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Current Developments in Mathematics 2023
April 7, 2023 - April 8, 2023     
Current Developments in Mathematics 2023 April 7-8, 2023 Harvard University Science Center Lecture Hall C Speakers: Amol Aggarwal - Columbia University (Columbia) Bhargav Bhatt -...
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August 31, 2023 - September 1, 2023      10:43 am
***** On August 31–Sep 1, 2023 the CMSA will host the ninth annual Conference on Big Data. The Big Data Conference features speakers from the Harvard community as...
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upcoming events

  • CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Strongly coupled ultraviolet fixed point and symmetric mass generation in four dimensions with 8 Kähler-Dirac fermions

    Speaker: Anna Hasenfratz – University of Colorado

    10:00 AM-11:30 AM
    March 3, 2023
    4-dimensional gauge-fermion systems exhibit a quantum phase transition from a confining, chirally broken phase to a conformal phase as the number of fermions is increased. While the existence of the conformal phase is well established, very little is known about the nature of the phase transition or the strong coupling phase.
    Lattice QCD methods can predict the RG $\beta$ function, but the calculations are often limited by non-physical bulk phase transition that prevent exploring the strong coupling region of the phase diagram. Even the critical flavor number is controversial, estimates vary between $N_f=8$ and 14 for fundamental fermions.
    Using an improved lattice actions that include heavy Pauli-Villars (PV) type bosons to reduce ultraviolet fluctuations, I was able to simulate an SU(3) system with 8 fundamental flavors at much stronger renormalized coupling than previously possibly. The numerical results indicate a smooth phase transition from weak coupling to a strongly coupled phase.
    I investigate the critical behavior of the transition using finite size scaling. The result of the scaling analysis is not consistent with a first order phase transition, but it is well described by   Berezinsky-Kosterlitz-Thouless or BKT scaling. BKT scaling could imply that the 8-flavor system is the opening of the conformal window, an exciting possibility that warrants further investigations.
    The strongly coupled phase appear to be chirally symmetric but gapped, suggesting symmetric mass generation (SMG). This could be the consequence of the lattice fermions used in this study. Staggered fermions in the massless limit are known to be anomaly free, allowing an SMG phase in the continuum limit.

    For more information on how to join, please see:

  • SEMINARS: Gauge Theory and Topology: The annular Bar-Natan category and handle-slides

    Speaker: Matthew Hogancamp – Northeastern University

    3:30 PM-4:30 PM
    March 3, 2023
    1 Oxford Street, Cambridge, MA 02138 USA

    Khovanov homology can be upgraded to an invariant of pairs (K,V) where K is a framed knot and V is an object of the annular Bar-Natan category (ABN). In this context, the pair (K,V) is called a colored knot, and its Khovanov invariant is called colored Khovanov homology.  In my talk I will discuss recent joint work with David Rose and Paul Wedrich, in which we construct an object in ABN (more accurately, an ind-object therein), called a Kirby color, whose associated colored Khovanov invariant satisfies the important handle-slide relation.  Our work gives an annular perspective on the Manolescu-Neithalath 2-handle formula for sl(2) skein lasagna modules.


  • CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Quantum entropy thermalization

    Speaker: Yichen Huang – Harvard University

    10:00 AM-11:00 AM
    March 10, 2023
    In an isolated quantum many-body system undergoing unitary evolution, the entropy of a subsystem (smaller than half the system size) thermalizes if at long times, it is to leading order equal to the thermodynamic entropy of the subsystem at the same energy. We prove entropy thermalization for a nearly integrable Sachdev-Ye-Kitaev model initialized in a pure product state. The model is obtained by adding random all-to-all 4-body interactions as a perturbation to a random free-fermion model. In this model, there is a regime of “thermalization without eigenstate thermalization.” Thus, the eigenstate thermalization hypothesis is not a necessary condition for thermalization.
    References: arXiv:2302.10165, 2209.09826; Joint work with Aram W. Harrow

    For more information on how to join, please see:

  • SEMINARS: Gauge Theory and Topology: Fillable contact structures from positive surgery

    Speaker: Thomas Mark – University of Virginia

    10:30 AM-11:30 AM
    March 10, 2023
    1 Oxford Street, Cambridge, MA 02138 USA

    For a Legendrian knot $K$ in a closed contact 3-manifold, we describe a necessary and sufficient condition for contact $n$-surgery along $K$ to yield a weakly symplectically fillable contact manifold, for some integer $n>0$. When specialized to knots in the standard 3-sphere this gives an effective criterion for the existence of a fillable positive surgery, along with various obstructions. These are sufficient to determine, for example, whether such a surgery exists for all knots of up to 10 crossings. The result also has certain purely topological consequences, such as the fact that a knot admitting a lens space surgery must have slice genus equal to its 4-dimensional clasp number. We will mainly explore these topologically-flavored aspects, but will give some hints of the general proof if time allows.


  • SEMINARS: CMSA Swampland: String theory scalar potentials and their critical points

    Speaker: David Andriot – LAPTH Annecy

    11:00 AM-12:00 PM
    March 13, 2023
    20 Garden Street, Cambridge, MA 02138

    Positive scalar potentials in string effective theories could provide an origin to Dark Energy, responsible for the accelerated expansion of our universe today or during inflation. It is thus crucial to characterise these scalar potentials, namely their slope, their critical points (de Sitter solutions) and the associated stability, as also advocated by the Swampland Program. We will present such characterisations. Going further, we will also discuss negative scalar potentials, and make related observations on anti-de Sitter solutions, in particular on a new mass bound, as well as comments on scale separation.

  • CMSA EVENT: CMSA Active Matter: Active chemical reactions in phase-separating systems

    Speaker: Jonathan Bauermann – Max Planck Institute for the Physics of Complex Systems

    1:00 PM-2:00 PM
    March 16, 2023
    20 Garden Street, Cambridge, MA 02138

    Motivated by the existence of membrane-less compartments in the chemically active environment of living cells, I will discuss the dynamics of droplets in the presence of active chemical reactions. Therefore, I will first introduce the underlying interplay between phase separation and active reactions, which can alter the droplet dynamics compared to equilibrium systems. A key feature of such systems is the emergence of concentration gradients even at steady states. In the second part of this talk, I will discuss how these gradients can trigger instabilities in the core of chemically active droplets, giving rise to a new non-equilibrium steady state of liquid spherical shells. Finally, I will present experimental and theoretical results discussing the existence and energetic cost of this non-equilibrium steady state in a coacervate system.

    This seminar will be held in person and on Zoom. For more information on how to join, please see:

  • CMSA EVENT: CMSA Colloquium: Synchronization in a Kuramoto Mean Field Game

    Speaker: Mete Soner – Princeton University

    12:30 PM-1:30 PM
    March 22, 2023
    20 Garden Street, Cambridge, MA 02138

    Originally 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.


  • HARVARD-MIT COMBINATORICS SEMINAR: Joint MIT-Harvard-MSR Combinatorics Seminar: Strong bounds for 3-progressions

    Speaker: Raghu Meka – UCLA

    3:00 PM-5:00 PM
    March 22, 2023

    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.


    For information about the Combinatorics Seminar, please visit…


    This is a two-hour talk with a break in the middle.

    “Note special location”


  • NUMBER THEORY SEMINAR: Number Theory Seminar

    Number Theory Seminar

    Speaker: Lillian Pierce – Duke

    3:00 PM-4:00 PM
    March 22, 2023

    Title: TBA

    Abstract: TBA

  • CMSA EVENT: CMSA Probability Seminar: Some rigorous results on the Lévy spin glass model

    Speaker: Wei-Kuo Chen – Minnesota

    3:30 PM-4:30 PM
    March 22, 2023

    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:

  • OPEN NEIGHBORHOOD SEMINAR: Open Neighborhood Seminar: The mathematics of democracy

    Speaker: Manon Revel – MIT

    4:30 PM-5:30 PM
    March 22, 2023
    1 Oxford Street, Cambridge, MA 02138 USA

    Is 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:

  • CMSA EVENT: CMSA General Relativity: New Phases of N=4 SYM

    Speaker: Prahar Mitra – University of Cambridge

    1:30 PM-2:30 PM
    March 23, 2023
    20 Garden Street, Cambridge, MA 02138

    We 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.
    **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:

  • SEMINARS: Introductory Mathematics Seminar: Designing a Culturally-Responsive Precalculus Curriculum Grounded in Tucson as Place and Identity

    Speaker: Guadalupe Lozano – University of Arizona

    4:00 PM-5:00 PM
    March 23, 2023

    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.


  • SEMINARS: Algebraic Dynamics Seminar: Sullivan’s Dictionary, Limits of deformations, and Modular Laminations

    Speaker: Jeremy Kahn – Brown University

    4:00 PM-6:00 PM
    March 23, 2023
    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

  • CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Traversable wormhole dynamics on a quantum processor

    Speaker: Alexander Zlokapa – MIT

    10:00 AM-11:30 AM
    March 24, 2023
    20 Garden Street, Cambridge, MA 02138

    The 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:

    Subscribe to Harvard CMSA Quantum Matter and other seminar videos
    (more to be uploaded):

    Subscribe to Harvard CMSA seminar mailing list:


  • Gauge Theory and Topology Seminar SEMINAR: Generalizing sliceness

    Gauge Theory and Topology Seminar SEMINAR
    Generalizing sliceness

    Speaker: Allison Miller – Swarthmore Colelge

    3:30 PM-4:30 PM
    March 24, 2023
    1 Oxford Street, Cambridge, MA 02138 USA

    A 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 EVENT: CMSA/MATH Bi-Annual Gathering
    4:30 PM-6:00 PM
    March 24, 2023

    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.

  • CMSA EVENT: CMSA General Relativity: Gravitational perturbations near to extreme Kerr

    Speaker: Alejandra Castro – University of Cambridge

    9:30 AM-10:30 AM
    March 30, 2023
    20 Garden Street, Cambridge, MA 02138

    Gravitational perturbations of a black hole illustrate the invaluable synergy between theory, experiment, and numerical simulations in general relativity. A recent development in the theory side has been the identification of the relevant degrees of freedom describing the low energy physics driving a black hole away from extremality.  For simple cases, this low energy sector determines important aspects of the gravitational backreaction, and several properties that are key to our microscopic (quantum) understanding of black hole physics.
    In this talk I will discuss these developments in the context of the (near-)extreme Kerr black hole. In particular, I will revisit the spectrum of linear axisymmetric gravitational perturbations of this black hole. The aim is to characterise those perturbations that are responsible for the deviations away from extremality, and to contrast them with the linearized perturbations treated in the Newman-Penrose formalism. I will show that for Kerr the low-lying mode sector is subtle and intricate—features that their charged spherical symmetric cousins do not display. This unveils new clues on how to decode a microscopic, and holographic, understanding of the Kerr black hole.


    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:

  • CMSA EVENT: CMSA Active Matter: The Role of Orientational Order in Development

    Speaker: Mark Bowick – Kavli Institute for Theoretical Physics, UCSB

    1:00 PM-2:00 PM
    March 30, 2023
    20 Garden Street, Cambridge, MA 02138

    Morphogenesis, the process through which genes generate form, establishes tissue scale order as a template for constructing the complex shapes of the body plan. The extensive growth required to build these ordered substrates is fueled by cell proliferation, which, naively, should disrupt order. Understanding how active morphogenetic mechanisms couple cellular and mechanical processes to generate order remains an outstanding question in animal development. I will review the statistical mechanics of orientational order and discuss the observation of a fourfold orientationally ordered phase (tetratic) in the model organism Parhyale hawaiensis. I will also discuss theoretical mechanisms for the formation of orientational order that require both motility and cell division, with support from self-propelled vertex models of tissue. The aim is to uncover a robust, active mechanism for generating global orientational order in a non-equilibrium system that then sets the stage for the development of shape and form.

    This seminar will be held in person and on Zoom. For more information on how to join, please see:

  • SEMINARS: Thursday Seminar: The coniveau tower

    Speaker: Mike Hopkins – Harvard

    3:30 PM-5:30 PM
    March 30, 2023
    1 Oxford Street, Cambridge, MA 02138 USA

    No additional detail for this event.

  • SEMINARS: Algebraic Dynamics Seminar: Arboreal Galois groups with colliding critical points

    Speaker: Rob Benedetto – Amherst College

    4:00 PM-6:00 PM
    March 30, 2023

    Let f(z) be a rational function of degree d>1 over a field K (usually K=C(t) or K=Q), and let x_0 be a point in P^1(K). The Galois groups of the equations f^n(z)=x_0 are known as arboreal Galois groups because they induce an action on a d-ary rooted tree. In 2013, Pink observed that when d=2 and the two critical points c_1, c_2 collide, meaning that f^m(c_1)=f^m(c_2) for some m>0, then the arboreal Galois groups are strictly smaller than the full automorphism group of the tree. We study these arboreal Galois groups when f is either a quadratic rational function or a cubic polynomial. When the critical points collide, we describe the maximum possible Galois groups in these cases, and we find sufficient conditions for these maximum groups to be attained.

    For more information, please see:  Algebraic Dynamics Seminar at Harvard