Is Behavior Cloning All You Need? Understanding Horizon in Imitation Learning
2024-11-06 14:00 - 15:00 (America/New_York) | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
New Technologies in Mathematics Seminar
Speaker: Dylan Foster, Microsoft Research
Title: Is Behavior Cloning All You Need? Understanding Horizon in Imitation Learning
Abstract: Imitation learning (IL) aims to mimic the behavior of an expert in a sequential decision making task by learning from demonstrations, and has been widely applied to robotics, autonomous driving, and autoregressive language generation. The simplest approach to IL, behavior cloning (BC), is thought to incur sample complexity with unfavorable quadratic dependence on the problem horizon, motivating a variety of different online algorithms that attain improved linear horizon dependence under stronger assumptions on the data and the learner’s access to the expert.In this talk, we revisit the apparent gap between offline and online IL from a learning-theoretic perspective, with a focus on general policy classes up to and including deep neural networks. Through a new analysis of behavior cloning with the logarithmic loss, we will show that it is possible to achieve horizon-independent sample complexity in offline IL whenever (i) the range of the cumulative payoffs is controlled, and (ii) an appropriate notion of supervised learning complexity for the policy class is controlled. When specialized to stationary policies, this implies that the gap between offline and online IL is smaller than previously thought. We will then discuss implications of this result and investigate the extent to which it bears out empirically.
Bio: Dylan Foster is a principal researcher at Microsoft Research, New York. Previously, he was a postdoctoral fellow at MIT, and received his PhD in computer science from Cornell University, advised by Karthik Sridharan. His research focuses on problems at the intersection of machine learning, AI, interactive decision making. He has received several awards for his work, including the best paper award at COLT (2019) and best student paper award at COLT (2018, 2019).

Representations of minimal W-algebras: unitarity and modular invariance
2024-11-08 10:00 - 11:30 | Virtual
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Victor Kac (MIT)
Title: Representations of minimal W-algebras: unitarity and modular invariance
Abstract: The minimal W-algebras, obtained by quantum Hamiltonian reduction from affina vertex algebras, form the most interesting class of vertex algebras, which includes all superconformal algebras: Virasoro, Neveu-Scharz, N=2, 3, 4, and big N=4. I will explain a unified classification of their unitary representations, and their character formulas. For N=0, 1, and 2 these vertex algebras are modular invariant (meaning that tr q^L_0-c/24 is a modular function). However for all other minimal W-algebra modular invariance fails, and one needs the “modification” of characters to restore modular invariance. Unfortunately the representation-theoretical or physical meaning of the modification is not known (at least to me).

ADHM spaces and their quantizations
2024-11-08 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Vasily Krylov, CMSA
Title: ADHM spaces and their quantizations
Abstract: In their paper “Construction of Instantons,” Atiyah, Drinfeld, Hitchin, and Manin introduced an algebraic construction of the moduli space of instantons on R^4, now also known as the “ADHM space.” This is a Poisson complex variety; it has been actively studied by both mathematicians and physicists. In this talk, I will review the ADHM construction, present examples, and discuss various geometric and algebraic properties of ADHM spaces. I will also describe natural quantizations of these Poisson varieties. I will explain a joint result with Etingof, Losev, and Simental, providing explicit formulas for the dimensions and characters of all finite-dimensional representations of these quantizations. Time permitting, I will illustrate some predictions of the 3D mirror symmetry in the example of ADHM spaces, following our joint paper with Shlykov.

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.

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.

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?

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.

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.

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.

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.

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.

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?

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.

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.

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

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.

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.

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.

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

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?
