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:20260404T094150Z UID:HASS21/1 DESCRIPTION:Title: Eigenfunctions on random hyperbolic surfaces\nby Etienne Le Mass on (Paris Cergy) as part of Harmonic Analysis and Symmetric Spaces 2021\n\ n\nAbstract\nHigh frequency eigenfunctions on hyperbolic surfaces are know n to exhibit some universal behaviour of delocalisation and randomness. We will introduce some results on the behaviour of eigenfunctions on random compact hyperbolic surfaces\, in the limit where the genus (or equivalentl y the volume) tends to infinity\, and the frequency is in a fixed window. These results suggest that in this large scale limit we can expect similar universal behaviour. We will focus on the Weil-Petersson model of random surfaces introduced by Mirzakhani.\n\nBased on joint works with Tuomas Sah lsten and Joe Thomas.\n LOCATION:https://stable.researchseminars.org/talk/HASS21/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Bart Michels (Sorbonne Paris Nord) DTSTART:20211027T151500Z DTEND:20211027T161500Z DTSTAMP:20260404T094150Z UID:HASS21/2 DESCRIPTION:Title: Mean square asymptotics and oscillatory integrals for maximal flat s ubmanifolds of locally symmetric spaces\nby Bart Michels (Sorbonne Par is Nord) as part of Harmonic Analysis and Symmetric Spaces 2021\n\n\nAbstr act\nGiven a compact locally symmetric space of non-compact type\, we pres ent a mean square asymptotic for integrals of eigenfunctions along maximal flat submanifolds\, constrained to eigenfunctions with suitably generic s pectral parameter. This is motivated by questions concerning the maximal s ize of automorphic periods. The proof uses the pre-trace formula. The anal ysis of orbital integrals requires knowledge about the geometry of maximal flat submanifolds of the globally symmetric space S. When S is the hyperb olic plane\, modeled by the upper half plane\, the maximal flat submanifol ds are geodesics\, and they are lines or half-circles orthogonal to the re al axis. The midpoints of the half-circles play a critical role\, as do th eir analogues in higher rank spaces\, and one is led to generalize their p roperties as well as other facts about maximal flat submanifolds.\n LOCATION:https://stable.researchseminars.org/talk/HASS21/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Matthew Blair (New Mexico) DTSTART:20211027T163000Z DTEND:20211027T173000Z DTSTAMP:20260404T094150Z UID:HASS21/3 DESCRIPTION:Title: Lp bounds for eigenfunctions at the critial exponent\nby Matthew Blair (New Mexico) as part of Harmonic Analysis and Symmetric Spaces 2021 \n\n\nAbstract\nWe consider upper bounds on the growth of $L^pa$ norms of eigenfunctions of the Laplacian on a compact Riemannian manifold in the hi gh frequency limit. In particular\, we seek to identify geometric or dynam ical conditions on the manifold which yield improvements on the universal $L^p$ bounds of C. Sogge. The emphasis will be on bounds at the "critical exponent"\, where a spectrum of scenarios for phase space concentration mu st be considered. We then discuss a recent work with C. Sogge which shows that when the sectional curvatures are nonpositive\, there is a logarithmi c type gain in the known $L^p$ bounds at the critical exponent.\n LOCATION:https://stable.researchseminars.org/talk/HASS21/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Yaiza Canzani (North Carolina) DTSTART:20211028T140000Z DTEND:20211028T150000Z DTSTAMP:20260404T094150Z UID:HASS21/4 DESCRIPTION:Title: Eigenfunction concentration via geodesic beams\nby Yaiza Canzani (North Carolina) as part of Harmonic Analysis and Symmetric Spaces 2021\n \n\nAbstract\nA vast array of physical phenomena\, ranging from the propag ation of waves to the location of quantum particles\, is dictated by the b ehavior of Laplace eigenfunctions. Because of this\, it is crucial to unde rstand how various measures of eigenfunction concentration respond to the background dynamics of the geodesic flow. In collaboration with J. Galkows ki\, we developed a framework to approach this problem that hinges on deco mposing eigenfunctions into geodesic beams. In this talk\, I will present these techniques and explain how to use them to obtain quantitative improv ements on the standard estimates for the eigenfunction's pointwise behavio r\, $L^p$ norms\, and Weyl Laws. One consequence of this method is a quant itatively improved Weyl Law for the eigenvalue counting function on all pr oduct manifolds.\n LOCATION:https://stable.researchseminars.org/talk/HASS21/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Emmett Wyman (Rochester) DTSTART:20211028T151500Z DTEND:20211028T161500Z DTSTAMP:20260404T094150Z UID:HASS21/5 DESCRIPTION:Title: Eigenfunctions restricted to submanifolds and their Fourier coeffici ents\nby Emmett Wyman (Rochester) as part of Harmonic Analysis and Sym metric Spaces 2021\n\n\nAbstract\nConsider a Laplace-Beltrami eigenfunctio n on some compact manifold\, and restrict it to a compact submanifold. We may write the restricted eigenfunction as a combination of eigenbasis elem ents intrinsic to the submanifold\, whose coefficients we will call Fourie r coefficients. What does the spectral decomposition of the restricted eig enfunction look like? How much of the mass of the Fourier coefficients is concentrated near the eigenvalue? Do the Fourier coefficients "feel" the g eometry of the submanifold or ambient manifold? If so\, how?\n\nI will pre sent joint work with Yakun Xi and Steve Zelditch on such questions. Indeed \, various aspects of these Fourier coefficients reflect the geometry of t he submanifold and ambient space. Of particular importance are configurati ons of "geodesic bi-angles\," which consist of a pair of geodesics\, one i n the ambient manifold and one intrinsic to the submanifold\, with shared endpoints. These bi-angles arise in the wavefront set analysis a la the Du istermaat-Guillemin theorem.\n LOCATION:https://stable.researchseminars.org/talk/HASS21/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Angela Pasquale (Lorraine) DTSTART:20211028T190000Z DTEND:20211028T200000Z DTSTAMP:20260404T094150Z UID:HASS21/6 DESCRIPTION:Title: Resonances of the Laplacian on Riemannian symmetric spaces of the no ncompact type of rank 2\nby Angela Pasquale (Lorraine) as part of Harm onic Analysis and Symmetric Spaces 2021\n\n\nAbstract\nLet $X=G/K$ be a Ri emannian symmetric space of non-compact type and let $\\Delta$ be the posi tive Laplacian of $X$\, with spectrum $\\sigma(\\Delta)$. Then the resolve nt $R(z)=(\\Delta-z)^{-1}$ is a holomorphic function on $\\mathbb{C}\\setm inus \\sigma(\\Delta)$ with values in the space of bounded linear operator s on $L^2(X)$. If $R$ admits a meromorphic continuation across $\\sigma(\\ Delta)$\, then the poles of the meromorphically extended resolvent are cal led 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 th is talk\, we will mostly focus on the case of rank two.\n\nThis is part of a joint project with J. Hilgert (Paderborn University) and T. Przebinda ( University of Oklahoma).\n LOCATION:https://stable.researchseminars.org/talk/HASS21/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Melissa Tacy (University of Auckland) DTSTART:20211028T201500Z DTEND:20211028T211500Z DTSTAMP:20260404T094150Z UID:HASS21/7 DESCRIPTION:Title: Applications of semiclassical analysis to harmonic analysis\nby Melissa Tacy (University of Auckland) as part of Harmonic Analysis and Sym metric Spaces 2021\n\n\nAbstract\nSemiclassical analysis is a form of micr olocal analysis specialised to study parameter problems. It is highly effe ctive for treating "high frequency/energy" style problems arising in harmo nic analysis. In this talk I will discuss some of the ideas\, heuristics a nd techniques of semiclassical analysis with a particular focus on applica tions in harmonic analysis.\n LOCATION:https://stable.researchseminars.org/talk/HASS21/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Yunfeng Zhang (Peking University) DTSTART:20211029T140000Z DTEND:20211029T150000Z DTSTAMP:20260404T094150Z UID:HASS21/8 DESCRIPTION:Title: Fourier restriction bounds on compact symmetric spaces\nby Yunfe ng Zhang (Peking University) as part of Harmonic Analysis and Symmetric Sp aces 2021\n\n\nAbstract\nIn this talk I will make a survey of bounds of "F ourier restriction" type on compact Lie groups and more generally compact globally symmetric spaces. These include Laplace-Beltrami eigenfunction bo und\, Strichartz estimate for the Schrodinger equation\, and joint eigenfu nction bound for invariant differential operators. Optimal bounds are all open\, for which a more refined combination of Lie theory and analysis wou ld be needed.\n LOCATION:https://stable.researchseminars.org/talk/HASS21/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Philippe Anker (Orléans) DTSTART:20211029T151500Z DTEND:20211029T161500Z DTSTAMP:20260404T094150Z UID:HASS21/9 DESCRIPTION:Title: Dispersive PDE on noncompact symmetric spaces\nby Jean-Philippe Anker (Orléans) as part of Harmonic Analysis and Symmetric Spaces 2021\n\ n\nAbstract\nMy talk will be devoted to the Schrödinger equation and to t he wave equation on general Riemannian symmetric spaces of noncompact type . The main issue consists in obtaining good pointwise estimates of their f undamental solutions. This is achieved by combining the inverse spherical Fourier transform with the following tools: on the one hand\, a barycentri c decomposition\, which allows us to handle the Plancherel density as if i t were a differentiable symbol\, and\, on the other hand\, an improved Had amard parametrix for the wave equation. As consequences\, we deduce disper sive estimates and Strichartz inequalities for the linear equations\, whic h are stronger than their Euclidean counterparts\, as well as better resul ts for the nonlinear equations. All this is based on joint works includin g several collaborators: Vittoria Pierfelice in rank one\, Hong-Wei Zhang in higher rank\, with contributions by Maria Vallarino and Stefano Meda.\n LOCATION:https://stable.researchseminars.org/talk/HASS21/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Jasmin Matz (Copenhagen) DTSTART:20211029T163000Z DTEND:20211029T173000Z DTSTAMP:20260404T094150Z UID:HASS21/10 DESCRIPTION:Title: Quantum ergodicity in the level aspect\nby Jasmin Matz (Copenha gen) as part of Harmonic Analysis and Symmetric Spaces 2021\n\n\nAbstract\ nA classical result of Shnirelman and others shows that closed Riemannian manifolds of negative curvature are quantum ergodic\, meaning that on aver age the probability measures $|f|^2 dx$ on $M$\, with $f$ running through normalized Laplace eigenfunctions on $M$ with growing eigenvalue\, converg e towards the Riemannian measure $dx$ on $M$.\n\nFollowing ideas of Abert\ , Bergeron\, Le Masson\, and Sahlsten\, we look at a related situation: We want to consider certain sequences of manifolds together with Laplace eig enfunctions of approximately the same eigenvalue instead of high energy ei genfunctions 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 sequen ces of compact quotients of $SL(n\,\\mathbb{R})/SO(n)$.\n LOCATION:https://stable.researchseminars.org/talk/HASS21/10/ END:VEVENT END:VCALENDAR