp and also provides further evidence for the string lamppost principle.

The Combinatorics of the Amplituhedron – Tiles, Tilings, and Cluster Algebras
2025-02-28 12:00 - 13:00
Member Seminar
Speaker: Matteo Parisi
Title: The Combinatorics of the Amplituhedron – Tiles, Tilings, and Cluster Algebras
Abstract: The amplituhedron is the image of the positive Grassmannian—the region of the Grassmannian where all Plücker coordinates are nonnegative—under a totally positive linear map. It is a far-reaching generalization of cyclic polytopes and hyperplane arrangements, and the positive Grassmannian itself. The “volume” of the amplituhedron encodes probabilities of particle interactions in the quantum field theory N=4 super Yang-Mills, and calculating this volume involves decomposing (or tiling) the amplituhedron into smaller pieces (or tiles) and summing their volumes. This talk will delve into the rich combinatorics of these tiles and tilings, presenting recent results on some of the central conjectures in this area, including the magic number, BCFW tiling, and cluster adjacency conjectures.

2d chiral Lagrangian for asymptotic dynamics for 4d (self-dual) Einstein gravity
2025-02-27 10:00 - 11:00
Mathematical Physics and Algebraic Geometry Seminar
Speaker: Wei Bu (Harvard University)
Title: 2d chiral Lagrangian for asymptotic dynamics for 4d (self-dual) Einstein gravity
Abstract: In this talk, I will present a simple chiral 2d Lagrangian living on a 2d celestial sphere on the null boundary of 4d Minkowski space and briefly mention its first principal derivation using twistor theory. This 2d theory gives the asymptotic/edge dynamics of 4d (self-dual) Einstein gravity in asymptotically flat spacetimes. For example, using simple 2d CFT computations, one could recover generators of asymptomatic symmetries. If time permits, I’ll further discuss the potential of using this theory to produce a QFT computation of the entropy of a certain asymptotically flat black hole.

BKL bounces outside homogeneity
2025-02-25 11:00 - 12:00
General Relativity Seminar
Speaker: Warren Li ( Princeton University)
Title: BKL bounces outside homogeneity
Abstract: In work spanning the late 20th century, physicists Belinski, Khalatnikov and Lifshitz (BKL) proposed a general ansatz for solutions to the Einstein (vacuum) equations near singularities. They suggest that the spacetime dynamics at different spatial points on the singularity decouple and are well-approximated by a system of autonomous nonlinear ODEs, whose orbits are governed by a chaotic cascade of “BKL bounces”. In this talk, we present recent work verifying BKL’s heuristics in a large class of symmetric, but spatially inhomogeneous, spacetimes. In particular, we prove decoupling even in the presence of (up to one) BKL bounce. The proof uses nonlinear ODE analysis coupled to hyperbolic energy estimates, and one hopes our methods may be applied more generally.

Toward constructing a large-scale quantum computer based on TQFT
2025-02-24 15:00 - 16:00
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Liyuan Chen ( Harvard)
Title: Toward constructing a large-scale quantum computer based on TQFT
Abstract: Topological quantum computation, motivated by topological quantum field theory (TQFT), offers a promising path toward fault-tolerant universal quantum computation. However, the practical realization of such a system remains challenging due to the difficulty of finding suitable topological materials. In this work, we provide a comprehensive blueprint for constructing a fault-tolerant universal quantum computer based on the quantum double model $mathcal{D}(S_3)$, a specific non-Abelian topological order. We implement logical computations using quantum circuits on qubits and qutrits, including a single non-Clifford gate, compatible with near-term quantum devices. This work bridges the gap between abstract mathematical frameworks and noise-resilient quantum computation on near-term devices. Our proposal offers a promising path to realize a non-Abelian anyon-based large scale quantum computer.

Jack polynomials and enumeration of non-orientable maps
2025-02-14 12:00 - 13:00
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.

The Structure of the Flux Landscape
2025-02-13 10:00 - 11:00
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.

On the past maximal development of near-FLRW data for the Einstein scalar-field Vlasov system
2025-02-11 11:00 - 12:00
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
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.

Rational approximation and the AAA algorithm
2025-02-03 16:30 - 17:30
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
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
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.

A homotopy of 2d SCFTs and an implication for Topological Modular Forms
2025-01-27 15:00 - 16:00
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.

Nonlinear Bosonization of (Non-)Fermi Liquids
2024-12-13 10:00 - 11:30
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.

The Quantum GIT conjecture
2024-12-12 10:00 - 11:00
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.

The Einstein-Vlasov system in a large data regime
2024-12-10 11:00 - 12:00
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.

On the Coulomb branch scaling dimensions of 4d N=2 SCFTs
2024-12-06 12:00 - 13:00
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.

Quantum Cellular Automata
2024-12-05 10:30 - 12:00
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.

Can Transformers Reason Logically? A Study in SAT-Solving
2024-12-04 14:00 - 15:00
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.

Mass for the large and for the small
2024-12-03 11:00 - 12:00
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.

Computability on $mathbb R$ and other continuum-size structures
2024-12-02 16:30 - 17:30
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.

Mathematical Structures of Scattering Amplitudes
2024-11-25 16:30 - 17:30
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.

Identity crises phenomena in the large cardinal hierarchy
2024-11-22 12:00 - 13:00
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.

Skein valued curve counts for the topological vertex and knot conormals
2024-11-21 10:30 - 11:30
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.

CMSA/Tsinghua Math-Science Literature Lecture: Bjorn Poonen, MIT
2024-11-21 09:00 - 10:30
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.

A new construction of c = 1 conformal blocks
2024-11-20 15:00 - 16:00
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.

The Einstein-Euler system with a physical vacuum boundary in spherical symmetry
2024-11-19 11:00 - 12:00
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.

Emergent Non-Invertible Symmetries —The Adjoint QCD Example
2024-11-18 14:00 - 15:00
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.

Quantum Criticality in Black Hole Scattering
2024-11-15 12:00 - 13:00
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.

(Un)likely intersections
2024-11-14 10:00 - 11:00
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.
