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DTSTART;TZID=America/New_York:20240209T120000
DTEND;TZID=America/New_York:20240209T130000
DTSTAMP:20260501T114203
CREATED:20240208T143028Z
LAST-MODIFIED:20240208T143041Z
UID:10000669-1707480000-1707483600@cmsa.fas.harvard.edu
SUMMARY:The spectrum of some nonlinear random matrices
DESCRIPTION:CMSA Member Seminar \nSpeaker: Benjamin McKenna (Harvard) \nTitle: The spectrum of some nonlinear random matrices \nAbstract: Modern data science often requires one to consider “nonlinear random matrices\,” a broad term for random-matrix models whose construction involves a nonlinear function applied entrywise. Such models are typically far from classical random matrix theory\, and in principle entrywise nonlinearities can affect the eigenvalues in a complicated way. However\, recent years have seen a number of results on nonlinear models whose spectrum is surprisingly simple. We give one such result\, emphasizing general random-matrix techniques like free probability and orthogonal polynomials. Joint work with Sofiia Dubova\, Yue M. Lu\, and Horng-Tzer Yau.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-2924/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240202T120000
DTEND;TZID=America/New_York:20240202T130000
DTSTAMP:20260501T114203
CREATED:20240123T192516Z
LAST-MODIFIED:20240201T171531Z
UID:10000667-1706875200-1706878800@cmsa.fas.harvard.edu
SUMMARY:On complete Calabi-Yau metrics and Monge-Ampere equations
DESCRIPTION:CMSA Member Seminar \nSpeaker: Freid Tong (Harvard CMSA) \nTitle: On complete Calabi-Yau metrics and Monge-Ampere equations \nAbstract: Calabi-Yau metrics are central objects in K\”ahler geometry and also string theory. The existence of Calabi-Yau metrics on compact manifolds was answered by Yau in his solution of the Calabi conjecture\, but the situation in the non-compact setting is much more delicate\, and many questions related to the existence and uniqueness of non-compact Calabi-Yau metrics remain unanswered. I will give an introduction to this subject and discuss some ongoing joint work with T. Collins and S.-T. Yau\, on a new relationship between complete Calabi-Yau metrics and a new Monge-Ampere equation.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-2224/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Member-Seminar_2224.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240126T120000
DTEND;TZID=America/New_York:20240126T130000
DTSTAMP:20260501T114203
CREATED:20240102T203315Z
LAST-MODIFIED:20240125T174129Z
UID:10000803-1706270400-1706274000@cmsa.fas.harvard.edu
SUMMARY:Anti-Iitaka conjecture in positive characteristic
DESCRIPTION:CMSA Member Seminar \nSpeaker: Iacopo Brivio (Harvard) \nTitle: Anti-Iitaka conjecture in positive characteristic \nAbstract: Given a smooth projective variety\, its Kodaira dimension kappa(K_X) is an important invariant that measures the rate of growth of m-pluricanonical forms as a function of m. It serves as an higher-dimensional generalization of the genus of a Riemann surface. If f : X –> Y is a fibration with general fiber F\, a famous conjecture of Iitaka predicts the inequality kappa(K_X) \geq kappa(K_Y) + kappa(K_F). More recently it was shown by Chang that\, if the stable base locus of -K_X is vertical\, then the inequality kappa(-K_X) \leq kappa(-K_Y) + kappa(-K_F) holds. Both Iitaka’s conjecture and Chang’s theorem are known to fail in positive characteristic. In this talk I will explain how one can recover Chang’s theorem for a class of “tame” fibrations in characteristic p > 0. This is based on joint work with M. Benozzo and C.-K. Chang.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-12624/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Member-Seminar-01.26.24.docx-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231130T160000
DTEND;TZID=America/New_York:20231130T170000
DTSTAMP:20260501T114203
CREATED:20240223T052452Z
LAST-MODIFIED:20240223T052528Z
UID:10002815-1701360000-1701363600@cmsa.fas.harvard.edu
SUMMARY:A Gaussian convexity for logarithmic moment generating function
DESCRIPTION:Probability Seminar \nSpeaker: Wei-Kuo Chen (University of Minnesota) \nTitle: A Gaussian convexity for logarithmic moment generating function \nAbstract: Convex functions of Gaussian vectors are prominent objectives in many fields of mathematical studies. In this talk\, I will establish a new convexity for the logarithmic moment generating function for this object and draw two consequences. The first leads to the Paouris-Valettas small deviation inequality that arises from the study of convex geometry. The second provides a quantitative bound for the Dotsenko-Franz-Mezard conjecture in the Sherrington-Kirkpatrick mean-field spin glass model\, which states that the logarithmic anneal partition function of negative replica is asymptotically equal to the free energy. \n 
URL:https://cmsa.fas.harvard.edu/event/probability-113023/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-11.30.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231128T120000
DTEND;TZID=America/New_York:20231128T130000
DTSTAMP:20260501T114203
CREATED:20240222T113148Z
LAST-MODIFIED:20240222T113148Z
UID:10002809-1701172800-1701176400@cmsa.fas.harvard.edu
SUMMARY:A random matrix model towards the quantum chaos transition conjecture
DESCRIPTION:Probability Seminar \nSpeaker: Jun Yin (UCLA) \nTitle: A random matrix model towards the quantum chaos transition conjecture \nAbstract: The Quantum Chaos Conjecture has long fascinated researchers\, postulating a critical spectrum phase transition that separates integrable systems from chaotic systems in quantum mechanics. In the realm of integrable systems\, eigenvectors remain localized\, and local eigenvalue statistics follow the Poisson distribution. Conversely\, chaotic systems exhibit delocalized eigenvectors\, with local eigenvalue statistics mirroring the Sine kernel distribution\, akin to the standard random matrix ensembles GOE/GUE. \nThis talk delves into the heart of the Quantum Chaos Conjecture\, presenting a novel approach through the lens of random matrix models. By utilizing these models\, we aim to provide a clear and intuitive demonstration of the same phenomenon\, shedding light on the intricacies of this long-standing conjecture.
URL:https://cmsa.fas.harvard.edu/event/probability-112823/
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Special-Seminar-11.28.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231115T153000
DTEND;TZID=America/New_York:20231115T163000
DTSTAMP:20260501T114203
CREATED:20240223T053940Z
LAST-MODIFIED:20240223T054457Z
UID:10002818-1700062200-1700065800@cmsa.fas.harvard.edu
SUMMARY:Thresholds
DESCRIPTION:Probability Seminar \nSpeaker: Jinyoung Park (NYU) \nTitle: Thresholds \nAbstract: For a finite set X\, a family F of subsets of X is said to be increasing if any set A that contains B in F is also in F. The p-biased product measure of F increases as p increases from 0 to 1\, and often exhibits a drastic change around a specific value\, which is called a “threshold.” Thresholds of increasing families have been of great historical interest and a central focus of the study of random discrete structures (e.g. random graphs and hypergraphs)\, with estimation of thresholds for specific properties the subject of some of the most challenging work in the area. In 2006\, Jeff Kahn and Gil Kalai conjectured that a natural (and often easy to calculate) lower bound q(F) (which we refer to as the “expectation-threshold”) for the threshold is in fact never far from its actual value. A positive answer to this conjecture enables one to narrow down the location of thresholds for any increasing properties in a tiny window. In particular\, this easily implies several previously very difficult results in probabilistic combinatorics such as thresholds for perfect hypergraph matchings (Johansson–Kahn–Vu) and bounded-degree spanning trees (Montgomery). I will present recent progress on this topic. Based on joint work with Keith Frankston\, Jeff Kahn\, Bhargav Narayanan\, and Huy Tuan Pham.
URL:https://cmsa.fas.harvard.edu/event/probability-111523/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-11.15.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231108T153000
DTEND;TZID=America/New_York:20231108T163000
DTSTAMP:20260501T114203
CREATED:20240222T113928Z
LAST-MODIFIED:20240222T113941Z
UID:10002810-1699457400-1699461000@cmsa.fas.harvard.edu
SUMMARY:Fitting ellipsoids to random points
DESCRIPTION:Probability Seminar \nSpeaker: Antoine Maillard (ETH Zürich) \nTitle: Fitting ellipsoids to random points \nAbstract: We consider the problem of exactly fitting an ellipsoid (centered at 0) to n standard Gaussian random vectors in dimension d\, for very large n and d. This problem has connections to questions in statistical learning and theoretical computer science\, and is conjectured to undergo a sharp transition: with high probability\, it has a solution if n < d^2/4\, while it is not satisfiable if n > d^2/4. In this talk we will discuss the origin of this conjecture\, and highlight some recent progress\, in three different directions: \n\nA proof that the problem is feasible for n < d^2 / C\, for some (large) constant C\, significantly improving over previously-known bounds.\nA non-rigorous characterization of the conjecture\, as well as significant generalizations\, using analytical methods of statistical physics.\nA rigorous proof of a satisfiability transition exactly at n = d^2 / 4 in a slightly relaxed version of the problem\, the first rigorous result characterizing the expected phase transition in ellipsoid fitting. The proof is inspired by the non-rigorous characterization discussed above.\n\nThis talk is based on the three manuscripts: arXiv:2307.01181\, arXiv:2310.01169\, arXiv:2310.05787\, which are joint works with A. Bandeira\, Tim Kunisky\, Shahar Mendelson and Elliot Paquette.
URL:https://cmsa.fas.harvard.edu/event/probability-11823/
LOCATION:Virtual
CATEGORIES:Probability Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231102T153000
DTEND;TZID=America/New_York:20231102T163000
DTSTAMP:20260501T114203
CREATED:20240223T113003Z
LAST-MODIFIED:20240223T113003Z
UID:10002865-1698939000-1698942600@cmsa.fas.harvard.edu
SUMMARY:Solving spin systems\, the Babylonian way
DESCRIPTION:Probability Seminar \nSpeaker: Nicola Kistler (Johann Wolfgang Goethe-Universität Frankfurt am Main) \nTitle: Solving spin systems\, the Babylonian way \nAbstract: The replica method\, together with Parisi’s symmetry breaking mechanism\, is an extremely powerful tool to compute the limiting free energy of virtually any mean field disordered system. Unfortunately\, the tool is dramatically flawed from a mathematical point of view. I will discuss a truly elementary procedure which allows to rigorously implement two (out of three) steps of the replica method\, and conclude with some remarks on the relation between this new point of view and old work by Mezard and Virasoro on the microstructure of ultrametricity\, the latter being the fundamental yet unjustified Ansatz in the celebrated Parisi solution. We are still far from a clear understanding of the issues\, but quite astonishingly\, evidence is mounting that Parisi’s ultrametricity assumption\, the onset of scales and the universal hierarchical self-organisation of random systems in the infinite volume limit\, is intimately linked to hidden geometrical properties of large random matrices which satisfy rules reminiscent of the popular SUDOKU game.
URL:https://cmsa.fas.harvard.edu/event/probability-92023/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-09.20.23.docx-1-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231101T153000
DTEND;TZID=America/New_York:20231101T163000
DTSTAMP:20260501T114203
CREATED:20240223T054758Z
LAST-MODIFIED:20240223T054856Z
UID:10002821-1698852600-1698856200@cmsa.fas.harvard.edu
SUMMARY:Universality of max-margin classifiers
DESCRIPTION:Probability Seminar \nSpeaker: Youngtak Sohn (MIT) \nTitle: Universality of max-margin classifiers \nAbstract: Many modern learning methods\, such as deep neural networks\, are so complex that they perfectly fit the training data. Despite this\, they generalize well to the unseen data. Motivated by this phenomenon\, we consider high-dimensional binary classification with linearly separable data. First\, we consider Gaussian covariates and characterize linear classification problems for which the minimum norm interpolating prediction rule\, namely the max-margin classification\, has near-optimal prediction accuracy. Then\, we discuss universality of max-margin classification. In particular\, we characterize the prediction accuracy of the non-linear random features model\, a two-layer neural network with random first layer weights. The spectrum of the kernel random matrices plays a crucial role in the analysis. Finally\, we consider the wide-network limit\, where the number of neurons tends to infinity\, and show how non-linear max-margin classification with random features collapse to a linear classifier with a soft-margin objective. \nJoint work with Andrea Montanari\, Feng Ruan\, Jun Yan\, and Basil Saeed.
URL:https://cmsa.fas.harvard.edu/event/probability-11123/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-11.01.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231025T153000
DTEND;TZID=America/New_York:20231025T163000
DTSTAMP:20260501T114203
CREATED:20240223T055628Z
LAST-MODIFIED:20240223T055719Z
UID:10002822-1698247800-1698251400@cmsa.fas.harvard.edu
SUMMARY:Tail estimates for stationary KPZ models
DESCRIPTION:Probability Seminar \nSpeaker: Benjamin Landon (University of Toronto) \nTitle: Tail estimates for stationary KPZ models \nAbstract: The limiting distributions of the KPZ universality class exhibit tail exponents of 3/2 and 3. In this talk we will review recent work studying the upper tail exponent 3/2 in the moderate deviations regime of several KPZ models at finite size\, including the stochastic six vertex model\, the ASEP and a class of non-integrable interacting diffusions. \nJoint work with Christian Noack and Phil Sosoe. \n 
URL:https://cmsa.fas.harvard.edu/event/probability-102523/
LOCATION:Virtual
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-10.25.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231018T153000
DTEND;TZID=America/New_York:20231018T163000
DTSTAMP:20260501T114203
CREATED:20240223T075212Z
LAST-MODIFIED:20240223T075212Z
UID:10002829-1697643000-1697646600@cmsa.fas.harvard.edu
SUMMARY:Geometry of the doubly periodic Aztec dimer model
DESCRIPTION:Probability Seminar \nSpeaker: Tomas Berggren (MIT) \nTitle: Geometry of the doubly periodic Aztec dimer model \nAbstract: Random dimer models (or equivalently tiling models) have been a subject of extensive research in mathematics and physics for several decades. In this talk\, we will discuss the doubly periodic Aztec diamond dimer model of growing size\, with arbitrary periodicity and only mild conditions on the edge weights. In this limit\, we see three types of macroscopic regions — known as rough\, smooth and frozen regions. We will discuss how the geometry of the arctic curves\, the boundary of these regions\, can be described in terms of an associated amoeba and an action function. In particular\, we determine the number of frozen and smooth regions and the number of cusps on the arctic curves. We will also discuss the convergence of local fluctuations to the appropriate translation-invariant Gibbs measures. Joint work with Alexei Borodin. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/probability-101123/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-10.18.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230927T153000
DTEND;TZID=America/New_York:20230927T163000
DTSTAMP:20260501T114203
CREATED:20240223T112514Z
LAST-MODIFIED:20240223T112647Z
UID:10002862-1695828600-1695832200@cmsa.fas.harvard.edu
SUMMARY:Large deviations for the 3D dimer model
DESCRIPTION:Probability Seminar \nSpeaker: Catherine Wolfram (MIT) \nTitle: Large deviations for the 3D dimer model \nAbstract: A dimer tiling of Z^d is a collection of edges such that every vertex is covered exactly once. In 2000\, Cohn\, Kenyon\, and Propp showed that 2D dimer tilings satisfy a large deviations principle. In joint work with Nishant Chandgotia and Scott Sheffield\, we prove an analogous large deviations principle for dimers in 3D. A lot of the results for dimers in two dimensions use tools and exact formulas (e.g. the height function representation of a tiling or the Kasteleyn determinant formula) that are specific to dimension 2. In this talk\, I will try to give some intuition for why three dimensions is different from two\, explain how to formulate the large deviations principle in 3D\, show simulations\, and explain some of the ways that we use a smaller set of tools (e.g. Hall’s matching theorem or a double dimer swapping operation) in our arguments. \n 
URL:https://cmsa.fas.harvard.edu/event/probability-92723/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-09.27.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230907T133000
DTEND;TZID=America/New_York:20230907T143000
DTSTAMP:20260501T114203
CREATED:20240223T110205Z
LAST-MODIFIED:20240223T110205Z
UID:10002855-1694093400-1694097000@cmsa.fas.harvard.edu
SUMMARY:Correlation decay for finite lattice gauge theories
DESCRIPTION:Probability Seminar \nSpeaker: Arka Adhikari (Stanford) \nTitle: Correlation decay for finite lattice gauge theories \nAbstract: In the setting of lattice gauge theories with finite (possibly non-Abelian) gauge groups at weak coupling\, we prove exponential decay of correlations for a wide class of gauge invariant functions\, which in particular includes arbitrary functions of Wilson loop observables. Based on joint work with Sky Cao. \n 
URL:https://cmsa.fas.harvard.edu/event/probability-9723/
LOCATION:Science Center 232\, Harvard Science Center\, 1 Oxford Street\, Cambridge MA 02138
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-09.07.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230906T160000
DTEND;TZID=America/New_York:20230906T170000
DTSTAMP:20260501T114203
CREATED:20240223T110729Z
LAST-MODIFIED:20240223T110729Z
UID:10002857-1694016000-1694019600@cmsa.fas.harvard.edu
SUMMARY:Light cones for open quantum systems
DESCRIPTION:Probability Seminar \nSpeaker: Marius Lemm\, University of Tuebingen \nTitle: Light cones for open quantum systems\n\nAbstract: We consider non-relativistic Markovian open quantum dynamics in continuous space. We show that\, up to small probability tails\, the supports of quantum states propagate with finite speed in any finite-energy subspace. More precisely\, if the initial quantum state is localized in space\, then any finite-energy part of the solution of the von Neumann-Lindblad equation is approximately localized inside an energy-dependent light cone. We also obtain an explicit upper bound on the slope of this light cone (i.e.\, on the maximal speed). The general method can be used to derive propagation bounds for a variety of other quantum systems including Lieb-Robinson bounds for lattice bosons. Based on joint works with S. Breteaux\, J. Faupin\, D.H. Ou Yang\, I.M. Sigal\, and J. Zhang.\n 
URL:https://cmsa.fas.harvard.edu/event/probability-9623/
LOCATION:Science Center 232\, Harvard Science Center\, 1 Oxford Street\, Cambridge MA 02138
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-09.06.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230511T133000
DTEND;TZID=America/New_York:20230511T143000
DTSTAMP:20260501T114203
CREATED:20230808T180145Z
LAST-MODIFIED:20240111T084858Z
UID:10001199-1683811800-1683815400@cmsa.fas.harvard.edu
SUMMARY:How do the eigenvalues of a large non-Hermitian random matrix behave?
DESCRIPTION:Probability Seminar \nSpeaker: Giorgio Cipolloni (Princeton) \nTitle: How do the eigenvalues of a large non-Hermitian random matrix behave? \nAbstract: We prove that the fluctuations of the eigenvalues converge to the Gaussian Free Field (GFF) on the unit disk. These fluctuations appear on a non-natural scale\, due to strong correlations between the eigenvalues. Then\, motivated by the long time behaviour of the ODE \dot{u}=Xu\, we give a precise estimate on the eigenvalue with the largest real part and on the spectral radius of X. \nLocation: Science Center Room 232
URL:https://cmsa.fas.harvard.edu/event/probability-51123/
LOCATION:Harvard Science Center\, 1 Oxford Street\, Cambridge\, MA\, 02138
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-05.11.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230503T153000
DTEND;TZID=America/New_York:20230503T163000
DTSTAMP:20260501T114203
CREATED:20230808T175916Z
LAST-MODIFIED:20240111T083748Z
UID:10001198-1683127800-1683131400@cmsa.fas.harvard.edu
SUMMARY:Random Neural Networks
DESCRIPTION:Probability Seminar \nSpeaker: Boris Hanin (Princeton)\n\nTitle: Random Neural Networks \nAbstract: Fully connected neural networks are described two by structural parameters: a depth L and a width N. In this talk\, I will present results and open questions about the asymptotic analysis of such networks with random weights and biases in the regime where N (and potentially L) are large. The first set of results are for deep linear networks\, which are simply products of L random matrices of size N x N. I’ll explain how the setting where the ratio L / N is fixed with both N and L large reveals a number of phenomena not present when only one of them is large. I will then state several results about non-linear networks in which this depth-to-width ratio L / N again plays a crucial role and gives an effective notion of depth for a random neural network.
URL:https://cmsa.fas.harvard.edu/event/probability-5323/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-05.03.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230426T153000
DTEND;TZID=America/New_York:20230426T163000
DTSTAMP:20260501T114203
CREATED:20230808T175545Z
LAST-MODIFIED:20240111T083026Z
UID:10001197-1682523000-1682526600@cmsa.fas.harvard.edu
SUMMARY:Boundary current fluctuations for the half space ASEP
DESCRIPTION:Probability Seminar \nSpeaker: Jimmy He (MIT) \nTitle: Boundary current fluctuations for the half space ASEP \nAbstract: The half space asymmetric simple exclusion process (ASEP) is an interacting particle system on the half line\, with particles allowed to enter/exit at the boundary. I will discuss recent work on understanding fluctuations for the number of particles in the half space ASEP started with no particles\, which exhibits the Baik-Rains phase transition between GSE\, GOE\, and Gaussian fluctuations as the boundary rates vary. As part of the proof\, we find new distributional identities relating this system to two other models\, the half space Hall-Littlewood process\, and the free boundary Schur process\, which allows exact formulas to be computed.
URL:https://cmsa.fas.harvard.edu/event/probability-42623/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-04.26.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230419T153000
DTEND;TZID=America/New_York:20230419T163000
DTSTAMP:20260501T114203
CREATED:20230808T175217Z
LAST-MODIFIED:20240111T082259Z
UID:10001196-1681918200-1681921800@cmsa.fas.harvard.edu
SUMMARY:Diagonalizing Transition Matrices of Card Shuffles
DESCRIPTION:Probability Seminar \nSpeaker: Evita Nestoridi (Stonybrook)\n\nTitle: Diagonalizing Transition Matrices of Card Shuffles \nAbstract: In their seminal work\, Diaconis and Shahshahani used representation theory of the symmetric group to diagonalize the transition matrix of random transpositions. More recently\, Dieker and Saliola introduced another technique to diagonalize the random-to-random card shuffle. In this talk we will discuss connections between these techniques as well as application to card shuffling.
URL:https://cmsa.fas.harvard.edu/event/probability-41923/
LOCATION:Science Center 232\, Harvard Science Center\, 1 Oxford Street\, Cambridge MA 02138
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-04.19.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230412T153000
DTEND;TZID=America/New_York:20230412T163000
DTSTAMP:20260501T114203
CREATED:20230808T174934Z
LAST-MODIFIED:20240228T094844Z
UID:10001195-1681313400-1681317000@cmsa.fas.harvard.edu
SUMMARY:Large deviations of Selberg’s central limit theorem
DESCRIPTION:Probability Seminar \n\nSpeaker: Emma Bailey (CUNY) \nTitle: Large deviations of Selberg’s central limit theorem \nAbstract: Selberg’s CLT concerns the typical behaviour of the Riemann zeta function and shows that the random variable $\Re \log \zeta(1/2 + i t)$\, for a uniformly drawn $t$\, behaves as a Gaussian random variable with a particular variance.  It is natural to investigate how far into the tails this Gaussianity persists\, which is the topic of this work. There are also very close connections to similar problems in circular unitary ensemble characteristic polynomials.  It transpires that a `multiscale scheme’ can be applied to both situations to understand these questions of large deviations\, as well as certain maxima and moments. In this talk I will focus more on the techniques we apply to approach this problem and I will assume no number theoretic knowledge. This is joint work with Louis-Pierre Arguin.
URL:https://cmsa.fas.harvard.edu/event/probability-41223/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-04.12.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230410T150000
DTEND;TZID=America/New_York:20230410T160000
DTSTAMP:20260501T114203
CREATED:20230808T174720Z
LAST-MODIFIED:20240111T070433Z
UID:10001194-1681138800-1681142400@cmsa.fas.harvard.edu
SUMMARY:Localization for random band matrices
DESCRIPTION:Probability Seminar \n*Please note room change: Science Center 232* \n\nSpeaker: Ron Peled (Tel Aviv University) \nTitle: Localization for random band matrices \nAbstract: 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}. \nJoint work with Giorgio Cipolloni\, Jeffrey Schenker and Jacob Shapiro.
URL:https://cmsa.fas.harvard.edu/event/probability-41023/
LOCATION:Harvard Science Center\, 1 Oxford Street\, Cambridge\, MA\, 02138
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-04.10.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230405T153000
DTEND;TZID=America/New_York:20230405T163000
DTSTAMP:20260501T114203
CREATED:20230807T173206Z
LAST-MODIFIED:20240111T070226Z
UID:10001193-1680708600-1680712200@cmsa.fas.harvard.edu
SUMMARY:Sampling from the SK and mixed p-spin measures with stochastic localization
DESCRIPTION:Probability Seminar \n\nSpeaker: Ahmed El Alaoui (Cornell) \nTitle: Sampling from the SK and mixed p-spin measures with stochastic localization \nAbstract: 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.
URL:https://cmsa.fas.harvard.edu/event/probability-4523/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-04.05.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230322T153000
DTEND;TZID=America/New_York:20230322T163000
DTSTAMP:20260501T114203
CREATED:20230807T172858Z
LAST-MODIFIED:20240215T105007Z
UID:10001192-1679499000-1679502600@cmsa.fas.harvard.edu
SUMMARY:Some rigorous results on the Lévy spin glass model
DESCRIPTION:Probability Seminar \nSpeaker: Wei-Kuo Chen (Minnesota)\n\nTitle: Some rigorous results on the Lévy spin glass model \nAbstract: 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.
URL:https://cmsa.fas.harvard.edu/event/probability-32223/
LOCATION:Virtual
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-03.22.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230309T110000
DTEND;TZID=America/New_York:20230309T120000
DTSTAMP:20260501T114203
CREATED:20230807T171904Z
LAST-MODIFIED:20240215T105139Z
UID:10001191-1678359600-1678363200@cmsa.fas.harvard.edu
SUMMARY:On the free energy of spin glasses with multiple types
DESCRIPTION:Probability Seminar \n\nSpeaker: Jean-Christophe Mourrat (ENS Lyon) \nTitle: On the free energy of spin glasses with multiple types \nAbstract: 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.
URL:https://cmsa.fas.harvard.edu/event/probability-3923/
LOCATION:Virtual
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-03.09.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230222T153000
DTEND;TZID=America/New_York:20230222T163000
DTSTAMP:20260501T114203
CREATED:20230807T171541Z
LAST-MODIFIED:20240111T065432Z
UID:10001190-1677079800-1677083400@cmsa.fas.harvard.edu
SUMMARY:Thresholds for edge colorings
DESCRIPTION:Probability Seminar \nSpeaker: Vishesh Jain (University of Illinois Chicago)\n\nTitle: Thresholds for edge colorings\n\nAbstract: We show that if each edge of the complete bipartite graph K_{n\,n} is given a random list of C(\log n) colors from [n]\, then with high probability\, there is a proper edge coloring where the color of each edge comes from the corresponding list. We also prove analogous results for Latin squares and Steiner triple systems. This resolves several related conjectures of Johansson\, Luria-Simkin\, Casselgren-Häggkvist\, Simkin\, and Kang-Kelly-Kühn-Methuku-Osthus. I will discuss some of the main ingredients which go into the proof: the Kahn-Kalai conjecture\, absorption\, and the Lovasz Local Lemma distribution. Based on joint work with Huy Tuan Pham.
URL:https://cmsa.fas.harvard.edu/event/probability-22223/
LOCATION:Virtual
CATEGORIES:Probability Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230215T153000
DTEND;TZID=America/New_York:20230215T163000
DTSTAMP:20260501T114203
CREATED:20230807T170715Z
LAST-MODIFIED:20240228T100906Z
UID:10001189-1676475000-1676478600@cmsa.fas.harvard.edu
SUMMARY:Manifold Fitting: An Invitation to Statistics
DESCRIPTION:Probability Seminar \nSpeaker: Zhigang Yao (Harvard CMSA/National University of Singapore)\n\n\nTitle: Manifold Fitting: An Invitation to Statistics \nAbstract: This manifold fitting problem can go back to H. Whitney’s work in the early 1930s (Whitney (1992))\, and finally has been answered in recent years by C. Fefferman’s works (Fefferman\, 2006\, 2005). The solution to the Whitney extension problem leads to new insights for data interpolation and inspires the formulation of the Geometric Whitney Problems (Fefferman et al. (2020\, 2021a)): Assume that we are given a set $Y \subset \mathbb{R}^D$. When can we construct a smooth $d$-dimensional submanifold $\widehat{M} \subset \mathbb{R}^D$ to approximate $Y$\, and how well can $\widehat{M}$ estimate $Y$ in terms of distance and smoothness? To address these problems\, various mathematical approaches have been proposed (see Fefferman et al. (2016\, 2018\, 2021b)). However\, many of these methods rely on restrictive assumptions\, making extending them to efficient and workable algorithms challenging. As the manifold hypothesis (non-Euclidean structure exploration) continues to be a foundational element in statistics\, the manifold fitting Problem\, merits further exploration and discussion within the modern statistical community. The talk will be partially based on a recent work Yao and Xia (2019) along with some on-going progress. Relevant reference: https://arxiv.org/abs/1909.10228
URL:https://cmsa.fas.harvard.edu/event/probability-21523/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-02.15.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230208T153000
DTEND;TZID=America/New_York:20230208T163000
DTSTAMP:20260501T114203
CREATED:20230807T170441Z
LAST-MODIFIED:20240228T112614Z
UID:10001188-1675870200-1675873800@cmsa.fas.harvard.edu
SUMMARY:Bakry-Emery theory and renormalisation
DESCRIPTION:Probability Seminar \nSpeaker: Roland Bauerschmidt (Cambridge)\n\nTitle: Bakry-Emery theory and renormalisation \nAbstract: I will discuss an approach to log-Sobolev inequalities that\ncombines the Bakry-Emery theory with renormalisation and present several\napplications. These include log-Sobolev inequalities with polynomial\ndependence for critical Ising models on Z^d when d>4 and singular SPDEs\nwith uniform dependence of the log-Sobolev constant on both the\nregularisation and the volume. The talk is based on joint works with\nThierry Bodineau and Benoit Dagallier.
URL:https://cmsa.fas.harvard.edu/event/probability-2823/
LOCATION:Hybrid
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-02.08.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221207T153000
DTEND;TZID=America/New_York:20221207T163000
DTSTAMP:20260501T114203
CREATED:20230807T165823Z
LAST-MODIFIED:20240110T091938Z
UID:10001187-1670427000-1670430600@cmsa.fas.harvard.edu
SUMMARY:Fourier quasicrystals and stable polynomials
DESCRIPTION:Probability Seminar \nNote location change: Science Center Room 300H \nSpeaker: Lior Alon (MIT) \nTitle: Fourier quasicrystals and stable polynomials \nAbstract: The Poisson summation formula says that the countable sum of exp(int)\, over all integers n\, vanishes as long as t is not an integer multiple of 2 pi. Can we find a non-periodic discrete set A\, such that the sum of exp(iat)\, over a in A\, vanishes for all t outside of a discrete set? The surprising answer is yes. Yves Meyer called the atomic measure supported on such a set a crystalline measure. Crystalline measures provide another surprising connection between physics (quasicrystals) and number theory (the zeros of the Zeta and L functions under GRH). A recent work of Pavel Kurasov and Peter Sarnak provided a construction of crystalline measures with ‘good’ convergence (Fourier quasicrystals) using stable polynomials\, a family of multivariate polynomials that were previously used in proving the Lee-Yang circle theorem and the Kadison-Singer conjecture. After providing the needed background\, I will discuss a recent work in progress with Cynthia Vinzant on the classification of these Kurasov-Sarnak measures and their supporting sets. We prove that these sets have well-defined gap distributions. We show that each Kurasov-Sarnak measure decomposes according to the irreducible decomposition of its associated polynomial\, and the measures associated with each irreducible factor is either supported on an arithmetic progression\, or its support has a bounded intersection with any arithmetic progression. Finally\, we construct random Kurasov-Sarnak measures with gap distribution as close as we want to the eigenvalues spacing of a random unitary matrix. \nBased on joint work with Pravesh Kothari.
URL:https://cmsa.fas.harvard.edu/event/probability-12722/
LOCATION:Harvard Science Center\, 1 Oxford Street\, Cambridge\, MA\, 02138
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-12.07.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221202T110000
DTEND;TZID=America/New_York:20221202T120000
DTSTAMP:20260501T114203
CREATED:20230817T164654Z
LAST-MODIFIED:20240229T111029Z
UID:10001230-1669978800-1669982400@cmsa.fas.harvard.edu
SUMMARY:Compactness and Anticompactness Principles in Set Theory
DESCRIPTION:Member Seminar \nSpeaker: Alejandro Poveda \nTitle: Compactness and Anticompactness Principles in Set Theory \nAbstract: Several fundamental properties in Topology\, Algebra or Logic are expressed in terms of Compactness Principles.For instance\, a natural algebraic question is the following: Suppose that G is an Abelian group whose all small subgroups are free – Is the group G free? If the answer is affirmative one says that compactness holds; otherwise\, we say that compactness fails. Loosely speaking\, a compactness principle is anything that fits the following slogan: Suppose that M is a mathematical structure (a group\, a topological space\, etc) such that all of its small substructures N have certain property $\varphi$; then the ambient structure M has property $\varphi$\, as well. Oftentimes when these questions are posed for infinite sets the problem becomes purely set-theoretical and axiom-sensitive. In this talk I will survey the most paradigmatic instances of compactness and present some related results of mine. If time permits\, I will hint the proof of a recent result (joint with Rinot and Sinapova) showing that stationary reflection and the failure of the Singular Cardinal Hypothesis can co-exist. These are instances of two antagonist set-theoretic principles: the first is a compactness principle while the second is an anti-compactness one. This result solves a question by M. Magidor from 1982.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-12222/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221130T150000
DTEND;TZID=America/New_York:20221130T160000
DTSTAMP:20260501T114203
CREATED:20230807T165526Z
LAST-MODIFIED:20240110T091213Z
UID:10001186-1669820400-1669824000@cmsa.fas.harvard.edu
SUMMARY:Lipschitz properties of transport maps under a log-Lipschitz condition
DESCRIPTION:Probability Seminar \n\nLocation: Room 109\, Harvard Science Center\, 1 Oxford Street\, Cambridge MA 02138\nSpeaker: Dan Mikulincer (MIT) \n\n\nTitle: Lipschitz properties of transport maps under a log-Lipschitz condition \nAbstract: Consider the problem of realizing a target probability measure as a push forward\, by a transport map\, of a given source measure. Typically one thinks about the target measure as being ‘complicated’ while the source is simpler and often more structured. In such a setting\, for applications\, it is desirable to find Lipschitz transport maps which afford the transfer of analytic properties from the source to the target. The talk will focus on Lipschitz regularity when the target measure satisfies a log-Lipschitz condition. \nI will present a construction of a transport map\, constructed infinitesimally along the Langevin flow\, and explain how to analyze its Lipschitz constant. The analysis of this map leads to several new results which apply both to Euclidean spaces and manifolds\, and which\, at the moment\, seem to be out of reach of the classically studied optimal transport theory. \nJoint work with Max Fathi and Yair Shenfeld.
URL:https://cmsa.fas.harvard.edu/event/probability-113022/
LOCATION:Harvard Science Center\, 1 Oxford Street\, Cambridge\, MA\, 02138
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-11.30.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221118T110000
DTEND;TZID=America/New_York:20221118T120000
DTSTAMP:20260501T114203
CREATED:20230809T111725Z
LAST-MODIFIED:20240209T052933Z
UID:10001229-1668769200-1668772800@cmsa.fas.harvard.edu
SUMMARY:Light states in the interior of CY moduli spaces
DESCRIPTION:Member Seminar \nSpeaker: Damian van de Heisteeg \nTitle: Light states in the interior of CY moduli spaces \nAbstract: In string theory one finds that states become massless as one approaches boundaries in Calabi-Yau moduli spaces. In this talk we look in the opposite direction\, that is\, we search for points where the mass gap for these light states is maximized — the so-called desert. In explicit examples we identify these desert points\, and find that they correspond to special points in the moduli space of the CY\, such as orbifold points and rank two attractors.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-111822/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Member-Seminar-11.18.22.png
END:VEVENT
END:VCALENDAR