Calendar
- 19March 19, 2023No events
- 20March 20, 2023No events
- 21March 21, 2023
Harvard–MIT Algebraic Geometry Seminar: Non-abelian Hodge theory and the P=W conjecture
In the first part of my talk, I will introduce the P=W conjecture by de Cataldo, Hausel, and Migliorini (2010), predicting that the perverse filtration associated with the Hitchin system is identified with the weight filtration associated with the corresponding character variety, via non-abelian Hodge theory. Then I will discuss a proof of the conjecture in joint work with Davesh Maulik, where we combine some ideas from enumerative geometry and representation theory.
Mathematical Picture Language Seminar
17 Oxford Street, Cambridge, MA 02138 USATitle: TBA
Abstract: TBA
Applied Algebraic and Geometry Seminar: Conditions for Absolute Delay Stability
Some chemical and biological models use a system of delay differential equations (DDEs) instead of the usual ODEs, with the assumption of instantaneous consumption but delayed production. Stability of DDEs can be determined by solutions to a transcendental equation (similar to locating the roots of the characteristic equations in the case of ODEs). In this talk, I will motivate and introduce delay models for chemical systems, and provide a sufficient algebraic condition that guarantees its delay stability independent of parameters (i.e., absolute delay stability). In particular, this condition also implies asymptotic stability when there is no delay in the system. Time permitting, I will introduce a graph-theoretic condition for absolute delay stability that in certain cases is easier to check. This is joint work with Gheorghe Craciun, Maya Mincheva, Casian Pantea.CMSA 2023 Ding Shum Lecture
On March 21, 2023, the CMSA will host the fourth annual Ding Shum Lecture, given by Cynthia Dwork (Harvard SEAS).
For more information, please see: https://cmsa.fas.harvard.edu/event/2022-ding-shum-lecture/
- 22March 22, 2023
CMSA Colloquium: Synchronization in a Kuramoto Mean Field Game
20 Garden Street, Cambridge, MA 02138Originally motivated by systems of chemical and biological oscillators, the classical Kuramoto model has found an amazing range of applications from neuroscience to Josephson junctions in superconductors, and has become a key mathematical model to describe self organization in complex systems. These autonomous oscillators are coupled through a nonlinear interaction term which plays a central role in the long term behavior of the system. While the system is not synchronized when this term is not sufficiently strong, fascinatingly, they exhibit an abrupt transition to a full synchronization above a critical value of the interaction parameter. We explore this system in the mean field formalism. We treat the system of oscillators as an infinite particle system, but instead of positing the dynamics of the particles, we let the individual particles determine endogenously their behaviors by minimizing a cost functional and eventually, settling in a Nash equilibrium. The mean field game also exhibits a bifurcation from incoherence to self-organization. This approach has found interesting applications including circadian rhythms and jet-lag recovery. This is joint work with Rene Carmona of Princeton and Quentin Cormier of INRIA, Paris.
Joint MIT-Harvard-MSR Combinatorics Seminar: Strong bounds for 3-progressions
Suppose you have a set S of integers from \{1,2,\ldots,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 that this is indeed the case when C > \Omega(\log\log N), while Behrend in 1946 showed that C can be at most 2^{O(\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 that C >2^{\Omega((\log N)^{0.09), thus getting closer to Behrend’s construction. Based on joint work with Zander Kelley.
The first hour of the talk will be self-contained and describe the main ideas of the proof. The second hour will be a deeper follow-up of some elements of the proof.
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========================= For information about the Combinatorics Seminar, please visit…
http://math.mit.edu/seminars/c
ombin/ ==============================
====================== This is a two-hour talk with a break in the middle.
“Note special location”
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========================== CMSA Probability Seminar: Some rigorous results on the Lévy spin glass model
The Lévy spin glass model, proposed by Cizeau-Bouchaud, is a mean-field model defined on a fully connected graph, where the spin interactions are formulated through a power-law distribution. This model is well-motivated from the study of the experimental metallic spin glasses. It is also expected to bridge between some mean-field and diluted models. In this talk, we will discuss some recent progress on the Lévy model including its high temperature behavior and the existence and variational expression for the limiting free energy. Based on a joint work with Heejune Kim and Arnab Sen.This seminar will be held on Zoom. For information on how to join, please see: https://cmsa.fas.harvard.edu/event_category/probability-seminar/
Open Neighborhood Seminar: The mathematics of democracy
1 Oxford Street, Cambridge, MA 02138 USAIs democracy legitimate? It may come as a surprise that mathematicians have contributed to answering this question for a very (very) long time. In this talk, we will explore social choice theory (the maths field researching democratic governance), discuss some of its most striking results, and review the recent developments in understanding how we can make democracy more legitimate. We will look into the probability and random graphs theories underpinning these works, and assess their relevance to the current crises of democracies.
For more information, please see: https://people.math.harvard.edu/~ana/ons/
- 23March 23, 2023
CMSA General Relativity: New Phases of N=4 SYM
20 Garden Street, Cambridge, MA 02138We construct new static solutions to gauged supergravity that, via the AdS/CFT correspondence, are dual to thermal phases in N=4 SYM at finite chemical potential. These solutions dominate the micro-canonical ensemble and are required to ultimately reproduce the microscopic entropy of AdS black holes. These are constructed in two distinct truncations of gauged supergravity and can be uplifted to solutions of type IIB supergravity. Together with the known phases of the truncation with three equal charges, our findings permit a good understanding of the full phase space of SYM thermal states with three arbitrary chemical potentials. We will also discuss the status of hairy supersymmetric black hole solutions in this theory.Based on: https://arxiv.org/pdf/2207.07134.pdf [hep-th] **please note change from usual time**This seminar will be in person at CMSA, 20 Garden St, Room G-10, but will also be simultaneously broadcast over Zoom. For more information on how to join, please see: https://cmsa.fas.harvard.edu/event_category/general-relativity/
Introductory Mathematics Seminar: Designing a Culturally-Responsive Precalculus Curriculum Grounded in Tucson as Place and Identity
The University of Arizona is one of 16 Carnegie R1 Hispanic Serving Institutions (HSIs), and one of four R1, HSIs with membership in the prestigious Association of American Universities (AAU). We are also a land-grant university located in the US-Mexico borderland, a cradle of wisdom, identities, cultures, and people still only tenuosly centered in our campus’ vast curricular offerings. Framed by this institutional backdrop of commitment to excellent teaching, research, and servingness—the intentional enhancement of marginalized identities throughout the academic experience—this presentation discusses aims and design of a novel asset-based, culturally-responsive precalculus curriculum centering Tucson and the Southwestern US as place and identity. I will introduce course design principles and share specific precalculus content examples, aiming to illustrate how curricular rigor is not only uncompromised but actually enhanced through scenarios that relate to students’ lived experiences and make the mathematics come authentically alive within place-based, affirming contexts. The talk aims to offer a proof-of-concept for how might one go about creating other culturally-centering STEM curricula.
Algebraic Dynamics Seminar: Sullivan’s Dictionary, Limits of deformations, and Modular Laminations
Sullivan’s dictionary between Kleinian groups and rational maps reveals how many objects, such as limit sets and Julia sets, are different names for the same thing. On a deeper level, it provides conjectures in one field that are analogs of well-known theorems in the other. One such well-known theorem, proven by W. Thurston, is the compactness of the space of representations (in Isom(H^3)) of the fundamental group of a compact 3-manifold with acylindrical boundary. The analog of this theorem for rational maps was conjectured by C. McMullen in the early 1990’s. Because there is no quotient three-manifold for a rational map, new tools are needed to study degenerating sequences of deformations. We introduce the concept of an invariant modular lamination as a limit of degeneration and use it to prove this conjecture.For more information, please see: Algebraic Dynamics Seminar at Harvard
- 24March 24, 2023
CMSA Quantum Matter in Mathematics and Physics: Traversable wormhole dynamics on a quantum processor
20 Garden Street, Cambridge, MA 02138The holographic principle, theorized to be a property of quantum gravity, postulates that the description of a volume of space can be encoded on a lower-dimensional boundary. The anti-de Sitter (AdS)/conformal field theory correspondence or duality is the principal example of holography. The Sachdev–Ye–Kitaev (SYK) model of N >> 1 Majorana fermions has features suggesting the existence of a gravitational dual in AdS2, and is a new realization of holography. We invoke the holographic correspondence of the SYK many-body system and gravity to probe the conjectured ER=EPR relation between entanglement and spacetime geometry through the traversable wormhole mechanism as implemented in the SYK model. A qubit can be used to probe the SYK traversable wormhole dynamics through the corresponding teleportation protocol. This can be realized as a quantum circuit, equivalent to the gravitational picture in the semiclassical limit of an infinite number of qubits. Here we use learning techniques to construct a sparsified SYK model that we experimentally realize with 164 two-qubit gates on a nine-qubit circuit and observe the corresponding traversable wormhole dynamics. Despite its approximate nature, the sparsified SYK model preserves key properties of the traversable wormhole physics: perfect size winding, coupling on either side of the wormhole that is consistent with a negative energy shockwave, a Shapiro time delay, causal time-order of signals emerging from the wormhole, and scrambling and thermalization dynamics. Our experiment was run on the Google Sycamore processor. By interrogating a two-dimensional gravity dual system, our work represents a step towards a program for studying quantum gravity in the laboratory. Future developments will require improved hardware scalability and performance as well as theoretical developments including higher-dimensional quantum gravity duals and other SYK-like models.
This seminar offers the option to attend by Zoom. For information on how to join, please see:Quantum Matter in Mathematics and Physics (QMMP) 2023:
https://cmsa.fas.harvard.edu/event_category/quantum-matter- seminar/ ——–
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https://forms.gle/1ewa7KeP6BxBuBeRA Generalizing sliceness
1 Oxford Street, Cambridge, MA 02138 USAA knot in the 3-sphere is said to be smoothly slice if it bounds a smoothly embedded disc in the 4-ball. Sliceness questions are closely related to interesting phenomena in 4-manifold topology: for example, the existence of a non smoothly slice knot that bounds a flatly embedded disc can be used to give a relatively quick proof of the existence of nonstandard smooth structures on 4-dimensional euclidean space. There are (at least!) two reasonable generalizations of sliceness to arbitrary 4-manifolds: in each of these directions, we will highlight open questions and give some results from joint work with Kjuchokova-Ray-Sakallı and Marengon-Ray-Stipsicz.
CMSA/MATH Bi-Annual Gathering
On Friday, March 24th, 4:30PM – 6PM, the CMSA will host the CMSA/MATH Bi-Annual Gathering in the Common Room at 20 Garden Street, Cambridge MA 02138.
- 25March 25, 2023No events