CMSA

Spectral gap and two-point functions in spin glasses
2023-04-11 12:00 - 13:00 (America/New_York) | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Changji Xu
Title: Spectral gap and two-point functions in spin glasses
Abstract: Many have worked on spin glass models over the past 50 years, including physicists, mathematicians, and computers. A question that arises is whether computers yield dependable simulation results. In this talk, I will discuss some recent mathematical progress on spectral gap and two-point functions in spin glasses models.

Localization for random band matrices
2023-04-10 15:00 - 16:00 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
Probability Seminar
*Please note room change: Science Center 232*

Speaker: Ron Peled (Tel Aviv University)
Title: Localization for random band matrices
Abstract: I will explain an approach via “an adaptive Mermin-Wagner style shift” which proves localization of N x N Gaussian random band matrices with band width W satisfying W << N^{1/4}.
Joint work with Giorgio Cipolloni, Jeffrey Schenker and Jacob Shapiro.

Swampland bounds on the abelian gauge sectors
2023-04-10 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Swampland Seminar
Speaker: Seung-Joo Lee (IBS Daejeon)

Title: Swampland bounds on the abelian gauge sectors
Abstract: In this talk we will derive various bounds on the 0-form and the 1-form abelian gauge sectors of gravitational effective theories in 6 dimensions with minimal supersymmetry. We will start by considering 6-dimensional F-theory vacua with at least one tensor multiplets, to bound for them the number of the (0-form) U(1) gauge factors as well as the cyclic orders of the 1-form discrete gauge factors. While the two abelian gauge sectors may look rather independent, we will observe that both are heavily constrained by the solitonic heterotic strings present in the spectrum, which provide a common intuition for the derived bounds. Building upon the heterotic intuition, we will also try extending the arena to address analogous bounds for all F-theory vacua in 6 dimensions and even beyond. If time permits, several applications and future directions of research will be discussed at the end of the talk.

Current Developments in Mathematics Conference 2023
2023-04-07 14:00 - 2023-04-08 17:00 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
Current Developments in Mathematics 2023
Harvard University Science Center, Lecture Hall C
April 7-8, 2023
Speakers:
Amol Aggarwal – Columbia University
Bhargav Bhatt – Institute for Advanced Study, Princeton University, & University of Michigan
Paul Bourgade – New York University, Courant Institute
Vesselin Dimitrov – Institute for Advanced Study & Georgia Institute of Technology
Greta Panova – University of Southern California

For more information, and to register, please visit:
Current Developments in Mathematics 2023

Organizers: David Jerison, Paul Seidel, Nike Sun (MIT); Denis Auroux, Mark Kisin, Lauren Williams, Horng-Tzer Yau
Sponsored by the National Science Foundation, Harvard University Mathematics, Harvard University Center of Mathematical Sciences and Applications, and the Massachusetts Institute of Technology.
Harvard University is committed to maintaining a safe and healthy educational and work environment in which no member of the University community is, on the basis of sex, sexual orientation, or gender identity, excluded from participation in, denied the benefits of, or subjected to discrimination in any University program or activity. More information can be found here.

Modular graph forms and iterated integrals in string amplitudes
2023-04-07 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Algebraic Geometry in String Theory Seminar
Speaker: Oliver Schlotterer (Uppsala University)
Title: Modular graph forms and iterated integrals in string amplitudes
Abstract: I will discuss string amplitudes as a laboratory for special functions and period integrals that drive fruitful cross-talk with particle physicists and mathematicians. At genus zero, integration over punctures on a disk or sphere worldsheet generates multiple zeta values in the low-energy expansion of open- and closed-string amplitudes. At genus one, closed-string amplitudes introduce infinite families of non-holomorphic modular forms through the integration over torus punctures known as modular graph forms. The latter inspired Francis Brown’s alternative construction of non-holomorphic modular forms in the mathematics literature via iterated integrals, and I will report on recent progress in clarifying their connection with modular graph forms.

Enhancing Detection of Topological Order by Local Error Correction
2023-04-07 10:00 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter Seminar
Speaker: Nishad Maskara (Harvard)
Title: Enhancing Detection of Topological Order by Local Error Correction
Abstract: The exploration of topologically-ordered states of matter is a long-standing goal at the interface of several subfields of the physical sciences. Such states feature intriguing physical properties such as long-range entanglement, emergent gauge fields and non-local correlations, and can aid in realization of scalable fault-tolerant quantum computation. However, these same features also make creation, detection, and characterization of topologically-ordered states particularly challenging. Motivated by recent experimental demonstrations, we introduce a new paradigm for quantifying topological states—locally error-corrected decoration (LED)—by combining methods of error correction with ideas of renormalization-group flow. Our approach allows for efficient and robust identification of topological order, and is applicable in the presence of incoherent noise sources, making it particularly suitable for realistic experiments. We demonstrate the power of LED using numerical simulations of the toric code under a variety of perturbations, and we subsequently apply it to an experimental realization of a quantum spin liquid using a Rydberg-atom quantum simulator. Finally, we illustrate how LED can be applied to more general phases including non-abelian topological orders.

Rough solutions of the relativistic Euler equations
2023-04-06 09:30 - 10:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar
Speaker: Sifan Yu, Vanderbilt University
Title: Rough solutions of the relativistic Euler equations
Abstract: I will discuss recent works on the relativistic Euler equations with dynamic vorticity and entropy. We use a new formulation of the equations, which has geo-analytic structures. In this geometric formulation, we decompose the flow into geometric “sound-wave part” and “transport-div-curl part”. This allows us to derive sharp results about the dynamics, including the existence of low-regularity solutions. Then, I will discuss the results of rough solutions of the relativistic Euler equations and the role that nonlinear geometric optics plays in the framework. Our main result is that the Sobolev norm $H^{2+}$ of the variables in the “wave-part” and the H”older norm $C^{0,0+}$ of the variables in the “transport-part” can be controlled in terms of initial data for short times. We note that the Sobolev norm assumption $H^{2+}$ is the optimal result for the variables in the “wave-part.” This talk will include the main ideas of the proof, as well as a comparison of the relativistic and non-relativistic scenarios.

Sampling from the SK and mixed p-spin measures with stochastic localization
2023-04-05 15:30 - 16:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Probability Seminar

Speaker: Ahmed El Alaoui (Cornell)
Title: Sampling from the SK and mixed p-spin measures with stochastic localization
Abstract: I will present an algorithm which efficiently samples from the Sherrington-Kirkpatrick (SK) measure with no external field at high temperature. The approach is based on the stochastic localization process of Eldan, together with a subroutine for computing the mean vectors of a family of measures tilted by an appropriate external field. Conversely, we show that no ‘stable’ algorithm can approximately sample from the SK measure at low temperature. Time permitting, we discuss extensions to the p-spin model. This is based on a joint work with Andrea Montanari and Mark Sellke.

Optimal Dynamic Allocation: Simplicity through Information Design
2023-04-04 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Faidra Monachou
Title: Optimal Dynamic Allocation: Simplicity through Information Design
Abstract: We study dynamic nonmonetary markets where objects are allocated to unit-demand agents with private types. An agent’s value for an object is supermodular in her type and the quality of the object, and her payoff is quasilinear in her waiting cost. The social planner’s objective is a linear combination of allocative efficiency (i.e., the sum of values) and welfare (i.e., the sum of payoffs). We identify the optimal mechanism in the class of direct-revelation mechanisms that elicit agents’ types and assign them to objects over time. We show that, when the social planner can design the information disclosed to the agents about the objects, the optimal mechanism has a simple implementation: a first-come first-served waitlist with deferrals. In this implementation, the information disclosed about each object is an interval containing the object quality, rather than the exact quality. These intervals partition the quality space. We also show that when the planner’s objective weight on welfare increases, these intervals become coarser, and optimal disclosure policies less informative. A direct corollary is that mechanisms that achieve higher welfare also induce lower distributional inequality, in terms of the Lorenz order.

Black hole microstate counting from the gravitational path integral
2023-04-03 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Luca Iliesiu, Stanford
Title: Black hole microstate counting from the gravitational path integral
Abstract: Reproducing the integer count of black hole micro-states from the gravitational path integral is an important problem in quantum gravity. In the first part of the talk, I will show that, by using supersymmetric localization, the gravitational path integral for 1/16-BPS black holes in supergravity can reproduce the index obtained in the string theory construction of such black holes. A more refined argument then shows that not only the black hole index but also the total number of black hole microstates within an energy window above extremality that is polynomially suppressed in the charges also matches this string theory index. In the second part of the talk, I will present a second perspective on this state count and show how the BPS Hilbert space can be obtained by directly preparing states using the gravitational path integral. While such a preparation naively gives rise to a Hilbert space of BPS states whose dimension is much larger than expected, I will explain how non-perturbative corrections in the overlap of such states are again responsible for reproducing the correct dimension of the Hilbert space.

Kähler-Einstein metrics on families of Fano varieties
2023-04-03 10:00 - 11:00 | Virtual
Algebraic Geometry in String Theory Seminar
Speaker: Chung-Ming Pan, Institut de Mathématiques de Toulouse
Title: Kähler-Einstein metrics on families of Fano varieties
Abstract: This talk aims to introduce a pluripotential approach to study uniform a priori estimates of Kähler-Einstein (KE) metrics on families of Fano varieties. I will first recall basic tools in the pluripotential theory and the variational approach to complex Monge-Ampère equations. I will then define a notion of convergence of quasi-plurisubharmonic functions in families of normal varieties and extend several classical properties under this context. Last, I will explain how these elements help to obtain a purely analytic proof of the openness of existing singular KE metrics and a uniform $L^infty$ estimate of KE potentials. This is joint work with Antonio Trusiani.

The Role of Orientational Order in Development
2023-03-30 13:00 - 14:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Active Matter Seminar

Speaker: Mark Bowick, Kavli Institute for Theoretical Physics, UCSB
Title: The Role of Orientational Order in Development
Abstract: 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.

Gravitational perturbations near to extreme Kerr
2023-03-30 09:30 - 22:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar
Speaker: Alejandra Castro (University of Cambridge)
Title: Gravitational perturbations near to extreme Kerr
Abstract: 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.

Scattering amplitudes in quantum field theory
2023-03-29 12:30 - 13:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Speaker: Ruth Britto (Trinity College Dublin)
Title: Scattering amplitudes in quantum field theory
Abstract: Particle collider experiments require a detailed description of scattering events, traditionally computed through sums of Feynman diagrams. However, it is not practical to evaluate Feynman diagrams directly for all significant scattering processes. Moreover, adding all diagrams reveals many cancellations: scattering amplitudes in theories such as QCD take remarkably simple forms. This simplicity is a clue that the perturbative theory is perhaps best understood without reference to Feynman diagrams. In fact, it has recently become possible to explain some of this simplicity. I will show how to derive many amplitudes efficiently and elegantly, and propose taming the remaining complexity with ideas drawn from combinatorics and geometry.

Monotonicity of quasilocal mass for asymptotically flat Riemannian manifolds
2023-03-28 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Jue Liu
Title: Monotonicity of quasilocal mass for asymptotically flat Riemannian manifolds
Abstract: The study of quasilocal mass in general relativity has a long history. In previous papers by many authors we have a deep understanding of the properties of quasilocal mass such as positivity, rigidity and asymptotics etc. In this talk I will focus on the monotonicity of quasilocal mass, which means the quasilocal mass of a finite region is smaller than that of a larger region containing the previous region. Motivated by the definition of Bartnik mass and Brown-York mass, we define a new quasilocal mass using the Hamilton method. With this definition, we derive the sufficient condition such that the quasilocal mass is monotonic. As an application I will also discuss the relationship with the Bartnik conjecture, that is under what conditions there will be a static extension to the given Bartnik data.

Recent developments on the tidal Love numbers of black holes
2023-03-27 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Swampland Seminar
Speaker: Valerio De Luca (UPenn)

Title: Recent developments on the tidal Love numbers of black holes
Abstract: 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.

CMSA/MATH Bi-Annual Gathering
2023-03-24 16:30 - 18:00 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
On Friday, March 24th, 4:30PM – 6PM, the CMSA will host the CMSA/MATH Bi-Annual Gathering for Harvard CMSA and Math affiliates in the Common Room at 20 Garden Street, Cambridge MA 02138.

Traversable wormhole dynamics on a quantum processor
2023-03-24 10:00 - 11:30 | Hybrid – G10
Quantum Matter Seminar
Speaker: Alexander Zlokapa, MIT
Title: Traversable wormhole dynamics on a quantum processor
Abstract: 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.

New Phases of N=4 SYM
2023-03-23 13:30 - 14:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar
Speaker: Prahar Mitra (University of Cambridge)
Title: New Phases of N=4 SYM
Abstract: 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.
Based on: https://arxiv.org/pdf/2207.07134.pdf [hep-th]

Some rigorous results on the Lévy spin glass model
2023-03-22 15:30 - 16:30 | Virtual
Probability Seminar
Speaker: Wei-Kuo Chen (Minnesota)

Title: Some rigorous results on the Lévy spin glass model
Abstract: 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.

Synchronization in a Kuramoto Mean Field Game
2023-03-22 12:30 - 13:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Speaker: Mete Soner (Princeton University)
Title: Synchronization in a Kuramoto Mean Field Game
Abstract: 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.

2023 Ding Shum Lecture
2023-03-21 17:00 - 18:00 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
On March 21, 2023, the CMSA hosted the fourth annual Ding Shum Lecture, given by Cynthia Dwork (Harvard SEAS and Microsoft Research).

Time: 5:00-6:00 pm ET
Location: Harvard University Science Center Hall D
This event was be held in person and via Zoom webinar.

Title: Measuring Our Chances: Risk Prediction in This World and its Betters
Abstract: Prediction algorithms score individuals, assigning a number between zero and one that is often interpreted as an individual probability: a 0.7 “chance” that this child is in danger in the home; an 80% “probability” that this woman will succeed if hired; a 1/3 “likelihood” that they will graduate within 4 years of admission. But what do words like “chance,” “probability,” and “likelihood” actually mean for a non-repeatable activity like going to college? This is a deep and unresolved problem in the philosophy of probability. Without a compelling mathematical definition we cannot specify what an (imagined) perfect risk prediction algorithm should produce, nor even how an existing algorithm should be evaluated. Undaunted, AI and machine learned algorithms churn these numbers out in droves, sometimes with life-altering consequences.
An explosion of recent research deploys insights from the theory of pseudo-random numbers – sequences of 0’s and 1’s that “look random” but in fact have structure – to yield a tantalizing answer to the evaluation problem, together with a supporting algorithmic framework with roots in the theory of algorithmic fairness.
We can aim even higher. Both (1) our qualifications, health, and skills, which form the inputs to a prediction algorithm, and (2) our chances of future success, which are the desired outputs from the ideal risk prediction algorithm, are products of our interactions with the real world. But the real world is systematically inequitable. How, and when, can we hope to approximate probabilities not in this world, but in a better world, one for which, unfortunately, we have no data at all? Surprisingly, this novel question is inextricably bound with the very existence of nondeterminism.

Professor Cynthia Dwork is Gordon McKay Professor of Computer Science at the Harvard University John A. Paulson School of Engineering and Applied Sciences, Affiliated Faculty at Harvard Law School, and Distinguished Scientist at Microsoft. She uses theoretical computer science to place societal problems on a firm mathematical foundation.
Her recent awards and honors include the 2020 ACM SIGACT and IEEE TCMF Knuth Prize, the 2020 IEEE Hamming Medal, and the 2017 Gödel Prize.

Talk Chair: Horng-Tzer Yau (Harvard Mathematics & CMSA)

Moderator: Faidra Monachou (Harvard CMSA)

The 2020-2022 Ding Shum lectures were postponed due to Covid-19.

The 2019 Ding Shum Lecture featured Ronald Rivest on “Election Security.”

This event is made possible by the generous funding of Ding Lei and Harry Shum.

Watch the Lecture on Youtube:

Quantum Gravity constraints beyond asymptotic regimes
2023-03-21 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Max Wiesner
Title: Quantum Gravity constraints beyond asymptotic regimes
Abstract: Not every effective field theory that is consistent in the absence of gravity can be completed to a consistent theory of quantum gravity. The goal of the Swampland program is to find general criteria that distinguish effective field theories, that can be obtained as a low-energy approximation of quantum gravity, from those that are inconsistent in the presence of gravity. These criteria are oftentimes motivated by patterns observed in explicit compactifications of perturbative string theory and have passed many non-trivial tests in asymptotic regions of the field space such as, e.g., weak coupling limits. Still, the Swampland criteria should equally apply to effective theories that do not arise in asymptotic regions of the field space of string theory compactifications. In this talk I will summarize some of my recent works that studies the interior of regions of the field space of string theory in the context of the Swampland program.

Tensorial TQFT and disentangling modular Walker-Wang models
2023-03-17 10:00 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter Seminar
Speaker: Andreas Bauer (Freie Universität Berlin)
Title: Tensorial TQFT and disentangling modular Walker-Wang models
Abstract: I will introduce simple “tensorial” definitions for many algebraic and categorical structures appearing in the classification of topological phases of matter. Such “tensorial TQFTs” will be defined as maps that associate tensors to geometric/topological objects of some type, subject to gluing axioms. Tensorial TQFTs are very directly related to microscopic physical models in terms of discrete path integrals. I will use those tensorial definitions to construct invertible boundaries which disentangle modular Walker-Wang models.

Active chemical reactions in phase-separating systems
2023-03-16 13:00 - 14:00 | Virtual
Active Matter Seminar

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

Title: Active chemical reactions in phase-separating systems
Abstract: 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.

Randomized algorithms in combinatorics
2023-03-14 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Michael Simkin
Title: Randomized algorithms in combinatorics
Abstract: Randomized algorithms have been a computational workhorse for almost as long as there have been computers. Surprisingly, such algorithms can also be used to attack problems that are neither algorithmic nor probabilistic. Time permitting I will discuss the following combintorial examples:

Enumerative combinatorics and the n-queens problem: In how many ways can one place n queens on an n x n chessboard so that no queen threatens any other?
Constructions of combinatorial designs and the Erdos high-girth Steiner triple system problem: An order-n Steiner triple system (STS) is a collection of triples on n vertices such that every pair of vertices is contained in exactly one triple. In 1973 Erdos conjectured that there exist STSs with arbitrary large girth (informally, no small set of vertices spans many triples). I will discuss the use of randomized algorithms to prove this conjecture. Joint work with Kwan, Sah, and Sawhney.
Thresholds in random graphs and hypergraphs: I will discuss how randomized algorithms can be combined with the recent resolution of the Kahn–Kalai conjecture to determine thresholds in random (hyper) graph theory. Joint work with Pham, Sah, and Sawhney.

String theory scalar potentials and their critical points
2023-03-13 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Swampland Seminar

Speaker: David Andriot (Annecy, LAPTH)
Title: String theory scalar potentials and their critical points
Abstract: 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 characterize 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 characterizations. 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.

Quantum entropy thermalization
2023-03-10 10:00 - 11:00 | Virtual
Quantum Matter Seminar
Speaker: Yichen Huang (Harvard)
Title: Quantum entropy thermalization
Abstract: 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

On the free energy of spin glasses with multiple types
2023-03-09 11:00 - 12:00 | Virtual
Probability Seminar

Speaker: Jean-Christophe Mourrat (ENS Lyon)
Title: On the free energy of spin glasses with multiple types
Abstract: 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.

Pseudospectrum and black hole quasinormal mode instability: An ultraviolet universality conjecture
2023-03-09 09:30 - 10:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar
Speaker: Jose Luis Jaramillo (Bourgogne U.)
Title: Pseudospectrum and black hole quasinormal mode instability: an ultraviolet universality conjecture
Abstract: 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.
