CMSA

A model for studying the sign problem on quantum computers: Z(3) gauge theory with three fermion flavors in 1+1 dimensions
2024-03-08 09:00 - 10:00 (America/New_York) | Virtual
Quantum Matter in Mathematics and Physics Seminar
Speaker: Semeon Valgushev (Iowa State University)
Title: A model for studying the sign problem on quantum computers: Z(3) gauge theory with three fermion flavors in 1+1 dimensions
Abstract: Many properties of quantum field theories can be understood with the help of classical numerical methods. Yet there are several outstanding problems — most remarkably the behaviour of nuclear matter at finite density and out-of-equilibrium real-time dynamics — that require the use of quantum algorithms. We present a simple yet physically rich toy model of QCD/nuclear matter at finite density, termed “QZD”, where Z stands for Z(3) gauge theory coupled to Nf = 3 fermion flavors, suitable for simulation on near-term quantum devices. We study it using tensor networks and find that in weak coupling the spectrum is that of the expected mesons and baryons, although the corrections in weak coupling are nontrivial. In strong coupling, besides the usual baryon, the singlet meson is a baryon anti-baryon state. For two special values of the coupling constant, the lightest baryon is degenerate with the lightest octet meson, and the lightest singlet meson, respectively.

AQFT Lecture Series
2024-03-07 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
AQFT Lecture Series
Speaker: John Francis (Northwestern)
Title: Integrating braided categories over 3-manifolds
Abstract: I’ll describe a form of factorization homology, which gives an invariant of framed 3-manifolds given as input a rigid braided-monoidal category with duals. More generally, the construction gives an invariant of framed n-manifolds from an E_{n-1}-monoidal category with duals. This construction relies on a form of the tangle hypothesis, that a dualizable object in an E_{n-1}-monoidal category uniquely determines a functor from the category of tangles in n-space. This is joint work with David Ayala.

AQFT Lecture Series
2024-03-07 13:30 - 14:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
AQFT Lecture Series
Speaker: An Huang (Brandeis)
Title: Tate’s thesis and p-adic strings
Abstract: I shall explain the relation between a family of deformations of genus zero p-adic string worldsheet action and Tate’s thesis, which in particular, gives rise to an attempt of physically deriving quadratic reciprocity. I shall then propose a genus one p-adic string worldsheet action, where the key is an explicit definition of a p-adic Laplacian operator on a Tate curve, and the computation of its Green’s function. I shall also mention a very recent attempt of developing a Lorentzian version of the p-adic worldsheet action.

Geometric construction of toric NCRs
2024-03-07 10:30 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Algebraic Geometry in String Theory Seminar
Speaker: Jesse Huang, University of Alberta
Title: Geometric construction of toric NCRs
Abstract: The Rouquier dimension of a toric variety is recently shown to be achieved by the Frobenius pushforward of O via coherent-constructible correspondence. From the perspective of noncommutative geometry, this result leads to a geometric construction of toric NCR of the invariant ring of the Cox ring with respect to a multi-grading which also gives the information about its global dimension. From the perspective of mirror symmetry, the same construction provides a universal “wall skeleton” capturing VGIT wall-crossings, which contains a window for each chamber as a full subcategory. From the perspective of commutative algebra, the same construction indicates the existence of virtual resolutions of the multigraded diagonal bimodule, which agrees with a recent result of Hanlon-Hicks-Larzarev constructing one such resolution explicitly. In this talk, I will survey these perspectives. The talk is based on joint works with P. Zhou, joint works with D. Favero, and work in progress with D. Favero.

LILO: Learning Interpretable Libraries by Compressing and Documenting Code
2024-03-06 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
New Technologies in Mathematics Seminar
Speaker: Gabe Grand, MIT CSAIL and Dept. of EE&CS
Title: LILO: Learning Interpretable Libraries by Compressing and Documenting Code
Abstract: While large language models (LLMs) now excel at code generation, a key aspect of software development is the art of refactoring: consolidating code into libraries of reusable and readable programs. In this paper, we introduce LILO, a neurosymbolic framework that iteratively synthesizes, compresses, and documents code to build libraries tailored to particular problem domains. LILO combines LLM-guided program synthesis with recent algorithmic advances in automated refactoring from Stitch: a symbolic compression system that efficiently identifies optimal lambda abstractions across large code corpora. To make these abstractions interpretable, we introduce an auto-documentation (AutoDoc) procedure that infers natural language names and docstrings based on contextual examples of usage. In addition to improving human readability, we find that AutoDoc boosts performance by helping LILO’s synthesizer to interpret and deploy learned abstractions. We evaluate LILO on three inductive program synthesis benchmarks for string editing, scene reasoning, and graphics composition. Compared to existing neural and symbolic methods – including the state-of-the-art library learning algorithm DreamCoder – LILO solves more complex tasks and learns richer libraries that are grounded in linguistic knowledge.

CMSA Q&A Seminar 3/5/2024
2024-03-05 12:30 - 13:30 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q&A Seminar

Speaker: Yannai Gonczarowski, Harvard University

Question: What do people mean when they say ‘the intersection between theoretical computer science and economic theory’?

CMSA Q&A Seminar 3/5/2024
2024-03-05 12:30 - 13:30 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q and A Seminar

Speaker: Cumrun Vafa

Question: What is swampland?

High order WENO finite difference scheme for Einstein-Yang-Mills equations
2024-03-05 11:00 - 12:00 | Virtual
General Relativity Seminar
Speaker: Yuewen Chen, Tsinghua University
Title: High order WENO finite difference scheme for Einstein-Yang-Mills equations
Abstract: In this talk, we will show the convergence analysis of the first-order finite difference scheme for static spherically symmetric $SU(2)$ Einstein-Yang-Mills (EYM) equations. We also construct a new WENO scheme for EYM.

Strong bounds for arithmetic progressions
2024-03-04 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Raghu Meka (UCLA)
Title: Strong bounds for arithmetic progressions
Abstract: Suppose you have a set S of integers from {1,2,…,N} that contains at least N / C elements. Then for large enough N, must S contain three equally spaced numbers (i.e., a 3-term arithmetic progression)?
In 1953, Roth showed this is the case when C is roughly (log log N). Behrend in 1946 showed that C can be at most exp(sqrt(log N)). Since then, the problem has been a cornerstone of the area of additive combinatorics. Following a series of remarkable results, a celebrated paper from 2020 due to Bloom and Sisask improved the lower bound on C to C = (log N)^(1+c) for some constant c > 0.
This talk will describe a new work showing that C can be much closer to Behrend’s construction. Based on joint work with Zander Kelley.

AQFT Lecture Series
2024-03-01 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
AQFT Lecture Series
Speaker: Peng Shan (Tsinghua)
Title: Skein algebras and quantized Coulomb branches
Abstract: In this talk, we explain how to attach a quantized Coulomb branch in the sense of Braverman-Finkelberg-Nakajima to a compact oriented surface of genus at most one, and compare it to the Kauffman bracket Skein algebra in some special cases. This is based on a joint work with Dylan Allegretti.

Contract Design in Combinatorial Settings
2024-03-01 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Member Seminar
Speaker: Tomer Ezra (Harvard CMSA)
Title: Contract Design in Combinatorial Settings
Abstract: We study two combinatorial settings of the contract design problem, in which a principal wants to delegate the execution of a costly task. In the first setting, the principal delegates the task to an agent that can take any subset of a given set of unobservable actions, each of which has an associated cost. The principal receives a reward which is a combinatorial function of the actions taken by the agent. In the second setting, we study the single-principal multi-agent contract problem, in which the principal motivates a team of agents to exert effort toward a given task. We design (approximately) optimal algorithms for both settings along with impossibility results for various classes of combinatorial functions.
This talk is based on joint works with Paul Duetting, Michal Feldman, Thomas Kesselheim and Maya Schlesinger.

AQFT Lecture Series
2024-03-01 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
AQFT Lecture Series
Speaker: Chen Wan, Rutgers Newark
Title: Some examples of the relative Langlands duality
Abstract: In this talk I will discuss some examples of the relative Langlands duality (introduced by Ben-Zvi—Sakellaridis—Venkatesh) for strongly tempered spherical varieties. In some cases, I will introduce a relative trace formula comparison for the models and prove the fundamental lemma/smooth transfer. This is a joint work with Zhengyu Mao and Lei Zhang.

Fourth Annual Yip Lecture | Josh Tenenbaum | How to grow a mind from a brain: From guessing and betting to thinking and talking
2024-02-29 16:00 - 17:00 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
Josh Tenenbaum gave the Fourth Annual Yip Lecture on February 29, 2024.
Title: How to grow a mind from a brain: From guessing and betting to thinking and talking
Time: 4:00-5:00 pm ET
Location: Harvard Science Center
The Yip Lecture takes place thanks to the support of Dr. Shing-Yiu Yip.

The previous Yip Lecture featured Andrew Strominger (Harvard), who spoke on Black Holes.

Directed motion in active matter: Frictiotaxis and flocking
2024-02-29 13:00 - 14:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Active Matter Seminar
Speaker: Ricard Alert, Max Planck Institute for the Physics of Complex Systems
Title: Directed motion in active matter: Frictiotaxis and flocking
Abstract: A key feature of active matter is its ability to move directionally, both as individual particles and collectively. I will discuss two examples of directed motion: one in cell migration, and one in collections of self-propelled colloids. First, I will show that cells lacking cell-substrate adhesions migrate along friction gradients. We call this phenomenon frictiotaxis, which is a new type of cell guidance. Second, I will present a new mechanism for flocking whereby self-propelled particles can align and move collectively despite turning away from each other.

Classifying curves on Fano varieties
2024-02-29 10:30 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Algebraic Geometry in String Theory Seminar
Speaker: Brian Lehmann (Boston College)
Title: Classifying curves on Fano varieties
Abstract: How can we understand the set of curves on a Fano variety? One perspective is provided by Geometric Manin’s Conjecture, a collection of conjectures with roots in arithmetic and topology. While I will mention some recent progress, the main focus will be developing a conceptual framework for thinking about our question.

10-27-2016 Homological Mirror Symmetry Seminar
2024-02-27 19:03 | MA

AQFT Lecture Series
2024-02-27 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
AQFT Lecture Series
Speaker: Wei Zhang (MIT)
Title: Shtuka special cycles and their generating series

CMSA Q&A Seminar 2/27/2024
2024-02-27 12:30 - 13:30 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q&A Seminar

Speaker: Dan Freed

Question: What are Higgs bundles?

On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes
2024-02-27 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar
Speaker: Nishanth Gudapati, Clark University
Title: On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes
Abstract: The Kerr black hole stability problem is an important open problem in general relativity. In this talk, I will focus on the role of energy methods in the axisymmetric stability of Kerr black hole spacetimes. In particular, I will discuss the construction and the application of a positive Hamiltonian energy for axially symmetric Maxwell and Einstein perturbations of sub-extremal Kerr black hole spacetimes.

Factorization algebras in quite a lot of generality
2024-02-26 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Clark Barwick, University of Edinburgh
Title: Factorization algebras in quite a lot of generality
Abstract: The objects of arithmetic geometry are not manifolds. Some concepts from differential geometry admit analogues in arithmetic, but they are not straightforward. How then can we hope to make precise sense of quantum field theories on these objects? I will propose the beginnings of a mathematical framework via a general theory of factorization algebras. A new feature is a subtle piece of additional structure on our objects – what I call a world-structure – that is ordinarily left implicit.

AQFT Lecture Series
2024-02-26 13:00 - 14:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
AQFT Lecture Series
Speaker: Omer Offen (Brandeis)
Title: Period integrals of automorphic forms and the residue method
Abstract: I will discuss some aspects of period integrals of automorphic forms via examples. In particular, the residue method of Jacquet and Rallis and its recent application, joint with Friedberg and Ginzburg, to study new periods on the residual automorphic spectrum of the symplectic group.

Integrability and Hidden Symmetries in Black Hole Dynamics
2024-02-23 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Member Seminar
Speaker: Uri Kol (Harvard CMSA)
Title: Integrability and Hidden Symmetries in Black Hole Dynamics
Abstract: The last decade has produced a number of remarkable discoveries, such as the first direct observation of gravitational waves by the LIGO/Virgo collaboration and the first black hole image taken by the Event Horizon Telescope. These discoveries mark the beginning of a new precision era in black hole physics, which is expected to develop further by future experiments such as LISA, the Einstein Telescope and Cosmic Explorer.

In the era of precision black hole measurements, there is a need for precision theoretical methods and accurate predictions. In this talk I will describe an integrable sector of the gravitational scattering problem – analogous to the hydrogen atom in quantum mechanics – in which exact predictions can be made, and the implications for astrophysical black holes and binary mergers.

Spontaneously Broken (-1)-form symmetries
2024-02-23 10:00 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Motoo Suzuki (Harvard)
Title: Spontaneously Broken (-1)-form symmetries
Abstract: Spontaneous breaking of symmetries leads to universal phenomena. We extend this notion to (−1)-form U(1) symmetries. The spontaneous breaking is diagnosed by a dependence of the vacuum energy on a constant background field θ, which can be probed by the topological susceptibility. This leads to a reinterpretation of the Strong CP problem as arising from a spontaneously broken instantonic symmetry in QCD. We discuss how known solutions to the problem are unified in this framework and explore some, so far unsuccessful, attempts to find new solutions. I will also talk about our ongoing work on the explicit breaking by monopoles.

Geometric origins of values of the Riemann Zeta functions at positive integers
2024-02-22 10:30 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Algebraic Geometry in String Theory Seminar
Speaker: Yan Zhou, Northeastern
Title: Geometric origins of values of the Riemann Zeta functions at positive integers
Abstract: Given a Fano manifold, Iritani proposed that the asymptotic behavior of solutions to the quantum differential equation of the Fano should be given by the so-called ‘Gamma class’ in its cohomology ring. Later, Abouzaid-Ganatra-Iritani-Sheridan reformulated the ‘Gamma conjecture’ for Calabi-Yau manifolds via the tropical SYZ mirror symmetry and proposed that values of the Riemann Zeta function at positive integers have geometric origins in the tropical periods and singularities of the SYZ geometry. In this talk, we will first review the content of the Gamma conjecture. Then, we will discuss the first step of generalizing AGIS’ approach to Gamma conjecture for the Gross-Siebert mirror families of a Fano manifold in dimension 2 cases, based on joint work with Bohan Fang and Junxiao Wang.

Computers and mathematics in partial differential equations: New developments and challenges
2024-02-21 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
New Technologies in Mathematics Seminar
Speaker: Javier Gomez Serrano, Brown University
Title: Computers and mathematics in partial differential equations: new developments and challenges
Abstract: In this talk I will address the interaction between traditional and more modern mathematics and how computers have helped over the last decade providing rigorous (computer-assisted) proofs in the context of partial differential equations. I will also describe new exciting future directions in the field. No background is assumed.

Math Science Lectures in Honor of Raoul Bott: Maggie Miller: Fibered ribbon knots vs. major 4D conjectures
2024-02-20 16:00 - 17:30 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
Fibered ribbon knots vs. major 4D conjectures
Location: Harvard University Science Center Hall A & via Zoom webinar
Dates: Feb 20 & 22, 2024
Time: 4:00-5:30 pm
Maggie Miller is an assistant professor in the mathematics department at the University of Texas at Austin and a Clay Research Fellow.
This is the fourth annual Math Science Lecture Series held in Honor of Raoul Bott.
Talk topic: Fibered ribbon knots vs. major 4D conjectures

Feb. 20, 2024
Title: Fibered ribbon knots and the Poincaré conjecture
Abstract: A knot is “fibered” if its complement in S^3 is the total space of a bundle over the circle, and ribbon if it bounds a smooth disk into B^4 with no local maxima with respect to radial height. A theorem of Casson-Gordon from 1983 implies that if a fibered ribbon knot does not bound any fibered disk in B^4, then the smooth 4D Poincaré conjecture is false. I’ll show that unfortunately (?) many ribbon disks bounded by fibered knots are fibered, giving some criteria for extending fibrations and discuss how one might search for non-fibered examples.

Feb. 22, 2024
Title: Fibered knots and the slice-ribbon conjecture
Abstract: The slice-ribbon conjecture (Fox, 1962) posits that if a knot bounds any smooth disk into B^4, it also bounds a ribbon disk. The previously discussed work of Casson-Gordon yields an obstruction to many fibered knots being ribbon, yielding many interesting potential counterexamples to this conjecture — if any happy to bound a non-ribbon disk. In 2022, Dai-Kong-Mallick-Park-Stoffregen showed that unfortunately( ?) many of these knots don’t bound a smooth disk into B^4 and thus can’t disprove the conjecture. I’ll show a simple alternate proof that a certain interesting knot (the (2,1)-cable of the figure eight) isn’t slice and discuss remaining open questions. This talk is joint with Paolo Aceto, Nickolas Castro, JungHwan Park, and Andras Stipsicz.

Talk Chair: Cliff Taubes (Harvard Mathematics)
Moderator: Freid Tong (Harvard CMSA)

Raoul Bott (9/24/1923 – 12/20/2005) is known for the Bott periodicity theorem, the Morse–Bott functions, and the Borel–Bott–Weil theorem.

CMSA Q&A Seminar 2/20/2024
2024-02-20 12:30 - 13:30 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q and A Seminar

Speaker: Solomon Friedberg, Boston College

Question: What is the Langlands program?

Asymptotic decay for defocusing semilinear wave equations on Schwarzschild spacetimes
2024-02-20 09:30 - 10:30 | Virtual
General Relativity Seminar
Speaker: He Mei, Shenzhen University
Title: Asymptotic decay for defocusing semilinear wave equations on Schwarzschild spacetimes
Abstract: In this talk, I will present a work on the long time dynamics of solutions to the defocusing semilinear wave equations on the Schwarzschild black hole spacetimes. For sufficiently smooth and localized initial data, we show that the solution decays in the domain of outer communication. The proof relies on a vector field method of Dafermos-Rodnianski together with Strichartz estimates for linear waves by Marzuola-Metcalfe-Tataru-Tohaneanu.

Symmetries and algebraicity in the flux landscape
2024-02-16 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Member Seminar
Speaker: Damian van de Heisteeg (Harvard CMSA)
Title: Symmetries and algebraicity in the flux landscape
Abstract: In this talk I consider potentials coming from fluxes in string theory. The minima of these potentials trace out special loci in the moduli space of Calabi-Yau manifolds. I discuss the structure that underlies these minima from a Hodge-theoretic point of view.

Programmable Simulations of Molecules and Materials with present-day Reconfigurable Quantum Processors
2024-02-16 10:30 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Susanne Yelin (Harvard)
Title: Programmable Simulations of Molecules and Materials with present-day Reconfigurable Quantum Processors
Abstract: Simulations of quantum chemistry and quantum materials are believed to be among the most important potential applications of quantum information processors, but realizing practical quantum advantage for such problems is challenging. We introduce a simulation framework for strongly correlated quantum systems that can be represented by model spin Hamiltonians. Our approach leverages reconfigurable qubit architectures to programmably simulate real-time dynamics and introduces an algorithm for extracting chemically relevant spectral properties via classical co-processing of quantum measurement results. We develop a digital-analog simulation toolbox for efficient Hamiltonian time evolution utilizing digital Floquet engineering and hardware-optimized multi-qubit operations to accurately realize complex spin-spin interactions, and as an example present an implementation proposal based on Rydberg atom arrays. Then, we show how detailed spectral and other relevant chemical information can be extracted from these dynamics through snapshot measurements and single-ancilla control, enabling the evaluation of excitation energies and finite-temperature susceptibilities from a single-dataset. To illustrate the approach, we show how this method can be used to compute key properties of a polynuclear transition-metal catalyst and 2D magnetic materials.
