## news

##### Harvard Makes Strong Showing at 83rd Putnam Mathematical Competition

Harvard scored second place among the winning teams at the 83rd annual William Lowell Putnam Mathematical Competition. Over 3,400 students from over 450 institutions participated...

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## announcements

##### 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 -...
##### Master Class in Teaching Math Modeling for Life Sciences
July 9, 2023 - July 14, 2023
Where: Harvard University, Cambridge, MA When: July 9 - July 14, 2023   There is a growing realization that traditional “Calculus for Life Sciences” courses...
##### CMSA CONFERENCE ON BIG DATA
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

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• CMSA EVENT: CMSA Conference on Geometry and Statistics

##### CMSA EVENTCMSA Conference on Geometry and Statistics

All day
March 1, 2023-March 1, 2023

On Feb 27-March 1, 2023 the CMSA will host a Conference on Geometry and Statistics.

• NUMBER THEORY SEMINAR: Number Theory Seminar

##### NUMBER THEORY SEMINARNumber Theory Seminar

3:00 PM-4:00 PM
March 1, 2023

Title: TBA

Abstract: TBA

• NUMBER THEORY SEMINAR: Number Theory: Counting integral points on symmetric varieties, and applications to arithmetic statistics

##### NUMBER THEORY SEMINARNumber Theory: Counting integral points on symmetric varieties, and applications to arithmetic statistics

Speaker: Ashvin Swaminathan –

3:00 PM-4:00 PM
March 1, 2023
1 Oxford Street, Cambridge, MA 02138 USA
Over the past few decades, significant progress has been made in arithmetic statistics by the following two-step process: (1) parametrize arithmetic objects of interest in terms of the integral orbits of a representation of a group G acting on a vector space V; and (2) use geometry-of-numbers methods to count the orbits of G(Z) on V(Z). But it often happens that the arithmetic objects of interest correspond to orbits that lie on a proper subvariety of V. In such cases, geometry-of-numbers methods do not suffice to obtain precise asymptotics, and more sophisticated point-counting techniques are required. In this talk, we explain how the Eskin–McMullen method for counting integral points on symmetric varieties can be used to study the distribution of 2-class groups in certain thin families of cubic number fields.
(Joint with Iman Setayesh, Arul Shankar, and Artane Siad)
• OPEN NEIGHBORHOOD SEMINAR: Open Neighborhood Seminar: The joy of negatives

##### OPEN NEIGHBORHOOD SEMINAROpen Neighborhood Seminar: The joy of negatives

Speaker: Elden Elmanto – Harvard

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

One of the first deep things we learned in elementary school is the act of taking negatives of numbers. I’ll explain the geometry that underlies this activity, which leads to algebraic K-theory and other gadgets. I also want to explain the joy of doing math with your friends.

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• THURSDAY SEMINAR SEMINAR: Thursday Seminar: Basic properties of biconnectivity

##### THURSDAY SEMINAR SEMINARThursday Seminar: Basic properties of biconnectivity

Speaker: Stephen McKean –

3:30 PM-5:30 PM
March 2, 2023
1 Oxford Street, Cambridge, MA 02138 USA

This seminar will take place in SC 507 at 3:30pm.

• CMSA EVENT: CMSA Colloquium: The string/black hole transition in anti de Sitter space

##### CMSA EVENTCMSA Colloquium: The string/black hole transition in anti de Sitter space

Speaker: Erez Urbach – Weizmann Institute

4:00 PM-5:00 PM
March 2, 2023
20 Garden Street, Cambridge, MA 02138

String stars, or Horowitz-Polchinski solutions, are string theory saddles with normalizable condensates of thermal-winding strings. In the past, string stars were offered as a possible description of stringy (Euclidean) black holes in asymptotically flat spacetime, close to the Hagedorn temperature. I will discuss the thermodynamic properties of string stars in asymptotically (thermal) anti-de Sitter background (including AdS3 with NS-NS flux), their possible connection to small black holes in AdS, and their implications for holography. I will also present new “winding-string gas” saddles for confining holographic backgrounds such as the Witten model, and their relation to the deconfined phase of 3+1 pure Yang-Mills.

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• 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

##### CMSA EVENTCMSA 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.

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

##### SEMINARSGauge 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.

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• HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR: Harvard–MIT Algebraic Geometry Seminar: Syzygies of adjoint linear series on projective varieties

##### HARVARD-MIT ALGEBRAIC GEOMETRY SEMINARHarvard–MIT Algebraic Geometry Seminar: Syzygies of adjoint linear series on projective varieties

Speaker: Justin Lacini – Kansas

3:00 PM-4:00 PM
March 7, 2023
1 Oxford Street, Cambridge, MA 02138 USA

Syzygies of algebraic varieties have long been a topic of intense interest among algebraists and geometers alike. Starting with the pioneering work of Mark Green on curves, numerous attempts have been made to extend these results to higher dimensions. Ein and Lazarsfeld proved that if A is a very ample line bundle, then K_X + mA satisfies property N_p for any m>=n+1+p. It has ever since been an open question if the same holds true for A ample and basepoint free. In joint work with Purnaprajna Bangere we give a positive answer to this question.

• HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR: Harvard–MIT Algebraic Geometry Seminar

##### HARVARD-MIT ALGEBRAIC GEOMETRY SEMINARHarvard–MIT Algebraic Geometry Seminar

3:00 PM-4:00 PM
March 7, 2023

Title: TBA

Abstract: TBA

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• CMSA EVENT: CMSA Colloquium: Conformal symmetry, Optimization algorithms and the Critical Phenomena

##### CMSA EVENTCMSA Colloquium: Conformal symmetry, Optimization algorithms and the Critical Phenomena

Speaker: Ning Su – University of Pisa

12:30 PM-1:30 PM
March 8, 2023
20 Garden Street, Cambridge, MA 02138

In the phase diagram of many substances, the critical points have emergent conformal symmetry and are described by conformal field theories. Traditionally, physical quantities near the critical point can be computed by perturbative field theory method, where conformal symmetry is not fully utilized. In this talk, I will explain how conformal symmetry can be used to determine certain physical quantities, without even knowing the fine details of the microscopic structure. To compute the observables precisely, one needs to develop powerful numerical techniques. In the last few years, we have invented many computational tools and algorithms, and predicted critical exponents of Helium-4 superfluid phase transition and Heisenberg magnet to very high precision.

• NUMBER THEORY SEMINAR: Number Theory Seminar

##### NUMBER THEORY SEMINARNumber Theory Seminar

3:00 PM-4:00 PM
March 8, 2023

Title: TBA

Abstract: TBA

• SEMINARS: Informal Seminar:The horocycle flow in moduli space

##### SEMINARSInformal Seminar:The horocycle flow in moduli space

Speaker: Barak Weiss – Tel Aviv University and CMSA

4:00 PM-5:00 PM
March 8, 2023

This seminar will be held in Science Center 530 at 4:00pm on Wednesday, March 8th.

Please see the seminar page for more details: https://www.math.harvard.edu/~ctm/sem

• HARVARD-MIT COMBINATORICS SEMINAR: Harvard-MIT Combinatorics Seminar: Geometry of the Chromatic Symmetric Function of Trees

##### HARVARD-MIT COMBINATORICS SEMINARHarvard-MIT Combinatorics Seminar: Geometry of the Chromatic Symmetric Function of Trees

Speaker: Mario Sanchez – Cornell

4:15 PM-5:15 PM
March 8, 2023

Stanley’s chromatic symmetric function is a generalization of the chromatic polynomial of a graph that encodes coloring information for graphs. One open conjecture is that non-isomorphic trees have different chromatic symmetric functions. In this talk, I will give two geometric interpretations of these functions for trees. The first interprets the chromatic symmetric function of a tree as an element in the Chow ring of the permutahedral variety opening the conjecture to algebraic geometric methods. The second describes this open conjecture in terms of the theory of valuations on generalized permutahedra. These are functions on polytopes which satisfy certain inclusion-exclusion relations with respect to subdivisions. From this perspective, we make progress on the conjecture by constructing new valuations on generalized permutahedra. We will primarily focus on this convex geometric interpretation for this talk.

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• CMSA EVENT: CMSA General Relativity: Pseudospectrum and black hole quasinormal mode instability: an ultraviolet universality conjecture

##### CMSA EVENTCMSA General Relativity: Pseudospectrum and black hole quasinormal mode instability: an ultraviolet universality conjecture

Speaker: Professor Jose Luis Jaramillo – Bourgogne U.

9:30 AM-10:30 AM
March 9, 2023

Can we measure the ‘effective regularity’ of spacetime from the perturbation of quasi-normal mode (QNM) overtones? Black hole (BH) QNMs encode the resonant response of black holes under linear perturbations, their associated complex frequencies providing an invariant probe into the background spacetime geometry. In the late nineties, Nollert and Price found evidence of a BH QNM instability phenomenon, according to which perturbed QNMs of Schwarzschild spacetime migrate to new perturbed branches of different qualitative behaviour and asymptotics. Here we revisit this BH QNM instability issue by adopting a pseudospectrum approach. Specifically, we cast the QNM problem as an eigenvalue problem for a non-selfadjoint operator by adopting a hyperboloidal formulation of spacetime. Non-selfadjoint (more generally non-normal) operators suffer potentially of spectral instabilities, the notion of pseudospectrum providing a tool suitable for their study. We find evidence that perturbed Nollert & Price BH QNMs track the pseudospectrum contour lines, therefore probing the analytic structure of the resolvent, showing the following (in)stability behaviour: i) the slowest decaying (fundamental) mode is stable, whereas ii) (all) QNM overtones are ultraviolet unstable (for sufficiently high frequency). Building on recent work characterizing Burnett’s conjecture as a low-regularity problem in general relativity, we conjecture that (in the infinite-frequency limit) generic ultraviolet spacetime perturbations make BH QNMs migrate to ‘Regge QNM branches’ with a precise universal logarithmic pattern. This is a classical general relativity (effective) low-regularity phenomenon, agnostic to possible detailed (quantum) descriptions of gravity at higher-energies and potentially observationally accessible.

This seminar will be held on Zoom. For more information on how to join, please see: https://cmsa.fas.harvard.edu/event_category/general-relativity/

• CMSA EVENT: CMSA Probability Seminar: On the free energy of spin glasses with multiple types

##### CMSA EVENTCMSA Probability Seminar: On the free energy of spin glasses with multiple types

Speaker: Vishesh JainJean-Christophe Mourrat – ENS Lyon

11:00 AM-12:00 PM
March 9, 2023

In the simplest spin-glass model, due to Sherrington and Kirkpatrick, the energy function involves interaction terms between all pairs of spins. A bipartite version of this model can be obtained by splitting the spins into two groups, which we can visualize as forming two layers, and by keeping only interaction terms that go from one to the other layer. For this and other models that incorporate a finite number of types of spins, the asymptotic behavior of the free energy remains mysterious (at least from the mathematical point of view). I will present the difficulties arising there, and some partial progress.

This seminar will be held on Zoom. For more information on how to join, please see: https://cmsa.fas.harvard.edu/event_category/probability-seminar/

• THURSDAY SEMINAR SEMINAR: Thursday Seminar: Modified whitehead towers and motivic infinite loop spaces

##### THURSDAY SEMINAR SEMINARThursday Seminar: Modified whitehead towers and motivic infinite loop spaces

Speaker: Elden Elmanto – Harvard

3:30 PM-5:30 PM
March 9, 2023
1 Oxford Street, Cambridge, MA 02138 USA

This seminar will take place in SC 507 at 3:30pm.

• CMSA EVENT: CMSA Special Lectures on Machine Learning and Protein Folding

##### CMSA EVENTCMSA Special Lectures on Machine Learning and Protein Folding

3:30 PM-5:00 PM
March 9, 2023
20 Garden Street, Cambridge, MA 02138

The CMSA will host a series of three 90-minute lectures on the subject of machine learning for protein folding.

Thursday, Feb 9, 2023:  3:30–5:00 pm ET

Thursday, Feb 16, 2023:  3:30–5:00 pm ET

Thursday, March 9, 2023: 3:30–5:00 pm ET

Further details TBA.

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

##### CMSA EVENTCMSA 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

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

##### SEMINARSGauge 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.

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

##### SEMINARSCMSA 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.

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• HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR: Harvard–MIT Algebraic Geometry Seminar: Higher Tsen Theorem

##### HARVARD-MIT ALGEBRAIC GEOMETRY SEMINARHarvard–MIT Algebraic Geometry Seminar: Higher Tsen Theorem

Speaker: Tomer Schlank – MIT

3:00 PM-4:00 PM
March 14, 2023

Tsen’s Theorem gives a simple sufficient criterion for an algebraic variety to have a point over a complex function field. In the talk we shall discuss a way to define on the collection of such points a structure of a stack and show that this stack is homologically contractible. We shall explain a variant of this phenomenon that can be employed for the study of Beilinson-Drinfeld Opers for reductive groups. This is joint work with D. Beraldo and D. Kazhdan.

• HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR: Harvard–MIT Algebraic Geometry Seminar

##### HARVARD-MIT ALGEBRAIC GEOMETRY SEMINARHarvard–MIT Algebraic Geometry Seminar

3:00 PM-4:00 PM
March 14, 2023

Title: TBA

Abstract: TBA

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

##### CMSA EVENTCMSA 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: https://cmsa.fas.harvard.edu/event_category/active-matter-seminar/

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• HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR: Harvard–MIT Algebraic Geometry Seminar: Non-abelian Hodge theory and the P=W conjecture

##### HARVARD-MIT ALGEBRAIC GEOMETRY SEMINARHarvard–MIT Algebraic Geometry Seminar: Non-abelian Hodge theory and the P=W conjecture

Speaker: Junliang Shen – Yale University

3:00 PM-4:00 PM
March 21, 2023

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: Mathematical Picture Language Seminar

##### MATHEMATICAL PICTURE LANGUAGE SEMINARMathematical Picture Language Seminar

Speaker: Peter Love – Tufts University

3:30 PM-4:30 PM
March 21, 2023
17 Oxford Street, Cambridge, MA 02138 USA

Title: TBA

Abstract: TBA

• SEMINARS: Applied Algebraic and Geometry Seminar: Conditions for Absolute Delay Stability

##### SEMINARSApplied Algebraic and Geometry Seminar: Conditions for Absolute Delay Stability

Speaker: Polly Yu – Harvard University

4:00 PM-5:00 PM
March 21, 2023

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 EVENT: CMSA 2023 Ding Shum Lecture

##### CMSA EVENTCMSA 2023 Ding Shum Lecture

Speaker: Cynthia Dwork – Harvard SEAS

5:00 PM-6:00 PM
March 21, 2023

On March 21, 2023, the CMSA will host the fourth annual Ding Shum Lecture, given by Cynthia Dwork (Harvard SEAS).

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

##### CMSA EVENTCMSA 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

##### HARVARD-MIT COMBINATORICS SEMINARJoint 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.

=======================================================

http://math.mit.edu/seminars/combin/

====================================================

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

“Note special location”

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• NUMBER THEORY SEMINAR: Number Theory Seminar

##### NUMBER THEORY SEMINARNumber 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

##### CMSA EVENTCMSA 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: https://cmsa.fas.harvard.edu/event_category/probability-seminar/

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

##### OPEN NEIGHBORHOOD SEMINAROpen 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.

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

##### CMSA EVENTCMSA 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: https://cmsa.fas.harvard.edu/event_category/general-relativity/

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

##### SEMINARSIntroductory 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

##### SEMINARSAlgebraic 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.

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

##### CMSA EVENTCMSA 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:
https://cmsa.fas.harvard.edu/event_category/quantum-matter-seminar/

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• Gauge Theory and Topology Seminar SEMINAR: Generalizing sliceness

##### Gauge Theory and Topology Seminar SEMINARGeneralizing 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

##### CMSA EVENTCMSA/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.

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• CMSA EVENT: CMSA Swampland Seminar: Recent developments on the tidal Love numbers of black holes

##### CMSA EVENTCMSA Swampland Seminar: Recent developments on the tidal Love numbers of black holes

Speaker: Valerio De Luca – University of Pennsylvania

11:00 AM-12:00 PM
March 27, 2023
20 Garden Street, Cambridge, MA 02138

Tidal Love numbers describe the deformability of compact objects under the presence of external tidal perturbations, and are found to be exactly zero for black holes in pure General Relativity.  This property is however fragile, since they receive corrections from higher-order derivative terms in the theory. We show that the tidal deformability of neutral black holes is constrained by the Weak Gravity Conjecture.
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• NUMBER THEORY SEMINAR: Number Theory Seminar: Selmer averages in families of elliptic curves and applications

##### NUMBER THEORY SEMINARNumber Theory Seminar: Selmer averages in families of elliptic curves and applications

Speaker: Wei Ho – Princeton / IAS

3:00 PM-4:00 PM
March 29, 2023
1 Oxford Street, Cambridge, MA 02138 USA

Orbits of many coregular representations of algebraic groups are closely linked to moduli spaces of genus one curves with extra data. We may use these orbit parametrizations to compute the average size of Selmer groups of elliptic curves in certain families, e.g., with marked points, thus obtaining upper bounds for the average ranks of the elliptic curves in these families. (This is joint work with Manjul Bhargava.) We will also describe some other applications and related work (some joint with collaborators, including Levent Alpöge, Manjul Bhargava, Tom Fisher, Jennifer Park).

• HARVARD-MIT COMBINATORICS SEMINAR: Joint MIT-Harvard-MSR Combinatorics Seminar: Hilbert series of matroid Chow rings and intersection cohomology

##### HARVARD-MIT COMBINATORICS SEMINARJoint MIT-Harvard-MSR Combinatorics Seminar: Hilbert series of matroid Chow rings and intersection cohomology

Speaker: Luis Ferroni – KTH

4:15 PM-5:15 PM
March 29, 2023

Starting with a matroid M one can construct three important algebraic objects: the Chow ring, the augmented Chow ring and the intersection cohomology module. They play instrumental roles within the proofs of the log-concavity of the Whitney numbers of the first kind, and the top-heaviness of the Whitney numbers of the second kind. We will describe the combinatorics of their Hilbert series for matroids in general and uniform matroids in particular. Several aspects such as unimodality, gamma-positivity and real-rootedness will be discussed under different perspectives. Based on joint work with Jacob Matherne, Matthew Stevens and Lorenzo Vecchi.

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http://math.mit.edu/seminars/combin/

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

##### CMSA EVENTCMSA 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: https://cmsa.fas.harvard.edu/event_category/general-relativity/

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

##### CMSA EVENTCMSA 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: https://cmsa.fas.harvard.edu/event_category/active-matter-seminar/

• SEMINARS: Thursday Seminar: The coniveau tower

##### SEMINARSThursday 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

##### SEMINARSAlgebraic 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.

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• CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: A Plane Defect in the 3d O(N) Model

##### CMSA EVENTCMSA Quantum Matter in Mathematics and Physics: A Plane Defect in the 3d O(N) Model

Speaker: Abijith Krishnan – MIT

10:00 AM-11:30 AM
March 31, 2023
20 Garden Street, Cambridge, MA 02138

It was recently found that the classical 3d O(N) model in the semi-infinite geometry can exhibit an “extraordinary-log” boundary universality class, where the spin-spin correlation function on the boundary falls off as (log x)^(-q). This universality class exists for a range 2≤N<Nc and Monte-Carlo simulations and conformal bootstrap indicate Nc>3. In this talk, I’ll extend this result to the 3d O(N) model in an infinite geometry with a plane defect. I’ll explain using the renormalization group (RG) that the extraordinary-log universality class is present for any finite N≥2, and that a line of defect fixed points is present at N=∞. This line of defect fixed points is lifted to the ordinary, special (no defect) and extraordinary-log universality classes by

1/N corrections. I’ll show that the line of defect fixed points and the 1/N corrections agree with an a-theorem by Jensen and O’Bannon for 3d CFTs with a boundary. Finally, I’ll conclude by noting some physical systems where the extraordinary-log universality class can be observed.

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

• CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: A Plane Defect in the 3d O(N) Model

##### CMSA EVENTCMSA Quantum Matter in Mathematics and Physics: A Plane Defect in the 3d O(N) Model

Speaker: Abijith Krishnan – MIT

10:00 AM-11:30 AM
March 31, 2023
20 Garden Street, Cambridge, MA 02138

It was recently found that the classical 3d O(N) model in the semi-infinite geometry can exhibit an “extraordinary-log” boundary universality class, where the spin-spin correlation function on the boundary falls off as (log x)^(-q). This universality class exists for a range 2≤N<Nc and Monte-Carlo simulations and conformal bootstrap indicate Nc>3. In this talk, I’ll extend this result to the 3d O(N) model in an infinite geometry with a plane defect. I’ll explain using the renormalization group (RG) that the extraordinary-log universality class is present for any finite N≥2, and that a line of defect fixed points is present at N=∞. This line of defect fixed points is lifted to the ordinary, special (no defect) and extraordinary-log universality classes by

1/N corrections. I’ll show that the line of defect fixed points and the 1/N corrections agree with an a-theorem by Jensen and O’Bannon for 3d CFTs with a boundary. Finally, I’ll conclude by noting some physical systems where the extraordinary-log universality class can be observed.

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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• SEMINARS: Informal Seminar: Jordan curves with piecewise geodesic property

##### SEMINARSInformal Seminar: Jordan curves with piecewise geodesic property

Speaker: Yilin Wang – IHES

1:30 PM-2:30 PM
March 31, 2023
1 Oxford Street, Cambridge, MA 02138 USA

This seminar will be held in Science Center 507 at 1:30pm on Friday, March 31st.

Please see the seminar page for more details: https://www.math.harvard.edu/~ctm/sem

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