BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Nelia Charalambous (University of Cyprus) DTSTART:20201217T143000Z DTEND:20201217T153000Z DTSTAMP:20260404T095423Z UID:VMWinGeomAnalysis/1 DESCRIPTION:Title: The form spectrum of open manifolds\nby Nelia Charala mbous (University of Cyprus) as part of Virtual Mini-Workshop in Geometric Analysis\n\n\nAbstract\nThe computation of the essential spectrum of the Laplacian requires the construction of a large class of test differential forms. On a general open manifold this is a difficult task\, since there e xists only a small collection of canonically defined differential forms to work with. In our work with Zhiqin Lu\, we compute the essential k-form s pectrum over asymptotically flat manifolds by combining two methods: First \, we introduce a new version of the generalized Weyl criterion\, which gr eatly reduces the regularity and smoothness of the test differential forms \; second\, we make use of Cheeger-Fukaya-Gromov theory and Cheeger-Coldin g theory to obtain a new type of test differential forms at the ends of th e manifold. We also use the generalized Weyl criterion to obtain other int eresting facts about the k-form essential spectrum over an open manifold.\ n LOCATION:https://stable.researchseminars.org/talk/VMWinGeomAnalysis/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Strohmaier (University of Leeds) DTSTART:20201217T154500Z DTEND:20201217T164500Z DTSTAMP:20260404T095423Z UID:VMWinGeomAnalysis/2 DESCRIPTION:Title: The spectral shift function and a relative trace formula< /a>\nby Alexander Strohmaier (University of Leeds) as part of Virtual Min i-Workshop in Geometric Analysis\n\n\nAbstract\nSpectral theory of the Lap lace operator on asymptotically Euclidean manifolds is described to a cert ain extent by stationary scattering theory. I will define the spectral shi ft function in this context and review some results for scattering of p-fo rms and their application. \nIn the second part of the talk I will special ise to obstacle scattering and explain a new trace formula and its relatio n to the spectral shift function. If there is time I will give some applic ations in physics. (based on joint work with Y. Fang\, F. Hanisch and A. W aters)\n LOCATION:https://stable.researchseminars.org/talk/VMWinGeomAnalysis/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Theodora Bourni (University of Tennessee) DTSTART:20201217T183000Z DTEND:20201217T193000Z DTSTAMP:20260404T095423Z UID:VMWinGeomAnalysis/3 DESCRIPTION:Title: Ancient solutions to mean curvature flow\nby Theodora Bourni (University of Tennessee) as part of Virtual Mini-Workshop in Geom etric Analysis\n\n\nAbstract\nMean curvature flow (MCF) is the gradient fl ow of the area functional\; it moves the surface in the direction of steep est decrease of area. An important motivation for the study of MCF comes from its potential geometric applications\, such as classification theorem s and geometric inequalities. MCF develops ``singularities'' (curvature bl ow-up)\, which obstruct the flow from existing for all times and therefore understanding these high curvature regions is of great interest. This is done by studying ancient solutions\, solutions that have existed for all times in the past\, and which model singularities. In this talk we will di scuss their importance and ways of constructing and classifying such solut ions. In particular\, we will focus on ``collapsed'' solutions and constru ct\, in all dimensions $n\\ge 2$\, a large family of new examples\, includ ing both symmetric and asymmetric examples\, as well as many eternal examp les that do not evolve by translation. Moreover\, we will show that colla psed solutions decompose ``backwards in time'' into a canonical configurat ion of Grim hyperplanes which satisfies certain necessary conditions. This is joint work with Mat Langford and Giuseppe Tinaglia.\n LOCATION:https://stable.researchseminars.org/talk/VMWinGeomAnalysis/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Lazaro Recht (IAM) DTSTART:20201217T194500Z DTEND:20201217T204500Z DTSTAMP:20260404T095423Z UID:VMWinGeomAnalysis/4 DESCRIPTION:Title: The Poincaré Half Space of a C* Algebra\nby Lazaro Recht (IAM) as part of Virtual Mini-Workshop in Geometric Analysis\n\n\nAb stract\nFor the abstract\, please look at the homepage of the event:\nhttp s://matematicas.uniandes.edu.co/es/workshop-geometric-analysis.\n LOCATION:https://stable.researchseminars.org/talk/VMWinGeomAnalysis/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Florent Schaffhauser (Universidad de los Andes) DTSTART:20201218T143000Z DTEND:20201218T153000Z DTSTAMP:20260404T095423Z UID:VMWinGeomAnalysis/5 DESCRIPTION:Title: Twisted local systems and equivariant harmonic maps\n by Florent Schaffhauser (Universidad de los Andes) as part of Virtual Mini -Workshop in Geometric Analysis\n\n\nAbstract\nDiscrete subgroups of PSL(2 \;R) can be interpreted geometrically as hyperbolic 2-orbifolds. In the ab sence of torsion\, a finite-dimensional representation of such a group giv es a rise to a local system on a surface. To classify the latter up to iso morphism (on a compact surface)\, it is useful to equip these objects with special Hermitian metrics. Corlette's theory gives a construction of such metrics in terms of equivariant harmonic maps\, going from the hyperbolic plane to the symmetric space of a semisimple Lie group. In this talk\, we recall the main features of this theory and discuss how to generalize it in order to include discrete subgroups of PSL(2\;R) that are no longer tor sion-free.\n LOCATION:https://stable.researchseminars.org/talk/VMWinGeomAnalysis/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Ksenia Fedosova (University of Freiburg) DTSTART:20201218T154500Z DTEND:20201218T164500Z DTSTAMP:20260404T095423Z UID:VMWinGeomAnalysis/6 DESCRIPTION:Title: On a generalization of transfer operators\nby Ksenia Fedosova (University of Freiburg) as part of Virtual Mini-Workshop in Geom etric Analysis\n\n\nAbstract\nFor hyperbolic manifolds\, there exists a st raightforward connection between the spectral and the geometric data. More precisely\, the lengths of its closed geodesics and the spectrum of its L aplace operator acting on functions are connected by the Selberg trace for mula\, that can be considered a sibling of the Poisson summation formula. Selberg trace formula provides the information on the eigenvalues of the L aplace operator\, however\, completely ignoring its eigenfunctions.\n \nTh ere exists a method\, originated from the classical statistical mechanics\ , that allows to obtain more information on the eigenfunctions. The method \, called the transfer operator approach\, involves a construction of a so -called transfer operator from a certain discretisation of the geodesic fl ow on the manifold. For a modular surface\, this transfer operator is ulti mately connected to a Gauss map. One can show that the 1-eigenfunctions of this operator correspond via a certain integral transform to the eigenfun ctions of the Laplace operator. The integral transform mirrors the Eichler -Shimura-Manin isomorphism.\n \nIn this talk\, inspired by Bismut's hypoel liptic Laplacians\, we try to construct an analogue of the transfer operat or\, using the Brownian paths on the manifold instead of the geodesics. We obtain an operator\, whose 1-eigenfunctions turn out to be the boundary f orms of eigenfunctions of the Laplace operator.\n LOCATION:https://stable.researchseminars.org/talk/VMWinGeomAnalysis/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Rafe Mazzeo (Stanford University) DTSTART:20201218T183000Z DTEND:20201218T193000Z DTSTAMP:20260404T095423Z UID:VMWinGeomAnalysis/7 DESCRIPTION:Title: ALG spaces and Hitchin systems\nby Rafe Mazzeo (Stanf ord University) as part of Virtual Mini-Workshop in Geometric Analysis\n\n \nAbstract\nAn ALG space is a 4-dimensional hyperkaehler manifold with a v ery special asymptotic structure. I will survey some known results about t heir geometry and topology and some recent results by others about their m oduli. These spaces can also arise as moduli spaces for solutions of the H itchin equations. The precise correspondence between these two rather dif ferent pictures is a special case of Boalch’s `modularity conjecture’. This talk will focus mostly on describing the various ingredients and tec hniques that go into this\, leading to a description of some recent progre ss obtained in collaboration with Fredrickson\, Swoboda and Weiss.\n LOCATION:https://stable.researchseminars.org/talk/VMWinGeomAnalysis/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Raquel Perales (IMATE-UNAM) DTSTART:20201218T194500Z DTEND:20201218T204500Z DTSTAMP:20260404T095423Z UID:VMWinGeomAnalysis/8 DESCRIPTION:Title: Limits of manifolds with boundary\nby Raquel Perales (IMATE-UNAM) as part of Virtual Mini-Workshop in Geometric Analysis\n\n\nA bstract\nI will discuss available convergence results for manifolds with b oundary. \nIn particular\, we will focus on intrinsic flat and Gromov-Haus dorff convergence results. \nWe will first consider convergence of sequenc es of manifolds with Ricci curvature and mean curvature bounds and we will finalize with a convergence result for sequences of the form $(M\,g_j)$\, $j=0\,1\,...$\, that satisfy $d_{g_0} \\leq d_{g_j}$\, among other con ditions\, and where we are able to show that the limit equals $(M\,g_0)$.\ n LOCATION:https://stable.researchseminars.org/talk/VMWinGeomAnalysis/8/ END:VEVENT END:VCALENDAR