The Definition of Differential Privacy - Cynthia Dwork Institute for Advanced Study 2016-11-14 | Differential Privacy Symposium: Four Facets of Differential PrivacySaturday, November 12, 2016https://www.ias.edu/differential-privacyMore videos on http://video.ias.edu
’t Hooft Anomaly Detection in 2+1d Lattice Systems - Wilbur Shirley Institute for Advanced Study 2024-05-24 | IAS High Energy Theory SeminarTopic: ’t Hooft Anomaly Detection in 2+1d Lattice SystemsSpeaker: Wilbur ShirleyAffiliation: Institute for Advanced StudyDate: May 24, 2024I will discuss two methods for diagnosing ’t Hooft anomalies of internal symmetries in 2+1d lattice systems. Anomalous symmetries of this kind arise naturally at the boundary of 3+1D symmetry-protected topological phases, and are known to be classified by the group cohomology of the symmetry group. The first method is purely kinematical: using only the form of the symmetry operators themselves, the anomaly cocycle is computed via a concrete procedure of operator truncation and dimensional reduction. The second method is dynamical in nature, entailing a choice of Hamiltonian that spontaneously breaks the symmetry. The anomaly is exposed in the algebraic structure of the ensuing domain wall excitations.
New Algebraic Invariants of Legendrian Links - Lenhard Ng Institute for Advanced Study 2024-05-24 | Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry ZoominarTopic: New Algebraic Invariants of Legendrian LinksSpeaker: Lenhard NgAffiliation: Duke UniversityDate: May 24, 2024For the past 25 years, Legendrian contact homology has played a key role in contact topology. I'll discuss a package of new invariants for Legendrian knots and links that builds on Legendrian contact homology and is derived from rational symplectic field theory. This includes a Poisson bracket on Legendrian contact homology and a symplectic structure on augmentation varieties. Time permitting, I'll also describe an unexpected connection to cluster theory for a family of Legendrian links associated to positive braids. Parts of this are joint work in progress with Roger Casals, Honghao Gao, Linhui Shen, and Daping Weng.
A Glimpse into the Langlands Program IV - Ana Caraiani Institute for Advanced Study 2024-05-24 | 2024 Program for Women+ and MathematicsTopic: A Glimpse into the Langlands Program IVSpeaker: Ana CaraianiAffiliation: Imperial College, LondonDate: May 24, 2024The goal of this lecture series is to give you a glimpse into the Langlands program, a central topic at the intersection of algebraic number theory, algebraic geometry and representation theory. In the first lecture, we will look at a celebrated instance of the Langlands correspondence, namely the modularity of elliptic curves. I will try to give you a sense of the different meanings of modularity and of the multitude of ingredients that go into establishing such a result. In the following lectures, I will focus on the more geometric ingredients, first in the special case of the modular curve and then for higher-dimensional Shimura varieties.
Deligne-Lusztig theory: examples and applications IV - Charlotte Chan Institute for Advanced Study 2024-05-24 | 2024 Program for Women and MathematicsTopic: Deligne-Lusztig theory: examples and applications IVSpeaker: Charlotte ChanAffiliation: University of MichiganDate: May 24, 2024Geometry and representation theory are intertwined in deep and foundational ways. One of the most important instances of this relationship was uncovered in the 1970s by Deligne and Lusztig: the representation theory of matrix groups over finite fields is encoded in the geometry of a natural "partition" of flag varieties. Recent developments have revealed rich connections between Deligne-Lusztig varieties and geometry studied in number-theoretic contexts. In this lecture series, we give an example-based tour of these ideas, focusing on how to extract concrete information from theory.
An introduction to representations of p-adic groups - Jessica Fintzen Institute for Advanced Study 2024-05-23 | 2024 Program for Women+ and Mathematics ColloquiumTopic: An introduction to representations of p-adic groupsSpeaker: Jessica FintzenDate: May 21, 2024
A Glimpse into the Langlands Program III - Ana Caraiani Institute for Advanced Study 2024-05-23 | 2024 Program for Women+ and MathematicsTopic: A Glimpse into the Langlands Program IIISpeaker: Ana CaraianiAffiliation: Imperial College, LondonDate: May 23, 2024The goal of this lecture series is to give you a glimpse into the Langlands program, a central topic at the intersection of algebraic number theory, algebraic geometry and representation theory. In the first lecture, we will look at a celebrated instance of the Langlands correspondence, namely the modularity of elliptic curves. I will try to give you a sense of the different meanings of modularity and of the multitude of ingredients that go into establishing such a result. In the following lectures, I will focus on the more geometric ingredients, first in the special case of the modular curve and then for higher-dimensional Shimura varieties.
Deligne-Lusztig theory: examples and applications III - Charlotte Chan Institute for Advanced Study 2024-05-23 | 2024 Program for Women and Mathematics9:30am|Simonyi Hall 101Topic: Deligne-Lusztig theory: examples and applications IIISpeaker: Charlotte ChanAffiliation: University of MichiganDate: May 23, 2024Geometry and representation theory are intertwined in deep and foundational ways. One of the most important instances of this relationship was uncovered in the 1970s by Deligne and Lusztig: the representation theory of matrix groups over finite fields is encoded in the geometry of a natural "partition" of flag varieties. Recent developments have revealed rich connections between Deligne-Lusztig varieties and geometry studied in number-theoretic contexts. In this lecture series, we give an example-based tour of these ideas, focusing on how to extract concrete information from theory.
The Power of Song: Creation, Embodiment, Effect with Joyce DiDonato | Institute for Advanced Study Institute for Advanced Study 2024-05-21 | On Friday, May 3, 2024, world-renowned mezzo-soprano Joyce DiDonato returned to the Institute for Advanced Study for a second Director’s Conversation with Director and Leon Levy Professor David Nirenberg.Their dialogue touched on topics ranging from female authors in opera to the future of the arts. They also discussed DiDonato’s recent visit to the site of ancient Olympia with her “Eden” project, where she created a film slated for release at the Paris 2024 Summer Olympics.As part of the Conversation, DiDonato conducted a master class with rising soprano Jeysla Rosario Santos and collaborative artist Justina Lee. The program concluded with an audience Q&A.The clip of DiDonato performing the role of Sister Helen Prejean in the opera Dead Man Walking, which was screened during the Conversation and taken from an early rehearsal at the Metropolitan Opera, can be viewed here: youtube.com/watch?v=0PQM9kte6QAWolfensohn Hall, Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ May 3, 2024
A Glimpse into the Langlands Program II - Ana Caraiani Institute for Advanced Study 2024-05-21 | 2024 Program for Women+ and MathematicsTopic: A Glimpse into the Langlands Program IISpeaker: Ana CaraianiAffiliation: Imperial College, LondonDate: May 21, 2024The goal of this lecture series is to give you a glimpse into the Langlands program, a central topic at the intersection of algebraic number theory, algebraic geometry and representation theory. In the first lecture, we will look at a celebrated instance of the Langlands correspondence, namely the modularity of elliptic curves. I will try to give you a sense of the different meanings of modularity and of the multitude of ingredients that go into establishing such a result. In the following lectures, I will focus on the more geometric ingredients, first in the special case of the modular curve and then for higher-dimensional Shimura varieties.
Deligne-Lusztig theory: examples and applications II - Charlotte Chan Institute for Advanced Study 2024-05-21 | 2024 Program for Women and MathematicsTopic: Deligne-Lusztig theory: examples and applications IISpeaker: Charlotte ChanAffiliation: University of MichiganDate: May 21, 2024Geometry and representation theory are intertwined in deep and foundational ways. One of the most important instances of this relationship was uncovered in the 1970s by Deligne and Lusztig: the representation theory of matrix groups over finite fields is encoded in the geometry of a natural "partition" of flag varieties. Recent developments have revealed rich connections between Deligne-Lusztig varieties and geometry studied in number-theoretic contexts. In this lecture series, we give an example-based tour of these ideas, focusing on how to extract concrete information from theory.
A Glimpse into the Langlands Program - Ana Caraiani Institute for Advanced Study 2024-05-20 | 2024 Program for Women+ and MathematicsTopic: A Glimpse into the Langlands ProgramSpeaker: Ana CaraianiAffiliation: Imperial College, LondonDate: May 20, 2024The goal of this lecture series is to give you a glimpse into the Langlands program, a central topic at the intersection of algebraic number theory, algebraic geometry and representation theory. In the first lecture, we will look at a celebrated instance of the Langlands correspondence, namely the modularity of elliptic curves. I will try to give you a sense of the different meanings of modularity and of the multitude of ingredients that go into establishing such a result. In the following lectures, I will focus on the more geometric ingredients, first in the special case of the modular curve and then for higher-dimensional Shimura varieties.
Deligne-Lusztig theory: examples and applications - Charlotte Chan Institute for Advanced Study 2024-05-20 | 2024 Program for Women and MathematicsTopic: Deligne-Lusztig theory: examples and applicationsSpeaker: Charlotte ChanAffiliation: University of MichiganDate: May 20, 2024Geometry and representation theory are intertwined in deep and foundational ways. One of the most important instances of this relationship was uncovered in the 1970s by Deligne and Lusztig: the representation theory of matrix groups over finite fields is encoded in the geometry of a natural "partition" of flag varieties. Recent developments have revealed rich connections between Deligne-Lusztig varieties and geometry studied in number-theoretic contexts. In this lecture series, we give an example-based tour of these ideas, focusing on how to extract concrete information from theory.
Bordism of Flow Modules and Exact Lagrangians - Ivan SmithJoint Institute for Advanced Study 2024-05-17 | Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar9:15am|Remote AccessTopic: Bordism of Flow Modules and Exact LagrangiansSpeaker: Ivan SmithAffiliation: University of CambridgeDate: May 17, 2024We discuss constraints on exact Lagrangian embeddings obtained from considering bordism classes of flow modules over Lagrangian Floer flow categories. This talk reports on joint work with Noah Porcelli.
Paths to Math: Karen Uhlenbeck | Institute for Advanced Study Institute for Advanced Study 2024-05-15 | The Institute for Advanced Study’s “Paths to Math” series comes to a close with a special edition video featuring one of our most beloved veteran mathematicians: Distinguished Visiting Professor Karen Uhlenbeck.Watch to see Uhlenbeck, the first woman to win the Abel Prize, chart her career from her undergraduate days, when an introduction to calculus course awakened her love for mathematics, to the spirited female colleagues that she worked alongside at the University of Illinois Chicago, who helped to dispel any lingering doubts about being a woman in math.Karen also introduces her abundant fields of interest within mathematics, which include the calculus of variations, dispersive equations, and integrable systems, as well as the questions that continue to intrigue her today.“Paths to Math” chronicles the academic journeys of individual scholars from the Institute for Advanced Study, highlighting the moments that ignited their passion for math. With each unique story, this series celebrates the universality of mathematics and the inclusive community of practitioners at IAS, spanning a deep array of backgrounds, interests, geography, ethnicity, and gender.“Paths to Math” is produced by OFC (ofc.tv)
Resolution of the Kohayakawa Kreuter Conjecture - Raphael Steiner Institute for Advanced Study 2024-05-14 | Computer Science/Discrete Mathematics Seminar IITopic: Resolution of the Kohayakawa--Kreuter ConjectureSpeaker: Raphael SteinerAffiliation: ETH ZürichDate: May 14, 2024A graph G is said to be Ramsey for a tuple of graphs (H1,...,Hr) if every r-coloring of the edges of G contains a monochromatic copy of Hi in color i, for some i. A fundamental question at the intersection of Ramsey theory and the theory of random graphs is to determine the threshold at which the binomial random graph Gn,p becomes a.a.s. Ramsey for a fixed tuple (H1,...,Hr), and a famous conjecture of Kohayakawa and Kreuter predicts this threshold. Earlier work of Mousset-Nenadov-Samotij, Bowtell-Hancock-Hyde, and Kuperwasser-Samotij-Wigderson has reduced this probabilistic problem to a deterministic graph decomposition conjecture.In this talk, I will discuss history and background of this problem and sketch our recent proof (joint with M. Christoph, A. Martinsson, Y. Wigderson) that the deterministic graph decomposition conjecture is true, thus resolving the Kohayakawa-Kreuter conjecture.
Quantum Mechanics, Semidefinite Programming, and Graph Invariants - Matthew Hastings Institute for Advanced Study 2024-05-13 | Computer Science/Discrete Mathematics Seminar ITopic: Quantum Mechanics, Semidefinite Programming, and Graph InvariantsSpeaker: Matthew HastingsAffiliation: Microsoft ResearchDate: May 13, 2024The central problem of physics and quantum chemistry is to find the ground state energy of some physical system governed by quantum mechanics. In mathematical terms, this means finding the lowest eigenvalue of some linear operator on a vector space with a tensor product structure. Since the dimension of the vector space grows exponentially with the size of the physical system, the problem quickly becomes computationally intractable. Semidefinite programming methods are one interesting way of approximating the solution. Even these methods can become computationally difficult as the order of the semidefinite program increases, but low order methods can provide useful information. I will review some of these methods, and give some positive and negative results showing their power and limitations on various physical systems. Finally, I will explain an interesting new graph invariant suggested by these methods and give some preliminary results on that invariant.
Supersymmetric Approach to the Analysis of Random Band Matrices - Mariya Shcherbina Institute for Advanced Study 2024-05-13 | Analysis and Mathematical PhysicsTopic: Supersymmetric Approach to the Analysis of Random Band MatricesSpeaker: Mariya ShcherbinaAffiliation: Institute for Advanced StudyDate: May 10, 2024We discuss an application of the SUSY approach to the analysis of spectral characteristics of hermitian and non hermitian random band matrices. In 1D case the obtained integral representations for correlation functions of characteristic polynomials allow to analyze the mechanism of phase transition between “localized” and “delocalized” spectral behavior.
Dance: Past, Present, and Future with Jennifer Homans and Tamara Rojo | Institute for Advanced Study Institute for Advanced Study 2024-05-10 | On Friday, April 26, 2024, the Institute for Advanced Study’s Director and Leon Levy Professor David Nirenberg was joined by dance historian Jennifer Homans and Tamara Rojo, Artistic Director of the San Francisco Ballet, for a conversation on the place and practice of dance in the past, present, and future of our arts and culture.Nirenberg, Homans, and Rojo discussed the relationship that ballet has with its canon, how the present moment is shaping the evolution and animation of new dance forms, and how artificial intelligence can be used as a partner when composing ballets. They also considered the commonalities that might be found between ballet and IAS: both the discipline and the Institute push the boundaries of their respective practices, propelling the next generation of dancers and scholars forward.The clip of NYC Ballet’s presentation of George Balanchine's Agon, screened as part of the Conversation, can be viewed here: youtube.com/watch?v=qjhF5x9To6A Wolfensohn Hall, Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ April 26, 2024
Algebra of the Infrared with Twisted Masses - Ahsan Z Khan Institute for Advanced Study 2024-05-10 | IAS High Energy Theory SeminarTopic: Algebra of the Infrared with Twisted MassesSpeaker: Ahsan Z KhanAffiliation: Institute for Advanced StudyDate: May 10, 2024 The Gaiotto-Moore-Witten "Algebra of the Infrared" allows one to construct the category of supersymmetric boundary conditions for a wide class of massive N=(2,2) QFTs in two dimensions. In particular, it applies to N=(2,2) QFTs defined by a Morse superpotential W. However, the formalism breaks down if we consider an N=(2,2) QFT with a non-trivial twisted mass, or if the one-form dW is not globally exact and has a non-trivial period. Many of the N=(2,2) QFTs of interest are exactly of this type. In this talk I will show how one can generalize the GMW framework to include such models, illustrating the basic idea in a simple toy model.
Invariant Sets and Hyperbolic Periodic Orbits - Viktor Ginzburg Institute for Advanced Study 2024-05-10 | Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar9:15am|Remote AccessTopic: Invariant Sets and Hyperbolic Periodic OrbitsSpeaker: Viktor GinzburgAffiliation: University of California Santa CruzDate: May 10, 2024The presence of hyperbolic periodic orbits or invariant sets often has an affect on the global behavior of a dynamical system. In this talk we discuss two theorems along the lines of this phenomenon, extending some properties of Hamiltonian diffeomorphisms to dynamically convex Reeb flows on the sphere in all dimensions. The first one, complementing other multiplicity results for Reeb flows, is that the existence of a hyperbolic periodic orbit forces the flow to have infinitely many periodic orbits. This result can be thought of as a step towards Franks’ theorem for Reeb flows. The second result is a contact analogue of the higher-dimensional Le Calvez-Yoccoz theorem proved by the speaker and Gurel and asserting that no periodic orbit of a Hamiltonian pseudo-rotation is locally maximal. The talk is based on a joint work with Erman Cineli, Basak Gurel and Marco Mazzucchelli.
Derived Hecke Action For Weight One Modular Forms Via Classicality - Gyujin Oh Institute for Advanced Study 2024-05-10 | Joint PU/IAS Number TheoryTopic: Derived Hecke Action For Weight One Modular Forms Via ClassicalitySpeaker: Gyujin OhAffiliation: Columbia UniversityDate: May 9, 2024Simonyi 101It is known that a p-adic family of modular forms does not necessarily specialize into a classical modular form at weight one, unlike the modular forms of weight 2 or higher. We will explain how this obstruction to classicality leads to a "derived" action on modular forms of weight one, which can be understood as the so-called derived Hecke operator at p. We will also investigate the role of the derived action in the study of p-adic periods of the adjoint of the weight one modular forms.
The Geometric Langlands Conjecture - Sam Raskin Institute for Advanced Study 2024-05-07 | Joint IAS/Princeton Arithmetic Geometry SeminarTopic: The Geometric Langlands ConjectureSpeaker: Sam RaskinAffiliation: Yale UniversityDate: May 06, 2024 I will describe the main ideas that go into the proof of the (unramified, global) geometric Langlands conjecture. All of this work is joint with Gaitsgory and some parts are joint with Arinkin, Beraldo, Chen, Faergeman, Lin, and Rozenblyum. I will also describe recent work on understanding the structure of Hecke eigensheaves (where the attributions are varied and too complicated for an abstract).
Symplectic Aspects of the Hilbert-Smith Conjecture and p-adic Actions - Egor Shelukhin Institute for Advanced Study 2024-05-06 | Symplectic Geometry SeminarTopic: Symplectic Aspects of the Hilbert-Smith Conjecture and p-adic ActionsSpeaker: Egor ShelukhinAffiliation: University of MontrealDate: May 06, 2024 I will discuss a recent proof of new cases of the Hilbert-Smith conjecture for actions by homeomorphisms of symplectic nature. In particular, it rules out faithful actions of the additive p-adic group in this setting and provides further obstructions to group actions in symplectic topology. The proof relies on a new approach to this circle of questions combined with power operations in Floer cohomology and quantitative symplectic topology.
Rounding Large Independent Sets on Expanders - Tim Hsieh Institute for Advanced Study 2024-05-06 | Computer Science/Discrete Mathematics Seminar ITopic: Rounding Large Independent Sets on ExpandersSpeaker: Tim HsiehAffiliation: Carnegie Mellon UniversityDate: May 06, 2024 In this talk, we will present a new approach for approximating large independent sets when the input graph is a one-sided expander—that is, the uniform random walk matrix of the graph has second eigenvalue bounded away from 1. Specifically, we show a polynomial time algorithm that can find linear-sized independent sets in one-sided expanders that are almost 3-colorable or promised to contain a 0.499n-sized independent set.All prior algorithms that beat the worst-case guarantees for the problem rely on bottom eigenspace enumeration techniques, which build on a classical work of Alon and Kahale and require two-sided expansion (i.e., bounded number of negative eigenvalues of magnitude close to 1). Such techniques provably fail in our setting because in contrast to bottom eigenspace enumeration that naturally extends to k-colorable graphs for any fixed constant k, we observe that finding linear-sized independent sets in almost 4-colorable expanding graphs (as opposed to almost 3-colorable graphs in our algorithmic result above) is NP-hard assuming the Unique Games Conjecture.Our algorithms rely on a new framework for rounding sum-of-squares relaxations of the independent set problem based on a combinatorial approximate packing property—in any graph that satisfies one-sided spectral expansion (in fact, a weaker vertex expansion property suffices), the total number of large independent sets with small pairwise intersections is small.Based on joint work with Mitali Bafna and Pravesh K. Kothari.Hsieh-2024-05-06
Symplectic Structures from Almost Symplectic Structures - Agustin Moreno Institute for Advanced Study 2024-05-03 | Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry ZoominarTopic: Symplectic Structures from Almost Symplectic StructuresSpeaker: Agustin MorenoAffiliation: Heidelberg UniversityDate: May 03, 2024In this talk, we will consider a stabilized version of the fundamental existence problem of symplectic structures (cf. Open Problem 1 in McDuff & Salamon). Given a formal symplectic manifold, i.e. a closed manifold M with a non-degenerate 2-form and a non-degenerate second cohomology class, we investigate when its natural stabilization to M × T2 can be realized by a symplectic form.We show that this can be done whenever the formal symplectic manifold admits a positive symplectic divisor. It follows that if a formal symplectic 4-manifold, which either satisfies that its positive/negative second betti numbers are both at least 2, or that is simply connected, then M × T2 is symplectic.This is joint work with Fabio Gironella, Fran Presas, Lauran Touissant.
Testing Galaxy Formation Models with Large-scale Surveys of the Milky Way.... - Emily Cunningham Institute for Advanced Study 2024-05-02 | Institute for Advanced Study Astrophysics SeminarTopic: Testing Galaxy Formation Models with Large-scale Surveys of the Milky Way Stellar HaloSpeaker: Emily CunninghamAffiliation: Columbia UniversityDate: May 2, 2024While the vast majority of the light from our galaxy comes from the Galactic disk, the vast majority of the mass of the Milky Way (MW) is in its dark matter halo. Because we cannot directly observe the MW's dark matter halo, we must use luminous tracer populations (i.e., stars) to study the mass distribution indirectly. Fortunately, there are stars strewn throughout the MW's dark matter halo. We believe the MW built up its halo of dark matter over cosmic time by consuming smaller dwarf galaxies; the remnants of these dwarf galaxies make up the MW's stellar halo. Halo stars can therefore be used both to constrain the dark matter distribution of the MW as well as inform us about the dwarf galaxies in which they formed. I will present my ongoing theoretical and observational work using halo stars to map the dark matter distribution and disequilibrium in the MW, as well as study the faint, low-mass galaxies that were consumed by the MW during its formation. I will discuss the crucial roles of current and upcoming large-scale surveys of the MW halo (such as the Rubin Observatory Legacy Survey of Space and Time) for addressing fundamental questions in galaxy formation.
Incidence Bounds via Extremal Graph Theory - Istvan Tomon Institute for Advanced Study 2024-04-30 | Computer Science/Discrete Mathematics Seminar IITopic: Incidence Bounds via Extremal Graph TheorySpeaker: Istvan TomonAffiliation: Umeå UniversityDate: April 30, 2024 A cornerstone result in geometry is the Szemerédi–Trotter theorem, which gives a sharp bound on the maximum number of incidences between m points and n lines in the real plane. A natural generalization of this is to consider point-hyperplane incidences in higher dimensions. As proposed by Chazelle in the 90's, we are interested in the maximum number of incidences between m points and n hyperplanes, assuming no s points lie in the intersection of s hyperplanes. The latter condition is needed to avoid trivialities, like all hyperplanes intersecting in a line, and all points contained in this line. Starting from dimension 3, matching lower and upper bounds are no longer known for this problem. I will talk about how to prove sharp bounds over arbitrary fields using methods from extremal graph theory, and discuss analogues of this problem concerning point-variety incidences and unit distance graphs.Based on a joint work with Aleksa Milojević and Benny Sudakov.
Triangulated Surfaces in Moduli Space - Sahana Vasudevan Institute for Advanced Study 2024-04-29 | Members' ColloquiumTopic: Triangulated Surfaces in Moduli SpaceSpeaker: Sahana VasudevanAffiliation: Institute for Advanced StudyDate: April 29, 2024 Triangulated surfaces are Riemann surfaces formed by gluing together equilateral triangles. They are also the Riemann surfaces defined over the algebraic numbers. Brooks, Makover, Mirzakhani and many others proved results about the geometric properties of random large genus triangulated surfaces, and similar results about the geometric properties of random large genus hyperbolic surfaces. These results motivated the question: how are triangulated surfaces distributed in the moduli space of Riemann surfaces, quantitatively? I will talk about results related to this question.
Lower Bounds for Set-Multilinear Branching Programs - Shubhangi Saraf Institute for Advanced Study 2024-04-29 | Computer Science/Discrete Mathematics Seminar ITopic: Lower Bounds for Set-Multilinear Branching ProgramsSpeaker: Shubhangi SarafAffiliation: University of TorontoDate: April 29, 2024In this talk, I will discuss lower bounds for a certain set-multilinear restriction of algebraic branching programs. The significance of the lower bound and the model is underscored by the recent work of Bhargav, Dwivedi, and Saxena (2023), which showed that super-polynomial lower bounds for the model of sum of ordered set multilinear ABPs -- when the underlying polynomial of sufficiently low degree -- would imply super-polynomial lower bounds against general ABPs, thereby resolving Valiant's longstanding conjecture that the permanent polynomial cannot be computed efficiently by ABPs. We will discuss a recent result which "almost" meets this low-degree demand.This is based on joint work with Prerona Chatterjee, Deepanshu Kush and Amir Shpilka.
Aspects of Topological Symmetry, Holography, and Branes - Ibrahima Bah Institute for Advanced Study 2024-04-26 | IAS High Energy Theory SeminarTopic: Aspects of Topological Symmetry, Holography, and BranesSpeaker: Ibrahima BahAffiliation: Johns Hopkins UniversityDate: April 26, 2024In this talk I will discuss holographic duals of topological operators. At low energy sugra, they can be realized by Page charge associated to Gauss law constraints. In the UV string theory, topological operators can be characterized by various brane configurations. This provides a way of exploring generalized symmetries with dynamical bulk physics.
Micromirror confinement of sub-TeV cosmic rays in galaxy clusters - Patrick Reichherzer Institute for Advanced Study 2024-04-25 | Institute for Advanced Study Astrophysics SeminarTopic: Micromirror confinement of sub-TeV cosmic rays in galaxy clustersSpeaker: Patrick Reichherzer Affiliation: University of OxfordDate: April 25, 2024Recent observations reveal that cosmic rays (CRs) are more tightly confined in various astrophysical systems (e.g. radio bubbles) than current theories predict. I show that microscale magnetic fluctuations, particularly from the mirror instability, significantly influence CR transport. Our theory is supported by simulations of CRs in the intracluster medium (ICM) of galaxy clusters. Our results indicate that sub-TeV CR confinement in the ICM is much more efficient than previously thought based on extrapolating existing Galactic-transport theories.
Random Cayley Graphs From a Combinatorial Perspective - Huy Tuan Pham Institute for Advanced Study 2024-04-23 | Computer Science/Discrete Mathematics Seminar IITopic: Random Cayley Graphs From a Combinatorial PerspectiveSpeaker: Huy Tuan PhamAffiliation: Stanford UniversityDate: April 22, 2024Cayley graphs provide interesting bridges between graph theory, additive combinatorics and group theory. Fixing an ambient finite group, random Cayley graphs are constructed by choosing a generating set at random. These graphs reflect interesting symmetries and properties of the group, at the cost of inducing complex dependencies. I will discuss several results on clique and independence numbers of random Cayley graphs in general groups, progress towards a conjecture of Alon on existence of Ramsey Cayley graphs, and a proof of a conjecture of Alon and Orlitsky. These questions are naturally connected with some fundamental problems in additive combinatorics. Surprisingly, our insights suggest that in many of these problems, the group structure is superfluous and can be replaced by much more general combinatorial structures. I will discuss the main general combinatorial models and ideas behind these results. I will also discuss how they relate to the additive combinatorial corollaries discussed in Monday’s talk. Based on joint work with David Conlon, Jacob Fox and Liana Yepremyan.
Algebraic K-Theory and P-Adic Arithmetic Geometry - Matthew Morrow Institute for Advanced Study 2024-04-23 | Members' ColloquiumTopic: Algebraic K-Theory and P-Adic Arithmetic GeometrySpeaker: Matthew MorrowAffiliation: Institute for Advanced StudyDate: April 22, 2024To any unital, associative ring R one may associate a family of invariants known as its algebraic K-groups. Although they are essentially constructed out of simple linear algebra data over the ring, they see an extraordinary range of information: depending on the ring, its K-groups can be related to zeta functions, corbordisms, algebraic cycles and the Hodge conjecture, elliptic operators, Grothendieck's theory of motives, and so on.Our understanding of algebraic K-groups, at least as far as they appear in algebraic and arithmetic geometry, has rapidly improved in the past few years. This talk will present some of the fundamentals of the subject and explain why K-groups are related to the ongoing special year in p-adic Arithmetic Geometry. The intended audience is non-specialists
“Unnecessary” Quantum Critical Points in Condensed Matter and Field Theory - Senthil Todadri Institute for Advanced Study 2024-04-22 | IAS High Energy Theory SeminarTopic: “Unnecessary” Quantum Critical Points in Condensed Matter and Field TheorySpeaker: Senthil TodadriAffiliation: Massachusetts Institute of TechnologyDate: April 22, 2024Quantum critical points usually separate two distinct phases of matter. Here I will discuss a class of "unnecessary" quantum critical points that lie within a single phase of matter (much like the liquid-gas transition, except that they are continuous) so that there is a path that avoids them. First found in critical non-abelian gauge theories, there are by now a number of simpler examples of such quantum critical points. In this talk, I will focus on the conformal fixed point of massless QED3. I will show that this theory describes an unnecessary quantum critical point living inside the most familiar Neel antiferromagnetic phase of spin-1/2 square lattice magnets.
Big Fiber Theorems, Ideal-Valued Measures, and Symplectic Topology - Leonid Polterovich Institute for Advanced Study 2024-04-22 | Symplectic Geometry SeminarTopic: Big Fiber Theorems, Ideal-Valued Measures, and Symplectic TopologySpeaker: Leonid PolterovichAffiliation: Tel Aviv UniversityDate: April 22, 2024I will discuss an adaptation of Gromov's ideal-valued measures to symplectic topology. It leads to a unified viewpoint at three "big fiber theorems": the Centerpoint Theorem in combinatorial geometry, the Maximal Fiber Inequality in topology, and the Non-displaceable Fiber Theorem in symplectic topology, and yields applications to symplectic rigidity. Joint work with Adi Dickstein, Yaniv Ganor, and Frol Zapolsky.
Additive Combinatorics Without Groups - Huy Tuan Pham Institute for Advanced Study 2024-04-22 | Computer Science/Discrete Mathematics Seminar ITopic: Additive Combinatorics Without GroupsSpeaker: Huy Tuan PhamAffiliation: Stanford UniversityDate: April 22, 2024Subsets A of an abelian group with a small doubling |A+A|/|A| have been extensively studied, and results of Freiman, Ruzsa and Green give fundamental structural descriptions of such sets. These have important applications across combinatorics and computer science, and have motivated the development of a number of influential techniques. In this talk, I will discuss a new combinatorial approach to several problems involving sets with small doubling. Over abelian groups where all elements have order at most r, the Freiman-Ruzsa theorem says that a set A with |A+A|≤K|A| is contained in a subgroup of size at most Or,K(|A|), and Ruzsa conjectured a tight dependence on K. In the first application, I will discuss a short complete resolution of Ruzsa’s conjecture. In the second application, we show that random functions give good sumset extractors in general (possibly nonabelian) groups. Surprisingly, our approach is crucially motivated by purely combinatorial graph-theoretic insights, where we find that the group structure is superfluous and can be replaced by much more general combinatorial structures. In particular, I will describe a further corollary, which is a combinatorial generalization of the Freiman-Ruzsa theorem over 𝔽n2. Based on joint work with David Conlon, Jacob Fox and Liana Yepremyan.
An Energy Model for Harmonic Graphs with Junctions - Ovidiu Savin Institute for Advanced Study 2024-04-19 | Joint IAS/PU Analysis SeminarTopic: An Energy Model for Harmonic Graphs with JunctionsSpeaker: Ovidiu SavinAffiliation: Columbia UniversityDate: April 19, 2024We consider an energy model for N ordered elastic membranes subject to forcing and boundary conditions. The heights of the membranes are described by real functions u_1, u_2,...,u_N, which minimize an energy functional involving the Dirichlet integral and a potential term depending on the cardinality of the set {u_1,..,u_N}. The potential term corresponds to the physical situation when consecutive membranes are glued to each other on their coincidence set. The problem can be understood as a system of N-1 coupled one-phase free boundary problems with interacting free boundaries. I will review the known results in the scalar case, and discuss the free boundary regularity when dealing with 3 or more membranes (joint with D. De Silva.)
Generalized Cylinder Limits of Ricci Flow Singularities - Natasa Sesum Institute for Advanced Study 2024-04-19 | Joint IAS/PU Analysis SeminarTopic: Generalized Cylinder Limits of Ricci Flow SingularitiesSpeaker: Natasa SesumAffiliation: Rutgers UniversityDate: April 19, 2024We study multiply warped product geometries MN:=Bn×Fn1×···×FnA g = g_B + \sum_{a=1}^A v_a^2 g_{F^{n_a}} and show that for an open set of initial data within multiply warped product geometries the Ricci flow starting at any of those develops generalized cylinder as singularity model. More precisely, for any p and q we construct an open set of initial data within multiply warped product geometris whose Ricci flows develop S^p\times R^q as a singularity model.
Equinox Jukebox: A Retrospective Concert by Derek Bermel | Institute for Advanced Study Institute for Advanced Study 2024-04-19 | On March 21, 2024, Derek Bermel, thrice-Grammy-nominated composer and clarinetist and past IAS Artist-in-Residence (2009–13), returned to the Institute to perform this spring-forward retrospective, celebrating three generations of American concert music.Bermel was joined on the stage of Wolfensohn Hall by the award-winning Jasper String Quartet and pianist Steven Beck (NY Philharmonic/Talea Ensemble). They played music by Derek Bermel, Paquito D'Rivera, and Leonard Bernstein.Prior to the performance, Bermel engaged in conversation with Helmut Hofer, Hermann Weyl Professor in the Institute’s School of Mathematics. Bermel and Hofer reflected on Bermel’s journey into a career in music, his fascination with astrophysics, and his time as IAS Artist-in-Residence, which saw him collaborate with Nima Arkani-Hamed, Professor in the School of Natural Sciences, on a musical composition.The program was introduced by IAS Director and Leon Levy Professor David Nirenberg.Wolfensohn Hall, Institute for Advanced Study, 1 Einstein Drive, Princeton, N.J. March 21, 2024
From Gromov–Witten Theory to the Closing Lemma - Shira Tanny Institute for Advanced Study 2024-04-19 | Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry ZoominarTopic: From Gromov–Witten Theory to the Closing LemmaSpeaker: Shira TannyAffiliation: Institute for Advanced StudyDate: April 19, 2024An old question of Poincaré concerns creating periodic orbits via perturbations of a flow/diffeomorphism. While pseudoholomorphic methods have successfully addressed this question in dimensions 2-3, the higher-dimensional case remains less understood. I will describe a connection between this question and Gromov–Witten invariants, which goes through a new class of invariants of symplectic cobordisms. This is a joint work with Julian Chaidez.
Margrethe Vestager: Three things Oppenheimer tells us about tech | Institute for Advanced Study Institute for Advanced Study 2024-04-19 | On Tuesday, April 9, 2024, Margrethe Vestager, the Executive Vice President of the European Commission for A Europe Fit for the Digital Age and a leading global voice on technology policy and equitable innovation, delivered the annual IAS Public Policy Lecture.The lecture, entitled "'This isn't a new weapon, it is a new world'—three things Oppenheimer tells us about tech," focused on lessons that can be drawn from the life and legacy of past IAS Director J. Robert Oppenheimer (1947–66). The topics covered included platform regulation, artificial intelligence, and economic security.Vestager concluded by shining a light on J. Robert Oppenheimer’s characteristic cross-disciplinary approach, exemplified at the Institute for Advanced Study when he hosted artists such as T.S. Eliot and invited historians such as George F. Kennan to join as Members.The Executive Vice President was introduced by Alondra Nelson, Harold F. Linder Professor in the Institute’s School of Social Science. Nelson also led a Q&A after the lecture.Wolfensohn Hall, Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ April 9, 2024
From Text to Song: Schubert as Translator | Institute for Advanced Study Institute for Advanced Study 2024-04-19 | This Spring, the Institute for Advanced Study welcomed Brian Zeger, world-renowned pianist and Artistic Director of Vocal Arts at Juilliard, and distinguished Juilliard bass-baritone Jared Werlein to the stage of Wolfensohn Hall. In this video, Zeger and Werlein demonstrate musical translation from poem to performance using the works of the great Austrian composer Franz Schubert. Zeger provides insightful commentary on how Schubert transformed two poems into musical structures. The first composition, “Im Frühling” (“In Spring”), based on a poem written by Ernst Schulze, speaks of a remembered love. Zeger outlines how Schubert uses harmonic modulation to convey both the ethereal, elevated memory of the poet being in the company of his beloved and the yearning that he experiences in the present, wanting to enter back into this past world. Next, Zeger and Werlein perform “Die Krähe” (“The Crow”), the fifteenth of twenty-four songs in Schubert’s “Winterreise” (“Winter Journey”) cycle, based on the poetry of Wilhelm Müller. In “The Crow,” the bird follows the narrator on his journey. Zeger explores how Schubert conveys the protagonist’s mental state through a keen use of both vocal and pianistic registers, subtle harmonic details, and an alert sense of poetic prosody. The program was introduced by IAS Director and Leon Levy Professor David Nirenberg. Wolfensohn Hall, Institute for Advanced Study, 1 Einstein Drive, Princeton, N.J. March 14, 2023
Zeta and Multizeta for Function Fields - Dinesh Thakur Institute for Advanced Study 2024-04-19 | Joint PU/IAS Number Theory4:30pm|Simonyi 101 and Remote AccessTopic: Zeta and Multizeta for Function FieldsSpeaker: Dinesh ThakurAffiliation: University of RochesterDate: April 18, 2024We will describe emerging understanding of the structures related to the arithmetic of Zeta and Multizeta values for function fields through various results and conjectures.
Decoding Supernova Remnants - Abigail Polin Institute for Advanced Study 2024-04-18 | Institute for Advanced Study Astrophysics SeminarTopic: Decoding Supernova RemnantsSpeaker: Abigail Polin Affiliation: Purdue UniversityDate: April 18, 2024I will discuss a new method for analyzing the morphology of supernova remnants (SNRs) by using power specula analysis to diagnose the drivers responsible for structure at different angular scales. Using a suite of hydrodynamic models of the Rayleigh–Taylor instability (RTI) as a supernova (SN) collides with its surrounding medium we demonstrate how power spectral analysis can be used to attribute which scales in an SNR are driven by RTI and which must be caused by intrinsic asymmetries in the initial explosion. We predict the power spectrum of turbulence driven by RTI and identify a dominant angular mode that represents the largest scale that efficiently grows via RTI. I will discuss the implications of this work as well as our ongoing and future plans to use this methodology; comparing increasingly detailed SN models directly to observed remnant data.
Paths to Math: Paul Minter | Institute for Advanced Study Institute for Advanced Study 2024-04-18 | This installment of the “Paths to Math” series features Paul Minter, Veblen Research Instructor (2022–23) and Veblen Fellow (2023–27) in the Institute’s School of Mathematics. Paul works on geometric analysis and geometric measure theory.Watch to see Paul outline the minimization principles that are integral for his research, which are exemplified by soap bubbles. He also describes how, despite being discouraged from applying to an elite school, his passion for mathematics brought him from a small U.K. seaside town, to Cambridge University, and then to IAS. Finally, Paul offers his advice to those wanting to pursue a career in mathematics.“Paths to Math” chronicles the academic journeys of individual scholars from the Institute for Advanced Study, highlighting the moments that ignited their passion for math. With each unique story, this series celebrates the universality of mathematics and the inclusive community of practitioners at IAS, spanning a deep array of backgrounds, interests, geography, ethnicity, and gender.“Paths to Math” is produced by OFC (ofc.tv)
Parallel Repetition for 3-Player XOR Games - Yang Liu Institute for Advanced Study 2024-04-16 | Computer Science/Discrete Mathematics Seminar IITopic: Parallel Repetition for 3-Player XOR GamesSpeaker: Yang LiuAffiliation: Institute for Advanced StudyDate: April 16, 2024In a 3-𝖷𝖮𝖱 game , the verifier samples a challenge (x,y,z)∼μ where μ is a probability distribution over Σ×Γ×Φ, and a map t:Σ×Γ×Φ→ for a finite Abelian group defining a constraint. The verifier sends the questions x, y and z to the players Alice, Bob and Charlie respectively, receives answers f(x), g(y) and h(z) that are elements in and accepts if f(x)+g(y)+h(z)=t(x,y,z). The value, 𝗏𝖺𝗅(), of the game is defined to be the maximum probability the verifier accepts over all players' strategies.We show that if is a 3-𝖷𝖮𝖱 game with value strictly less than 1, whose underlying distribution over questions μ does not admit Abelian embeddings into (ℤ,+), then the value of the n-fold repetition of is exponentially decaying. That is, there exists c=c() greater than 0 such that 𝗏𝖺𝗅(⊗n) less than or equal to 2−cn. This extends a previous result of [Braverman-Khot-Minzer, FOCS 2023] showing exponential decay for the GHZ game. Our proof combines tools from additive combinatorics and tools from discrete Fourier analysis.Based on joint work with Amey Bhangale, Mark Braverman, Subhash Khot, Dor Minzer.
Staggered Bosons, Kahler Dirac Bosons and Supersymmetry on the Lattice - David Berenstein Institute for Advanced Study 2024-04-16 | IAS High Energy Theory SeminarTopic: Staggered Bosons, Kahler Dirac Bosons and Supersymmetry on the LatticeSpeaker: David BerensteinAffiliation: University of California, Santa BarbaraDate: April 15, 2024I will describe constructions of lattice field theories that assign a single bosonic variable to each site, rather a conjugate pair x,p. The information to realize a non-trivial dynamics is realized by non-trivial Poisson brackets between nearest neighbors. The construction is similar to staggered fermions in 1+1 dimensions. I will show how this construction readily leads to critical field theories in various dimensions and realizes naturally certain non-invertible symmetries on the lattice fied theory. A more general version can be used on triangulations of manifolds, where the Poisson bracket utilizes the homology chain complex of the triangulation. I will show that when coupled to fermions this construction readiy gives rise to a supersymmetric Hamiltonian where the fermions are realized as Kahler-Dirac fermions.
On Effectivity for Integral Points on Some Curves of Genus 2 - Umberto Zannier Institute for Advanced Study 2024-04-16 | Truth and Beauty: Bombieri's Mathematical GardensTopic: On Effectivity for Integral Points on Some Curves of Genus 2Speaker: Umberto ZannierAffiliation: Scuola Normale SuperioreDate: April 12, 2024 Most effective results for integral points on affine curves use the works of Baker or Bombieri on Diophantine approximation by S-units. Still, no completely general result is known already in genus 2. I will briefly present some recent work with Corvaja and Lombardo, obtaining effectivity for sets of curves of genus 2 which are dense in the moduli space.
Walking Through the Large Sieve - Henryk Iwaniec Institute for Advanced Study 2024-04-16 | Truth and Beauty: Bombieri's Mathematical Gardens4:30pm|Simonyi 101 and Remote AccessTopic: Walking Through the Large SieveSpeaker: Henryk IwaniecAffiliation: Rutgers UniversityDate: April 12, 2024
Some More Gems - Peter Sarnak Institute for Advanced Study 2024-04-16 | Truth and Beauty: Bombieri's Mathematical GardensTopic: Some More GemsSpeaker: Peter SarnakAffiliation: Institute for Advanced StudyDate: April 12, 2024
