BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Etienne Le Masson (Paris Cergy) DTSTART:20211027T140000Z DTEND:20211027T150000Z DTSTAMP:20260422T212707Z UID:HASS21/1 DESCRIPTION:Title: E igenfunctions on random hyperbolic surfaces\nby Etienne Le Masson (Par is Cergy) as part of Harmonic Analysis and Symmetric Spaces 2021\n\n\nAbst ract\nHigh frequency eigenfunctions on hyperbolic surfaces are known to ex hibit some universal behaviour of delocalisation and randomness. We will i ntroduce some results on the behaviour of eigenfunctions on random compact hyperbolic surfaces\, in the limit where the genus (or equivalently the v olume) tends to infinity\, and the frequency is in a fixed window. These r esults suggest that in this large scale limit we can expect similar univer sal behaviour. We will focus on the Weil-Petersson model of random surface s introduced by Mirzakhani.\n\nBased on joint works with Tuomas Sahlsten a nd Joe Thomas.\n LOCATION:https://researchseminars.org/talk/HASS21/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Bart Michels (Sorbonne Paris Nord) DTSTART:20211027T151500Z DTEND:20211027T161500Z DTSTAMP:20260422T212707Z UID:HASS21/2 DESCRIPTION:Title: M ean square asymptotics and oscillatory integrals for maximal flat submanif olds of locally symmetric spaces\nby Bart Michels (Sorbonne Paris Nord ) as part of Harmonic Analysis and Symmetric Spaces 2021\n\n\nAbstract\nGi ven a compact locally symmetric space of non-compact type\, we present a m ean square asymptotic for integrals of eigenfunctions along maximal flat s ubmanifolds\, constrained to eigenfunctions with suitably generic spectral parameter. This is motivated by questions concerning the maximal size of automorphic periods. The proof uses the pre-trace formula. The analysis of orbital integrals requires knowledge about the geometry of maximal flat s ubmanifolds of the globally symmetric space S. When S is the hyperbolic pl ane\, modeled by the upper half plane\, the maximal flat submanifolds are geodesics\, and they are lines or half-circles orthogonal to the real axis . The midpoints of the half-circles play a critical role\, as do their ana logues in higher rank spaces\, and one is led to generalize their properti es as well as other facts about maximal flat submanifolds.\n LOCATION:https://researchseminars.org/talk/HASS21/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Matthew Blair (New Mexico) DTSTART:20211027T163000Z DTEND:20211027T173000Z DTSTAMP:20260422T212707Z UID:HASS21/3 DESCRIPTION:Title: L p bounds for eigenfunctions at the critial exponent\nby Matthew Blair (New Mexico) as part of Harmonic Analysis and Symmetric Spaces 2021\n\n\nA bstract\nWe consider upper bounds on the growth of $L^pa$ norms of eigenfu nctions of the Laplacian on a compact Riemannian manifold in the high freq uency limit. In particular\, we seek to identify geometric or dynamical co nditions on the manifold which yield improvements on the universal $L^p$ b ounds of C. Sogge. The emphasis will be on bounds at the "critical exponen t"\, where a spectrum of scenarios for phase space concentration must be c onsidered. We then discuss a recent work with C. Sogge which shows that wh en the sectional curvatures are nonpositive\, there is a logarithmic type gain in the known $L^p$ bounds at the critical exponent.\n LOCATION:https://researchseminars.org/talk/HASS21/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Yaiza Canzani (North Carolina) DTSTART:20211028T140000Z DTEND:20211028T150000Z DTSTAMP:20260422T212707Z UID:HASS21/4 DESCRIPTION:Title: E igenfunction concentration via geodesic beams\nby Yaiza Canzani (North Carolina) as part of Harmonic Analysis and Symmetric Spaces 2021\n\n\nAbs tract\nA vast array of physical phenomena\, ranging from the propagation o f waves to the location of quantum particles\, is dictated by the behavior of Laplace eigenfunctions. Because of this\, it is crucial to understand how various measures of eigenfunction concentration respond to the backgro und dynamics of the geodesic flow. In collaboration with J. Galkowski\, we developed a framework to approach this problem that hinges on decomposing eigenfunctions into geodesic beams. In this talk\, I will present these t echniques and explain how to use them to obtain quantitative improvements on the standard estimates for the eigenfunction's pointwise behavior\, $L^ p$ norms\, and Weyl Laws. One consequence of this method is a quantitative ly improved Weyl Law for the eigenvalue counting function on all product m anifolds.\n LOCATION:https://researchseminars.org/talk/HASS21/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Emmett Wyman (Rochester) DTSTART:20211028T151500Z DTEND:20211028T161500Z DTSTAMP:20260422T212707Z UID:HASS21/5 DESCRIPTION:Title: E igenfunctions restricted to submanifolds and their Fourier coefficients\nby Emmett Wyman (Rochester) as part of Harmonic Analysis and Symmetric Spaces 2021\n\n\nAbstract\nConsider a Laplace-Beltrami eigenfunction on so me compact manifold\, and restrict it to a compact submanifold. We may wri te the restricted eigenfunction as a combination of eigenbasis elements in trinsic to the submanifold\, whose coefficients we will call Fourier coeff icients. What does the spectral decomposition of the restricted eigenfunct ion look like? How much of the mass of the Fourier coefficients is concent rated near the eigenvalue? Do the Fourier coefficients "feel" the geometry of the submanifold or ambient manifold? If so\, how?\n\nI will present jo int work with Yakun Xi and Steve Zelditch on such questions. Indeed\, vari ous aspects of these Fourier coefficients reflect the geometry of the subm anifold and ambient space. Of particular importance are configurations of "geodesic bi-angles\," which consist of a pair of geodesics\, one in the a mbient manifold and one intrinsic to the submanifold\, with shared endpoin ts. These bi-angles arise in the wavefront set analysis a la the Duisterma at-Guillemin theorem.\n LOCATION:https://researchseminars.org/talk/HASS21/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Angela Pasquale (Lorraine) DTSTART:20211028T190000Z DTEND:20211028T200000Z DTSTAMP:20260422T212707Z UID:HASS21/6 DESCRIPTION:Title: R esonances of the Laplacian on Riemannian symmetric spaces of the noncompac t type of rank 2\nby Angela Pasquale (Lorraine) as part of Harmonic An alysis and Symmetric Spaces 2021\n\n\nAbstract\nLet $X=G/K$ be a Riemannia n symmetric space of non-compact type and let $\\Delta$ be the positive La placian of $X$\, with spectrum $\\sigma(\\Delta)$. Then the resolvent $R(z )=(\\Delta-z)^{-1}$ is a holomorphic function on $\\mathbb{C}\\setminus \\ sigma(\\Delta)$ with values in the space of bounded linear operators on $L ^2(X)$. If $R$ admits a meromorphic continuation across $\\sigma(\\Delta)$ \, then the poles of the meromorphically extended resolvent are called the resonances of $\\Delta$. At present\, there are no general results on the existence and the nature of resonances on a general $X=G/K$. In this talk \, we will mostly focus on the case of rank two.\n\nThis is part of a join t project with J. Hilgert (Paderborn University) and T. Przebinda (Univers ity of Oklahoma).\n LOCATION:https://researchseminars.org/talk/HASS21/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Melissa Tacy (University of Auckland) DTSTART:20211028T201500Z DTEND:20211028T211500Z DTSTAMP:20260422T212707Z UID:HASS21/7 DESCRIPTION:Title: A pplications of semiclassical analysis to harmonic analysis\nby Melissa Tacy (University of Auckland) as part of Harmonic Analysis and Symmetric Spaces 2021\n\n\nAbstract\nSemiclassical analysis is a form of microlocal analysis specialised to study parameter problems. It is highly effective f or treating "high frequency/energy" style problems arising in harmonic ana lysis. In this talk I will discuss some of the ideas\, heuristics and tech niques of semiclassical analysis with a particular focus on applications i n harmonic analysis.\n LOCATION:https://researchseminars.org/talk/HASS21/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Yunfeng Zhang (Peking University) DTSTART:20211029T140000Z DTEND:20211029T150000Z DTSTAMP:20260422T212707Z UID:HASS21/8 DESCRIPTION:Title: F ourier restriction bounds on compact symmetric spaces\nby Yunfeng Zhan g (Peking University) as part of Harmonic Analysis and Symmetric Spaces 20 21\n\n\nAbstract\nIn this talk I will make a survey of bounds of "Fourier restriction" type on compact Lie groups and more generally compact globall y symmetric spaces. These include Laplace-Beltrami eigenfunction bound\, S trichartz estimate for the Schrodinger equation\, and joint eigenfunction bound for invariant differential operators. Optimal bounds are all open\, for which a more refined combination of Lie theory and analysis would be n eeded.\n LOCATION:https://researchseminars.org/talk/HASS21/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Philippe Anker (Orléans) DTSTART:20211029T151500Z DTEND:20211029T161500Z DTSTAMP:20260422T212707Z UID:HASS21/9 DESCRIPTION:Title: D ispersive PDE on noncompact symmetric spaces\nby Jean-Philippe Anker ( Orléans) as part of Harmonic Analysis and Symmetric Spaces 2021\n\n\nAbst ract\nMy talk will be devoted to the Schrödinger equation and to the wave equation on general Riemannian symmetric spaces of noncompact type. The m ain issue consists in obtaining good pointwise estimates of their fundamen tal solutions. This is achieved by combining the inverse spherical Fourier transform with the following tools: on the one hand\, a barycentric decom position\, which allows us to handle the Plancherel density as if it were a differentiable symbol\, and\, on the other hand\, an improved Hadamard p arametrix for the wave equation. As consequences\, we deduce dispersive es timates and Strichartz inequalities for the linear equations\, which are s tronger than their Euclidean counterparts\, as well as better results for the nonlinear equations. All this is based on joint works including sever al collaborators: Vittoria Pierfelice in rank one\, Hong-Wei Zhang in high er rank\, with contributions by Maria Vallarino and Stefano Meda.\n LOCATION:https://researchseminars.org/talk/HASS21/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Jasmin Matz (Copenhagen) DTSTART:20211029T163000Z DTEND:20211029T173000Z DTSTAMP:20260422T212707Z UID:HASS21/10 DESCRIPTION:Title: Quantum ergodicity in the level aspect\nby Jasmin Matz (Copenhagen) as part of Harmonic Analysis and Symmetric Spaces 2021\n\n\nAbstract\nA clas sical result of Shnirelman and others shows that closed Riemannian manifol ds of negative curvature are quantum ergodic\, meaning that on average the probability measures $|f|^2 dx$ on $M$\, with $f$ running through normali zed Laplace eigenfunctions on $M$ with growing eigenvalue\, converge towar ds the Riemannian measure $dx$ on $M$.\n\nFollowing ideas of Abert\, Berge ron\, Le Masson\, and Sahlsten\, we look at a related situation: We want t o consider certain sequences of manifolds together with Laplace eigenfunct ions of approximately the same eigenvalue instead of high energy eigenfunc tions on a fixed manifold. In my talk I want to discuss joint work with F. Brumley in which we study this situation in higher rank for sequences of compact quotients of $SL(n\,\\mathbb{R})/SO(n)$.\n LOCATION:https://researchseminars.org/talk/HASS21/10/ END:VEVENT END:VCALENDAR