CMSA

The Andersen-Kashaev volume conjecture for FAMED geometric triangulations
2025-03-24 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: Ka Ho Wong (Yale)
Title: The Andersen-Kashaev volume conjecture for FAMED geometric triangulations
Abstract: In the early 2010s, Andersen and Kashaev defined a TQFT based on quantum Teichmuller theory. In particular, they define a partition function for every ordered ideal triangulation of hyperbolic knot complement in $mathbb{S}^3$ equipped with an angle structure. The Andersen-Kashaev volume conjecture suggests that the partition function can be expressed in terms of a Jones function of the knot which, in its semi-classical limit, decay exponentially with decay rate the hyperbolic volume of the knot complement. In this talk, we will introduce a purely combinatorial condition on triangulations which, together with the geometricity of the triangulations, imply the Andersen-Kashaev volume conjecture and its generalization. This talk is based on the joint work with Fathi Ben Aribi.

The Toda Lattice as a Soliton Gas
2025-03-24 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Amol Aggarwal, Columbia University
Title: The Toda Lattice as a Soliton Gas
Abstract: A basic tenet of integrable systems is that, under sufficiently irregular initial data, they can be thought of as dense collections of many solitons, or “soliton gases.” In this talk we focus on the Toda lattice, which is an archetypal example of an integrable Hamiltonian dynamical system. We explain how the system, under certain random initial data, can be interpreted through solitons, and provide a framework for studying how these solitons asymptotically evolve in time. The arguments use ideas from random matrix theory, particularly the analysis of Lyapunov exponents governing the decay rates of eigenvectors of random tridiagonal matrices.

Unstable Fluids in Expanding Cosmologies
2025-03-25 16:00 - 17:00 | Virtual
General Relativity Seminar
Speaker: Elliot Marshal, School of Mathematics at Monash University
Title: Unstable Fluids in Expanding Cosmologies
Abstract: The FLRW solution is the simplest cosmological model in general relativity, describing a fluid-filled, spatially homogeneous universe. While there is extensive literature in the physics community on cosmological models with a linear equation of state , rigorous stability results have, until recently, been limited to FLRW models with accelerated expansion and small sound speeds. In this talk, I will discuss numerical work on two types of instabilities which can occur in non-linearly perturbed FLRW models outside of this regime. The first concerns a longstanding conjecture of Alan Rendall on FLRW models with positive cosmological constant and super-radiative (K>1/3) equations of state. Our numerical work, in collaboration with F. Beyer and T.A. Oliynyk, supports Rendall’s conjecture and highlights the underlying mechanism for the instability. In the second case, I will discuss evidence that perturbations of slowly expanding (decelerated) FLRW models generically form shocks in finite time. This contrasts with known results for accelerated models where shock formation is suppressed for suitably small perturbations.

From quantum difference equations to Maulik-Okounkov quantum affine algebra
2025-03-27 10:00 - 11:00 | Virtual
Mathematical Physics and Algebraic Geometry Seminar
*via Zoom only*
Speaker: Tianqing Zhu (Tsinghua University)
Title: From quantum difference equations to Maulik-Okounkov quantum affine algebra
Abstract: Capping operator is one the core subject in the K-theoretic quasimap counting to quiver varieties. It has been shown by Okounkov and Smirnov that it satisfies a system of q-difference equations governed by the MO quantum affine algebras. In this talk we will show how to construct the similar quantum difference equation via the shuffle algebras. Then we will show how to use the monodromy data of these quantum difference equations to prove the isomorphism of the positive half of the MO quantum affine algebras of affine type A and the positive half of the quantum toroidal algebras. If time permits, I will also give a brief explanation on how to extend the proof to the general case.

AlphaProof: when reinforcement learning meets formal mathematics
2025-03-27 10:00 - 11:00 | Virtual
New Technologies in Mathematics Seminar
Speaker: Thomas Hubert (Google DeepMind)
Title: AlphaProof: when reinforcement learning meets formal mathematics
Abstract: Galileo, the renowned Italian astronomer, physicist, and mathematician, famously described mathematics as the language of the universe. Progress since only confirmed his intuition as the world we live in can be described with extreme precision with just a few mathematical equations.
In the last 70 years, the rise of computers has also enriched our understanding of and revolutionized the world we live in. Mathematics tremendously benefited from this digital revolution as well: while Gauss had to compute primes by hand, computers and computation are now routinely used in research mathematics and contribute to grand problems like the Birch and Swinnerton-Dyer conjecture, one of the Millennium Prize Problems.
Today, computers are entering a new age, one in which computation can be transformed into reasoning. In this talk, I would like to discuss two such developments that will undoubtedly have an integral role to play in the future of mathematics: the concurrent rise of formal mathematics and of machine intelligence.

The Competition Complexity of Dynamic Pricing
2025-03-28 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Tomer Ezra
Title: The Competition Complexity of Dynamic Pricing
Abstract: One of the most fundamental questions in mechanism design is the tradeoff between simplicity and optimality. A canonical example of this tradeoff is competition complexity in auctions, which quantifies how many additional bidders are needed for a simple mechanism to (approximately) match the revenue of the optimal mechanism.
In this talk, we analyze the competition complexity of dynamic pricing in the setting of selling a single item. We establish tight asymptotic guarantees for various scenarios, including when bidder values are i.i.d., independent, or correlated. Our results characterize the performance of different classes of dynamic pricing algorithms and provide insights into their effectiveness under varying market conditions.

Homotopical Methods for Free and Interacting Fermionic SPTs
2025-03-31 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Cameron Krulewski, MIT
Title: Homotopical Methods for Free and Interacting Fermionic SPTs
Abstract: We develop and compute homotopical “free-to-interacting maps” to compare classifications of fermionic symmetry-protected topological phases (SPTs), determining when such phases are stable under interactions or, alternatively, interaction-enabled. Generalizing work of Freed-Hopkins, we construct maps from K-theory to Anderson-dual spin bordism in two new situations: for weak phases, which are SPTs protected by discrete translation symmetry, and for the “Bott spiral” studied by Queiroz-Khalaf-Stern, who observed that the tenfold way classification of free theories breaks down to a large 2-torsion interacting classification. Along the way, we employ T-duality, generalizations of the spin orientation of KO-theory, and the Adams spectral sequence.
This talk is based on joint work with Omar Antolín Camarena, Arun Debray, Natalia Pacheco-Tallaj, Daniel Sheinbaum, and Luuk Stehouwer.

Low-regularity Local Well-posedness of the Elastic Wave System
2025-04-01 11:00 - 12:00 | Virtual
General Relativity Seminar
Speaker: Sifan Yu, National University of Singapore
Title: Low-regularity Local Well-posedness of the Elastic Wave System
Abstract: In this talk, I will present a recent work on the elastic wave system in three spatial dimensions. For admissible harmonic elastic materials, we prove a low-regularity local well-posedness result for the corresponding elastic wave equations. For such materials, we can split the dynamics into the “divergence-part” and the “curl-part,” and each part satisfies a distinct coupled quasilinear wave system with respect to different acoustical metrics. Our main result is that the Sobolev norm H^{3+} of the “divergence-part” (the “faster-wave part”) and the H^{4+} of the “curl-part” (the “slower-wave part”) can be controlled in terms of initial data for short times. We note that the Sobolev norm assumption H^{3+} is optimal for the “divergence-part.” This is a joint work with Xinliang An and Haoyang Chen.

Introduction to the probabilistic approach to Louville theory III
2025-04-01 16:15 - 18:15 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speaker: Bowen Yang, CMSA
Title: Introduction to the probabilistic approach to Louville theory III
Abstract: I will continue with the construction of Liouville CFT from probabilistic methods, following a review by Guillarmou, Kupiainen, and Rhodes (arXiv:2403.12780). The talk will emphasize technical aspects of Gaussian free fields (GFF) and contrast them with Brownian motion. The references is arXiv:2004.04720

Learning Dynamical Transport without Data
2025-04-02 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
New Technologies in Mathematics Seminar
Speaker: Michael Albergo (Harvard)
Title: Learning Dynamical Transport without Data
Abstract: Algorithms based on dynamical transport of measure, such as score-based diffusion models, have resulted in great progress in the field of generative modeling. However, these algorithms rely on access to an abundance of data from the target distribution. A complementary problem to this is learning to generate samples from a target distribution when only given query access to the unnormalized log-likelihood or energy function associated to it, with myriad application in statistical physics, chemistry, and Bayesian inference. I will present an algorithm based on dynamical transport to sample from a target distribution in this context, which can be seen as an augmentation of annealed importance sampling and sequential Monte Carlo. Time permitting, I will also discuss how to generalize these ideas to dynamics of discrete distributions. This is joint work with Eric Vanden-Eijnden, Peter Holderrieth, and Tommi Jaakkola.

(Strictly) Non-minimal Elliptic Threefolds and the Distance Conjecture
2025-04-03 10:00 - 11:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Mathematical Physics and Algebraic Geometry Seminar
Speaker: Rafael Álvarez García (Harvard University)
Title: (Strictly) Non-minimal Elliptic Threefolds and the Distance Conjecture
Abstract: We analyze infinite-distance limits in the complex structure moduli space of six-dimensional F-theory, providing an algebro-geometric classification and a physical interpretation. From the point of view of the Swampland Program, the motivation is to understand the fate of open-moduli infinite-distance limits in relation with the Distance Conjecture. From an F-theory perspective, the infinite-distance limits correspond to degenerations of elliptic threefolds leading to non-minimal singularities in codimension one and higher. We show how such non-crepant singularities can be removed by a systematic sequence of blow-ups of the bases of the infinite-distance degenerations, making their central fibers a union of log Calabi-Yau spaces glued together along their boundaries. We interpret said central fibers as either the endpoints of decompactification limits with six-dimensional defects or as emergent string limits, providing further evidence for the Emergent String Conjecture. Degenerations leading to strictly non-minimal singularities can correspond both to finite-distance and infinite-distance limits in the open moduli space. We analyze the chain of modifications and base changes necessary to unambiguously determine the fate of such families of F-theory models.

Current Developments in Mathematics 2025
2025-04-04 09:00 - 2025-04-05 17:00 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
When: April 4, 2025 – April 5, 2025

Where: Science Center Hall C
Address: 1 Oxford Street, Cambridge, MA 02138, United States

Speaker: Michael Chapman – NYU | Pazit Haim-Kislev – Institute for Advanced Study | Jianfeng Lin – Tsinghua University | Laura Monk – University of Bristol | Ramon van Handel – Princeton University

IN-PERSON REGISTRATION
Limited funding to help defray travel expenses is available for graduate students and recent PhDs. If you are a graduate student or postdoc and would like to apply for support, please register and send a letter to cdm@math.harvard.edu.
A letter indicating your name, address, current status, university affiliation, citizenship, and area of study. F1 visa holders are eligible to apply for support. If you are a graduate student, please send a brief letter of recommendation from a faculty member to explain the relevance of the conference to your studies or research.
Detailed schedule of lectures and events coming soon.
Organizers: David Jerison, Paul Seidel, Nike Sun (MIT); Denis Auroux, Mark Kisin, Lauren Williams, Horng-Tzer Yau, Shing-Tung Yau (Harvard).
Sponsored by the National Science Foundation (pending), Harvard University Mathematics, and the Massachusetts Institute of Technology.
Harvard University is committed to maintaining a safe and healthy educational and work environment in which no member of the University community is, on the basis of sex, sexual orientation, or gender identity, excluded from participation in, denied the benefits of, or subjected to discrimination in any University program or activity. More information can be found here.

Current Developments in Mathematics 2025

Learning diffusion models in high-dimensions
2025-04-04 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Hugo Cui
Title: Learning diffusion models in high-dimensions
Abstract: We consider the problem of learning a generative model parametrized by a two-layer auto-encoder, and trained with online stochastic gradient descent, to sample from a high-dimensional data distribution with an underlying low-dimensional structure. We provide a tight asymptotic characterization of low-dimensional projections of the resulting generated density, and evidence how mode(l) collapse can arise. On the other hand, we discuss how in a case where the architectural bias is suited to the target density, these simple models can efficiently learn to sample from a binary Gaussian mixture target distribution.

Quantum Field Theory and Physical Mathematics
2025-04-07 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Matthew Yu (Oxford)
Title: A new tangential structure for type IIA string theory
Abstract: The Green-Schwarz anomaly cancellation condition says that the target space of heterotic string theory must come with a string structure for the theory to be consistent. In this talk we discuss a new tangential structure called string^h, first introduced by Devalapurkar, as a spin^c analogue of string. Approximating the correct tangential structure of string theory has many implications, primarily is the Swampland program via the cobordism conjecture of Mcnamara and Vafa. We will show that the spectrum of string^h has the notable property that it orients tmf_1(n), just like how the spectrum of string orients tmf, by the work of Ando-Hopkins-Rezk. Finally we will show that the anomaly condition of the partition function of M-theory, studied by Diaconescu-Moore-Witten is implied by a string^h structure on the target space of type IIA, in parallel to the Green-Schwarz anomaly for heterotic string theory, and discuss applications for anomaly cancellation.

3-d Mirror Symmetry
2025-04-07 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Ben Webster, University of Waterloo & Perimeter Institute
Title: 3-d Mirror Symmetry
Abstract: I’ll give an introduction (or update, for those who’ve been introduced) to 3d mirror symmetry from the perspective of a mathematician.

CMSA/Tsinghua Math-Science Literature Lecture: Scott Sheffield (MIT): Yang-Mills theory and random surfaces
2025-04-08 09:00 - 10:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA/Tsinghua Math-Science Literature Lecture
Date: April 8, 2025
Time: 9:00 – 10:30 am ET
Location: CMSA G10, 20 Garden Street, Cambridge MA & via Zoom
Speaker: Scott Sheffield (MIT)
Title: Yang-Mills theory and random surfaces
Abstract: The Clay Institute famously offered one million dollars to anyone who could mathematically construct and understand a certain continuum version of “Yang-Mills gauge theory.” This theory is the basis of the standard model of physics, and the heart of the problem is to understand the so-called “Wilson loop expectations.” Following recent work with Sky Cao and Minjae Park, I will explain how the “Wilson loop expectations” in a lattice Yang-Mills model are equivalent to “insertion costs” of loops in a related random-closed-surface-ensemble model. In a sense, these results allow us to convert one famously hard problem into another presumably hard problem. But the new problem is all about random surfaces and random permutations, and it has a lot of relationships with and similarities to other problems we understand (think domino tilings, random planar maps, Young tableaux and symmetric group representation theory, and the Weingarten calculus). It gives us some intuition for *why* certain things should be true like the “area law” or “exponential correlation decay” (what physicists call “quark confinement” or “mass gap”) even if we can’t prove all of them yet.

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.

CMSA Q&A Seminar: Eric Maskin
2025-04-09 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q&A Seminar
Speaker: Eric Maskin, Harvard University
Topic: The Mathematics of Voting

Can Transformers Do Enumerative Geometry?
2025-04-09 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
New Technologies in Mathematics Seminar
Speaker: Baran Hashemi, Technical University of Munich
Title: Can Transformers Do Enumerative Geometry?
Abstract: How can Transformers model and learn enumerative geometry? What is a systematic procedure for using Transformers in abductive knowledge discovery within a mathematician-machine collaboration? In this work, we introduce a Neural Enumerative Reasoning model for computation of ψ-class intersection numbers on the moduli space of curves. By reformulating the problem as a continuous optimization task, we compute intersection numbers across a wide value range from 10e-45 to 10e45. To capture the recursive nature inherent in these intersection numbers, we propose the Dynamic Range Activator (DRA), a new activation function that enhances the Transformer’s ability to model recursive patterns and handle severe heteroscedasticity. Given precision requirements for computing the intersections, we quantify the uncertainty of the predictions using Conformal Prediction with a dynamic sliding window adaptive to the partitions of equivalent number of marked points. Beyond simply computing intersection numbers, we explore the enumerative “world-model” of Transformers. Our interpretability analysis reveals that the network is implicitly modeling the Virasoro constraints in a purely data-driven manner. Moreover, through abductive hypothesis testing, probing, and causal inference, we uncover evidence of an emergent internal representation of the large-genus asymptotic of ψ-class intersection numbers. This opens up new possibilities in inferring asymptotic closed-form expressions directly from limited amount of data.
This talk is based on https://openreview.net/pdf?id=4X9RpKH4Ls.

3d Mirror Symmetry is 2d Mirror Symmetry
2025-04-10 10:00 - 11:00 | Virtual
Mathematical Physics and Algebraic Geometry Seminar
Speaker: Ki Fung Chan (Chinese University of Hong Kong)
Title: 3d Mirror Symmetry is 2d Mirror Symmetry
Abstract: We introduce an approach to studying 3d mirror symmetry via 2d mirror symmetry. The main observations are: (1) 3d brane transforms are given by SYZ-type transforms; (2) the exchange of symplectic and complex structures in 2d mirror symmetry induces the exchange of Kähler and equivariant parameters in 3d mirror symmetry; and (3) the functionalities of 2d mirror symmetry control the gluing of 3d mirrors. If time permits, we will also discuss some applications to 2d mirror symmetry at the end of the talk. Joint works with Naichung Conan Leung.

Homological Invariants in Translation-Invariant Pauli Stabilizer Codes
2025-04-11 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Bowen Yang
Title: Homological Invariants in Translation-Invariant Pauli Stabilizer Codes
Abstract: Pauli stabilizer codes serve as foundational models in quantum error correction and the study of exotic quantum phases. In this talk, we explore the application of homological methods to translationally invariant Pauli stabilizer codes with qudits of varying dimensions. We introduce a series of invariants, termed charge modules, and delve into their properties and physical interpretations. A key focus is on codes whose charge modules exhibit zero Krull dimension, a condition indicative of the mobility of excitations. Notably, we demonstrate that this condition is universally met in two-dimensional codes with a unique ground state in infinite volume, extending prior findings beyond the realm of uniform, prime qudit dimensions. For systems where all excitations are mobile, we establish the existence of p-dimensional excitations and associated (D−p−1)-form symmetries corresponding to each element of the p-th charge module. Additionally, we define a braiding pairing between charge modules in complementary degrees.

The Extended Vertex Algebra of 4d N = 2 SCFTs and their Higher Products
2025-04-14 15:00 - 16:00 | Hybrid – G10
Quantum Field Theory and Physical Mathematics Seminar
Speaker: Mitch Weaver, KAIST
Title: The Extended Vertex Algebra of 4d N = 2 SCFTs and their Higher Products
Abstract: Every 4d N=2 superconformal field theory contains a BPS protected sub-algebra of local operators that has the structure of a vertex operator algebra (VOA). This VOA is identified by passing to the cohomology of a nilpotent supercharge, T, whose local operator cohomology is represented by twist-translated Schur operators with support in a Euclidean two-plane. When working in 4d Minkowski space, this cohomology admits a web of three extended operators (called descent operators) that are constructed from each Schur operator in the VOA, have worldvolume support in the Lorentzian two-plane that is transverse to the Euclidean plane supporting the VOA, and behave as point-like insertions in the plane of the VOA, i.e. as new chiral operators. The combined result is the extended vertex algebra (EVA): a universal extension of the VOA that canonically has the structure of a quasi-VOA, i.e. a vertex algebra (VA) with no conformal vector but which still possesses a representation of sl(2). After reviewing the VOA of Schur operators, I will explain the origin of the descent operators and present the OPEs for a subsector of the EVA in the free hyper SCFT.
Time permitting, I will also describe the construction and basic properties of a set of higher products that are associated to each descent operator. Such products function as higher dimensional versions of 2d chiral algebra λ-brackets, i.e. positive mode operators: they are defined on the EVA and map to the operators appearing in the singular terms of OPEs involving descent operators. Their existence offers a route toward sl(2) symmetry enhancement of the EVA and suggests the latter has structural properties that are common to the higher dimensional chiral algebras describing the minimal twists of 3d N = 2 and 4d N = 1 SQFTs. This talk is based on [2211.04410] and forthcoming work.

Quantum K-theory at roots of unity
2025-04-14 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Andrey Smirnov, University of North Carolina at Chapel Hill
Title: Quantum K-theory at roots of unity
Abstract: In this talk, I will discuss a version of quantum K-theory introduced by A.Okounkov, which can be defined through quasimap counts. In this framework, the quantum K-theory ring is obtained as a specialization of the equivariant quasimap count at $q=1$, where $q$ is the equivariant parameter associated with the torus action on the source of the quasimaps. A related, but less explored, structure emerges when $q$ is specialized at the roots of unity. I will outline the key ideas behind this construction and its implications. As an application, I’ll also describe the spectrum of $p$-curvature for the quantum connection, which offers a new proof of a recent result by P.Etingof and A.Varchenko. This talk is based on joint work with P. Koroteev.

Positive mass theorem for ALE(AE) and ALF(AF) Toric 4-Manifolds
2025-04-15 11:00 - 12:00 | CMSA G102, 20 Garden Street, Cambridge, MA, 02138
General Relativity Seminar
Speaker: Aghil Alaee, Clark University
Title: Positive mass theorem for ALE(AE) and ALF(AF) Toric 4-Manifolds
Abstract: One of the fundamental conjectures in mathematical relativity is the positivity of total mass (if it is defined!) for complete non-compact Riemannian manifolds assuming appropriate lower bounds on scalar curvature. This conjecture has been proved for AE manifolds using several techniques, starting with the celebrated results of Schoen-Yau and Witten. There are counter-examples to this conjecture in the AF, ALF, and ALE cases. In this talk, we will refine this conjecture and prove it for toric 4-manifolds. The proof is robust and can be extended to higher dimensions if additional assumptions are added. This is a joint work with Marcus Khuri and Hari Kunduri.

Instantons on Taub-NUT space and Bow Construction
2025-04-15 16:15 - 18:15 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speaker: Anadil Saeed Rao, Northeastern University
Title: Instantons on Taub-NUT space and Bow Construction
Abstract: In this talk I will discuss Yang-Mills Instantons in a very special geometric setting: the Taub-NUT space, which itself is a Gravitational Instanton. In the first part of the talk I will review the essentials of gravitational instanton theory from the differential geometry/physics perspective and discuss the geometry of Taub-NUT space in detail. Then I will review the essentials of the ADHM-Nahm construction which describe Instantons and Monopoles in Euclidean R^4 and R^3 respectively. In the second part of my talk I will extend the ADHM-Nahm description to Instantons on Taub-NUT space and show how the ADHM-Nahm data may be presented in terms of combinatorial diagrams called Bows and their representations.

CMSA Q&A Seminar: Noah Golowich
2025-04-16 12:00 - 13:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q&A Seminar
Speaker: Noah Golowich (MIT)
Topic: What is length generalization in large language models?

Fifth Annual Yip Lecture | Scott Aaronson (UT Austin): How Much Math Is Knowable?
2025-04-17 16:00 - 17:00 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
Speaker: Scott Aaronson, Department of Computer Science, University of Texas, Austin
Scott Aaronson is the founding director at the Quantum Information Center at the University of Texas at Austin.
Date: April 17, 2025
Time: 4:00-5:00 pm ET (Reception following in the Math Common Room)
Location: Harvard Science Center Hall A

Title: How Much Math Is Knowable?
Abstract: Theoretical computer science has over the years sought more and more refined answers to the question of which mathematical truths are knowable by finite beings like ourselves, bounded in time and space and subject to physical laws. I’ll tell a story that starts with Gödel’s Incompleteness Theorem and Turing’s discovery of uncomputability. I’ll then introduce the spectacular Busy Beaver function, which grows faster than any computable function. Work by me and Yedidia, along with recent improvements by O’Rear and Riebel, has shown that the value of BB(745) is independent of the axioms of set theory; on the other end, an international collaboration proved last year that BB(5) = 47,176,870. I’ll speculate on whether BB(6) will ever be known, by us or our AI successors. I’ll next discuss the P!=NP conjecture and what it does and doesn’t mean for the limits of machine intelligence. As my own specialty is quantum computing, I’ll summarize what we know about how scalable quantum computers, assuming we get them, will expand the boundary of what’s mathematically knowable. I’ll end by talking about hypothetical models even beyond quantum computers, which might expand the boundary of knowability still further, if one is able (for example) to jump into a black hole, create a closed timelike curve, or project oneself onto the holographic boundary of the universe.

The Yip Lecture takes place thanks to the support of Dr. Shing-Yiu Yip.

The previous Yip Lecture featured Josh Tenenbaum (MIT) who spoke on How to grow a mind from a brain: From guessing and betting to thinking and talking

Member Seminar
2025-04-18 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Han Shao

Modeling the emergence of complex cortical structure from simple precursors in the brain: maps, hierarchies, and modules
2025-04-21 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Ila Fiete, MIT
Title: Modeling the emergence of complex cortical structure from simple precursors in the brain: maps, hierarchies, and modules
Abstract: Modular and hierarchical structures are ubiquitous in the brain. Two distinct hypotheses for such morphogenesis involve genetic specification (the positional information hypothesis) or spontaneous structure emergence from symmetry breaking (the pattern formation hypothesis). Indeed, there is rich evidence supporting both hypotheses in different systems, and more recently evidence that both systems might interact, for instance with genetic specification providing an initial but relatively low-information scaffold of positional guidance and pattern formation constructing sharper structures by bootstrapping from this guidance. In this talk, I will consider the emergence of two systems in the brain: the visual processing hierarchy with topographic structure, and a modular cognitive circuit consisting of functionally independent grid cell networks that compute spatial location from velocity cues as animals move and navigate the world. I will describe how simple activity-driven growth and competition rules can lead to the emergence of topographically ordered sensory processing hierarchies, and how genetically specified smooth gradients with purely local recurrent interactions on two scales can lead to global module emergence. In sum, simple growth rules, local interactions and smooth gradients can interact to produce rich emergent order on multiple scales in the form of maps, modules, and hierarchies, with predictions that bridge scales from genes to connectivity to function.

Hyperbolic equations in a double null gauge
2025-04-22 11:00 - 12:00 | CMSA G102, 20 Garden Street, Cambridge, MA, 02138
General Relativity Seminar
Speaker: Christopher Stith, University of Michigan
Title: Hyperbolic equations in a double null gauge
Abstract: The hyperbolic nature of the Einstein equations is well-known and has been used in many different contexts. More recently, the double null gauge has proven to be a powerful tool for quantitative analysis of the Einstein equations. It has the advantage of reducing the equations for many dynamical quantities to ODEs along null curves, and the Bianchi equations to a first-order hyperbolic system. The double null gauge has been used extensively and to great effect in analyzing the structure of spacetime for many purposes, including (for instance) stability problems and trapped surface formation. However, the local existence problem for the Einstein equations in a double null gauge has never been treated in full in its own right. In this talk, we discuss how to formulate a general procedure for solving the linearized problem, namely, the local existence theory for systems of first-order hyperbolic equations in a double null gauge.

Classifying Space for Phases of Matrix Product States
2025-04-22 16:15 - 18:15 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Geometry and Quantum Theory Seminar
Speakers: Bryan Wang Peng Jun (Harvard) and Bowen Yang (CMSA)
Title: Classifying Space for Phases of Matrix Product States
Abstract: In this talk we will introduce recent work of Beaudry-Hermele-Pflaum-Qi-Spiegel-Stephen (arXiv:2501.14241), on constructing a classifying space for phases of matrix product states (MPS).
