BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Maciej Zworski (UC Berkeley) (UC Berkeley) DTSTART:20200908T200000Z DTEND:20200908T210000Z DTSTAMP:20260404T092654Z UID:PDEAnalysis/1 DESCRIPTION:Title: Mathematics of magic angles for bilayer graphene\nby Maciej Zworski (UC Berkeley) (UC Berkeley) as part of PDE Analysis Seminar\n\n\n Abstract\nMagic angles are a hot topic in condensed matter physics: when t wo sheets of graphene\nare twisted by those angles the resulting material is superconducting. Please do not be\nscared by the physics though: I will present a very simple operator whose spectral properties\nare thought to determine which angles are magical. It comes from a recent PR Letter\nby T arnopolsky–Kruchkov–Vishwanath. The mathematics behind this is an elem entary\nblend of representation theory (of the Heisenberg group in charact eristic three)\, Jacobi\ntheta functions and spectral instability of non-s elf-adjoint operators (involving Hörmander’s\nbracket condition in a ve ry simple setting). The results will be illustrated by colourful\nnumerics which suggest some open problems. The talk is based on a “summer relaxa tion\nproject” with S. Becker\, M. Embree and J. Wittsten.\n LOCATION:https://stable.researchseminars.org/talk/PDEAnalysis/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Ruoxuan Yang (MIT Mathematics) DTSTART:20200915T200000Z DTEND:20200915T210000Z DTSTAMP:20260404T092654Z UID:PDEAnalysis/2 DESCRIPTION:Title: Shock Formation for the Burgers-Hilbert Equation\nby Ruoxua n Yang (MIT Mathematics) as part of PDE Analysis Seminar\n\n\nAbstract\nWe will talk about the shock formation for the Burgers–Hilbert (BH) equati on. We begin with previous studies on BH equation\, including the vorticit y discontinuity model\, initial value problems and blowup results. Then we introduce the technique of modulated self-similarity\, show its backgroun d and apply it to the BH equation. Finally we sketch the proof and discuss its difficulty.\n\nZoom link: https://mit.zoom.us/j/94123420042?pwd=R2I3 aG53b0NHZk1wa1JPU3J5TXZKZz09\n\nZoom password: 577126\n LOCATION:https://stable.researchseminars.org/talk/PDEAnalysis/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Malo Jézéquel (MIT) DTSTART:20210914T200000Z DTEND:20210914T210000Z DTSTAMP:20260404T092654Z UID:PDEAnalysis/3 DESCRIPTION:Title: Real-analytic FBI transform and Anosov flows\nby Malo Jéz équel (MIT) as part of PDE Analysis Seminar\n\n\nAbstract\nAnosov flows f orm an extensively studied class of chaotic dynamical systems. In this tal k\, I will explain how PDE techniques developed by Helffer and Sj¨ostrand in the 80s-90s can be used to study the statistical properties of real-an alytic Anosov flows\, and the complex-analytic properties of associated ze ta functions. This is a joint work with Yannick Guedes Bonthonneau.\n LOCATION:https://stable.researchseminars.org/talk/PDEAnalysis/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Hou (Caltech) DTSTART:20211005T200000Z DTEND:20211005T210000Z DTSTAMP:20260404T092654Z UID:PDEAnalysis/4 DESCRIPTION:Title: Potential singularity of 3D incompressible Euler equations and the nearly singular behavior of 3D Navier-Stokes equations\nby Thomas Hou (Caltech) as part of PDE Analysis Seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/PDEAnalysis/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Maciej Zworski (UC Berkeley) DTSTART:20211019T200000Z DTEND:20211019T210000Z DTSTAMP:20260404T092654Z UID:PDEAnalysis/5 DESCRIPTION:Title: Title to be announced\nby Maciej Zworski (UC Berkeley) as p art of PDE Analysis Seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/PDEAnalysis/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Sylvia Serfaty (NYU Courant) DTSTART:20211026T200000Z DTEND:20211026T210000Z DTSTAMP:20260404T092654Z UID:PDEAnalysis/6 DESCRIPTION:Title: Title to be announced\nby Sylvia Serfaty (NYU Courant) as p art of PDE Analysis Seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/PDEAnalysis/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Yaiza Canzani (UNC Chapel Hill) DTSTART:20211130T210000Z DTEND:20211130T220000Z DTSTAMP:20260404T092654Z UID:PDEAnalysis/7 DESCRIPTION:Title: Title to be announced\nby Yaiza Canzani (UNC Chapel Hill) a s part of PDE Analysis Seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/PDEAnalysis/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Isabelle Gallagher (Ecole Normale Supérieure) DTSTART:20220405T200000Z DTEND:20220405T210000Z DTSTAMP:20260404T092654Z UID:PDEAnalysis/8 DESCRIPTION:Title: Dynamics of dilute gases at equilibrium: from the atomistic des cription to fluctuating hydrodynamics\nby Isabelle Gallagher (Ecole No rmale Supérieure) as part of PDE Analysis Seminar\n\n\nAbstract\nWe consi der the low density limit of a deterministic system of particles. Lanford ’s theorem in 1974 states that the empirical distribution converges in l aw to the solution to the Boltzmann equation\, for short times. Recently\, the fluctuation field has been shown to converge to a Gaussian process\, and this convergence holds for arbitrarily long times if the gas is at equ ilibrium. In this talk we will explain the main ideas of the proof\, and s how how linear fluctuating hydrodynamics can be derived from this model at equilibrium.\n\nhttps://mit.zoom.us/j/96019944889?pwd=em5VVFJab1o2NlZtWGZ VdDRQWmxQQT09\nZoom password: 140860\n LOCATION:https://stable.researchseminars.org/talk/PDEAnalysis/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Yaiza Canzani (UNC) DTSTART:20220419T191500Z DTEND:20220419T200500Z DTSTAMP:20260404T092654Z UID:PDEAnalysis/9 DESCRIPTION:Title: COUNTING CLOSED GEODESICS AND IMPROVING WEYL’S LAW FOR PREDOM INANT SETS OF METRICS\nby Yaiza Canzani (UNC) as part of PDE Analysis Seminar\n\n\nAbstract\nWe discuss the typical behavior of two important qu antities on compact manifolds with a Riemannian metric g: the number\, c(T \,g)\, of primitive closed geodesics of length smaller than T\, and the er ror\, E(L\,g)\, in the Weyl law for counting the number of Laplace eigenva lues that are smaller than L. For Baire generic metrics\, the qualitative behavior of both of these quantities has been understood since the 1970’ s and 1980’s. In terms of quantitative behavior\, the only available res ult is due to Contreras and it says that an exponential lower bound on c(T \,g) holds for g in a Baire-generic set. Until now\, no upper bounds on c( T\,g) or quantitative improvements on E(L\,g) were known to hold for most metrics\, not even for a dense set of metrics. In this talk\, we will intr oduce the concept of predominance in the space of Riemannian metrics. This is a notion that is analogous to having full Lebesgue measure in finite d imensions\, and which\, in particular\, implies density. We will then give stretched exponential upper bounds for c(T\,g) and logarithmic improvemen ts for E(L\,g) that hold for a predominant set of metrics. This is based o n joint work with J. Galkowski.\n LOCATION:https://stable.researchseminars.org/talk/PDEAnalysis/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Hao Jia (University of Minnesota) DTSTART:20220426T200000Z DTEND:20220426T210000Z DTSTAMP:20260404T092654Z UID:PDEAnalysis/10 DESCRIPTION:Title: VORTEX SYMMETRIZATION PROBLEM FOR THE 2D EULER EQUATION\nb y Hao Jia (University of Minnesota) as part of PDE Analysis Seminar\n\nLec ture held in Room 2-147 in the Simons Building.\n\nAbstract\nThe 2d incomp ressible Euler equation is globally well posed for smooth initial data. Ho wever the long term dynamics of general solutions is difficult to understa nd due to the lack of global relaxation mechanisms. Numerical simulations and physical experiments show that vortices (steady solutions with radial vorticity functions) play an important role in the global dynamics\, throu gh a process called vortex symmetrization of small perturbations. In this talk\, I will discuss some recent progress on this problem\, including a f ull nonlinear symmetrization result near a special point vortex and precis e linearized symmetrization result near general vortices. Difficulties of full nonlinear vortex symmetrization around general vortices will also be discussed. Joint work with Alexandru Ionescu.\n LOCATION:https://stable.researchseminars.org/talk/PDEAnalysis/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Tuomas Orponen (University of Jyväskylä) DTSTART:20220503T190000Z DTEND:20220503T200000Z DTSTAMP:20260404T092654Z UID:PDEAnalysis/11 DESCRIPTION:Title: On the dimension of A + BC\nby Tuomas Orponen (University of Jyväskylä) as part of PDE Analysis Seminar\n\n\nAbstract\nLet A\,B\,C be compact subsets of [0\,1]. What is the (Hausdorff) dimension of A + BC ? The problem is open\, but I will discuss the current partial results. Af ter briefly discussing the case of general compact sets\, I will focus on the case where A\,B are Ahlfors-regular.\n\nZoom link: https://mit.zoom.us /j/96019944889?pwd=em5VVFJab1o2NlZtWGZVdDRQWmxQQT09\nZoom password: 140860 \n LOCATION:https://stable.researchseminars.org/talk/PDEAnalysis/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Zaher Hani (University of Michigan) DTSTART:20220510T200000Z DTEND:20220510T210000Z DTSTAMP:20260404T092654Z UID:PDEAnalysis/12 DESCRIPTION:Title: Title to be announced\nby Zaher Hani (University of Michig an) as part of PDE Analysis Seminar\n\n\nAbstract\nAbstract to be shared\n LOCATION:https://stable.researchseminars.org/talk/PDEAnalysis/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Jani Lukkarinen (U Helsinki) DTSTART:20220927T190000Z DTEND:20220927T200000Z DTSTAMP:20260404T092654Z UID:PDEAnalysis/13 DESCRIPTION:Title: Estimation of propagation of chaos via cumulant hierarchies in two example models\nby Jani Lukkarinen (U Helsinki) as part of PDE An alysis Seminar\n\nLecture held in Room 2 - 136 in the Simons Building.\n\n Abstract\nPropagation and generation of “chaos” is an important ingred ient in rigorous control of applicability of kinetic theory\, in general. Chaos can here be understood as sufficient statistical independence of ran dom variables related to the “kinetic” observables of the system. Cumu lant hierarchy of these random variables thus often gives a way of control ling the evolution and the degree of such independence\, i.e.\, the amount of “chaos” in the system. In this talk\, we will consider two\, quali tatively different\, example cases for which kinetic theory is believed to be applicable: the discrete nonlinear Schrodinger evolution (DNLS) with s uitable random\, spatially homogeneous initial data\, and the stochastic K ac model. In both cases\, we set up suitable random variables and propose methods to control the evolution of their cumulant hierarchies. The talk i s based on joint work with Aleksis Vuoksenmaa\, and earlier works with Mat teo Marcozzi\, Alessia Nota\, and Herbert Spohn.\n LOCATION:https://stable.researchseminars.org/talk/PDEAnalysis/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Shaoming Guo (U Wisconsin\, Madison) DTSTART:20221018T190000Z DTEND:20221018T200000Z DTSTAMP:20260404T092654Z UID:PDEAnalysis/14 DESCRIPTION:Title: A dichotomy for Hormander-type oscillatory integral operators< /a>\nby Shaoming Guo (U Wisconsin\, Madison) as part of PDE Analysis Semin ar\n\nLecture held in Room 2-136 in the Simon's Building.\n\nAbstract\nHor mander 1973 proposed to study a generalized Fourier extension operator\, a nd asked whether the generalized operator satisfies the same L p bounds as that of the standard Fourier extension operator. Surprisingly\, Bourgain 1991 gave a negative answer to Hormander’s question. In this talk\, I wi ll discuss a modification of Hormander’s question whose answer may be af firmative. This is a joint work with Hong Wang and Ruixiang Zhang.\n LOCATION:https://stable.researchseminars.org/talk/PDEAnalysis/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Philip Gressman (UPenn) DTSTART:20221108T200000Z DTEND:20221108T210000Z DTSTAMP:20260404T092654Z UID:PDEAnalysis/15 DESCRIPTION:Title: Title to be shared\nby Philip Gressman (UPenn) as part of PDE Analysis Seminar\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/PDEAnalysis/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Benoit Pausader (Brown) DTSTART:20221115T200000Z DTEND:20221115T210000Z DTSTAMP:20260404T092654Z UID:PDEAnalysis/16 DESCRIPTION:Title: Stability of a point charge for the repulsive Vlasov-Poisson s ystem\nby Benoit Pausader (Brown) as part of PDE Analysis Seminar\n\nL ecture held in 2-136.\n\nAbstract\nWe consider solutions of the repulsive Vlasov-Poisson systems which are a combination of a point charge and a sma ll density with respect to Liouville measure (a “cloud”)\, and we show that these solutions exist globally\, that the electric field decay at an optimal rate and that the particle distribution converges along a modifie d scattering dynamics. This follows by a Lagrangian study of the linearize d equation\, which is integrated by means of an asymptotic action-angle co ordinate transformation\, and an Eulerian study of the nonlinear dynamic w hich exhibits the “mixing” mechanism responsible for the asymptotic be havior. This is joint work with Klaus Widmayer (U. Zurich) and Jiaqi Yang (ICERM).\n LOCATION:https://stable.researchseminars.org/talk/PDEAnalysis/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Semyon Dyatlov (MIT) DTSTART:20221025T200000Z DTEND:20221025T210000Z DTSTAMP:20260404T092654Z UID:PDEAnalysis/17 DESCRIPTION:Title: MICROLOCAL ANALYSIS OF INTERNAL WAVES IN 2D AQUARIA\nby Se myon Dyatlov (MIT) as part of PDE Analysis Seminar\n\nLecture held in Room 2-136 in the Simon's Building.\n\nAbstract\n\\noindent For a bounded smoo th planar domain Ω\, we study the forced evolution problem for the 4th or der PDE \n\n\\begin{equation}\n (\\partial^{2}_{t} \\Delta + \\partial^ {2}_{x_{2}} )u(t\,x)=f(x)cos(\\lambda t)\, t \\geq 0\, x \\in \\Omega\n\\ end{equation}\n\n\\vspace{1ex}\n\nwith homogeneous initial conditions and Dirichlet boundary conditions on $\\partial \\Omega$. This is motivated b y concentration of fluid velocity on attractors for stratified fluids in e ffectively 2-dimensional aquaria\, first observed experimentally in 1997. \\\\\n\n\\vspace{1ex}\n\n\\noindent The behavior of solutions to (1) is in timately tied to the chess billiard map on the boundary $\\partial \\Omega $\, which depends on the forcing frequency λ. Under the natural assumptio n that the chess billiard b has the Morse– Smale property\, we show that as $t \\rightarrow \\infty $ the singular part of the solution u concentr ates on the attractive cycle of b. The proof combines various tools from m icrolocal analysis\, scattering theory\, and hyperbolic dynamics. Joint wo rk with Jian Wang and Maciej Zworski. \\\\\n LOCATION:https://stable.researchseminars.org/talk/PDEAnalysis/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Dominique Maldague (MIT Mathematics) DTSTART:20221101T190000Z DTEND:20221101T200000Z DTSTAMP:20260404T092654Z UID:PDEAnalysis/18 DESCRIPTION:Title: A SHARP SQUARE FUNCTION ESTIMATE FOR THE MOMENT CURVE IN $\\ma thbb{R}^{3}$\nby Dominique Maldague (MIT Mathematics) as part of PDE A nalysis Seminar\n\n\nAbstract\n\\noindent We will present recent work whic h proves a sharp $L^{7}$ square function estimate for the moment curve in $\\mathbb{R}^{3}$. Consider a function f with Fourier support in a small n eighborhood of the moment curve. Partition the neighborhood into box-like subsets and form a square function in the Fourier projections of f onto th ese box-like regions. Bounding $f$ in $L_{p}$ by the square function in $L _{p}$ is an important way to quantify the cancellation that f has from its specialized Fourier support. As Guth\, Wang\, and Zhang did for the cone in 3 dimensions\, this is another example of using ideas and techniques fr om decoupling theory to prove a sharp square function estimate.\n LOCATION:https://stable.researchseminars.org/talk/PDEAnalysis/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Lior Alon (MIT) DTSTART:20221206T200000Z DTEND:20221206T210000Z DTSTAMP:20260404T092654Z UID:PDEAnalysis/19 DESCRIPTION:Title: Fourier quasicrystals and stable polynomials\nby Lior Alon (MIT) as part of PDE Analysis Seminar\n\nLecture held in Room 2-136 in th e Simon's Building.\n\nAbstract\nThe Poisson summation formula says that t he countable sum of exp(int)\, over all integers $n$\, vanishes as long as t is not an integer multiple of $2π$. Can we find a non-periodic discret e 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 calle d the atomic measure supported on such a set a crystalline measure. Crysta lline measures provide another surprising connection between physics (quas icrystals) and number theory (the zeros of the Zeta and L functions under GRH). A recent work of Pavel Kurasov and Peter Sarnak provided a construct ion of crystalline measures with ‘good’ convergence (Fourier quasicrys tals) using stable polynomials\, a family of multivariate polynomials that were previously used in proving the Lee-Yang circle theorem and the Kadis on-Singer conjecture. After providing the needed background\, I will discu ss a recent work in progress with Cynthia Vinzant on the classification of these Kurasov-Sarnak measures and their supporting sets. We prove that th ese sets have well-defined gap distributions. We show that each Kurasov-Sa rnak 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 h as a bounded intersection with any arithmetic progression. Finally\, we co nstruct random Kurasov-Sarnak measures with gap distribution as close as w e want to the eigenvalues spacing of a random unitary matrix.\n LOCATION:https://stable.researchseminars.org/talk/PDEAnalysis/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Hong Wang (UCLA) DTSTART:20221213T200000Z DTEND:20221213T210000Z DTSTAMP:20260404T092654Z UID:PDEAnalysis/20 DESCRIPTION:Title: Stick Kakeya sets in $R^3$\nby Hong Wang (UCLA) as part of PDE Analysis Seminar\n\n\nAbstract\nA Kakeya set is a set of points in $\ \mathbb{R}^n$ which contains a unit line segment in every direction. The K akeya conjecture states that the dimension of any Kakeya set is n. This co njecture remains wide open for all $n \\geq 3$. \\\\\n\nTogether with Jos h Zahl\, we study a special collection of the Kakeya sets\, namely the sti cky Kakeya sets\, where the line segments in nearby directions stay close. We prove that sticky Kakeya sets in $\\mathbb{R}^3$ have dimension 3. In the talk\, we will also discuss the connection to projection theory in ge ometric measure theory\n LOCATION:https://stable.researchseminars.org/talk/PDEAnalysis/20/ END:VEVENT END:VCALENDAR