BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Xuwen Zhu (Northeastern) DTSTART:20200925T161500Z DTEND:20200925T171500Z DTSTAMP:20260404T092654Z UID:analysisgeometryNE/1 DESCRIPTION:Title: Spectral properties of spherical conical metrics\nby Xuwen Zhu (Northeastern) as part of Analysis and Geometry Seminar\n\n\nA bstract\nThis talk will focus on the recent works on the spectral properti es of constant curvature metrics with conical singularities on surfaces. T he motivation comes from earlier works joint with Rafe Mazzeo on the study of deformation of such spherical metrics with large cone angles\, which s uggests that there is a deep connection between the geometric properties o f the moduli space and the analytical properties of the associated singula r Laplace operator. In this talk I will talk about a joint work with Bin X u on spectral characterization of the monodromy of such metrics\, and work in progress with Mikhail Karpukhin on the relation of spectral properties with harmonic maps.\n LOCATION:https://stable.researchseminars.org/talk/analysisgeometryNE/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Marina Prokhorova (Technion) DTSTART:20201002T161500Z DTEND:20201002T171500Z DTSTAMP:20260404T092654Z UID:analysisgeometryNE/2 DESCRIPTION:Title: Family index for self-adjoint elliptic operators on surf aces with boundary\nby Marina Prokhorova (Technion) as part of Analysi s and Geometry Seminar\n\n\nAbstract\nAn index theory for elliptic operato rs on a closed manifold was developed by Atiyah and Singer. For a family o f such operators parametrized by points of a compact space X\, they comput ed the $K^0(X)$-valued analytical index in purely topological terms. An an alog of this theory for self-adjoint elliptic operators on closed manifold s was developed by Atiyah\, Patodi\, and Singer\; the analytical index of a family in this case takes values in the $K^1$ group of a base space.\n If a manifold has non-empty boundary\, then boundary conditions come into play\, and situation becomes much more complicated. The integer-valued in dex of a single boundary value problem was computed by Atiyah\, Bott\, and Boutet de Monvel. This result was recently generalized to $K^0(X)$-valued family index by Melo\, Schrohe\, and Schick. The self-adjoint case\, howe ver\, remained open.\n In the talk I shall present a family index theore m for self-adjoint elliptic operators on a surface with boundary. I consid er such operators with self-adjoint elliptic local boundary conditions. Both operators and boundary conditions are parametrized by points of a com pact space $X$. I compute the $K^1(X)$-valued analytical index of such a f amily in terms of the topological data of the family over the boundary. A particular case of this result is the spectral flow formula for one-parame ter families of boundary value problems.\n LOCATION:https://stable.researchseminars.org/talk/analysisgeometryNE/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Shu Shen (Jussieu) DTSTART:20201009T161500Z DTEND:20201009T171500Z DTSTAMP:20260404T092654Z UID:analysisgeometryNE/3 DESCRIPTION:Title: Complex-valued analytic torsion and the dynamical zeta f unction\nby Shu Shen (Jussieu) as part of Analysis and Geometry Semina r\n\n\nAbstract\nThe relation between the spectrum of the Laplacian and th e closed geodesics on a closed Riemannian manifold is one of the central t hemes in differential geometry. Fried conjectured that the analytic torsio n\, which is an alternating product of regularized determinants of the Lap lacians\, equals the zero value of the dynamical zeta function. In this t alk\, I will explain a recent work on a relation between the complex value d analytic torsion and the dynamical zeta function with arbitrary twist on locally symmetric space\, which generalises the previous result of myself for unitary twists\, and the results of Müller and Spilioti on hyperboli c manifolds.\n LOCATION:https://stable.researchseminars.org/talk/analysisgeometryNE/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Yiannis Loizides (Cornell) DTSTART:20201023T161500Z DTEND:20201023T171500Z DTSTAMP:20260404T092654Z UID:analysisgeometryNE/4 DESCRIPTION:Title: Hamiltonian loop group spaces and a theorem of Teleman-W oodward\nby Yiannis Loizides (Cornell) as part of Analysis and Geometr y Seminar\n\n\nAbstract\nUsing algebro-geometric methods\, Teleman and Woo dward proved an interesting index formula (generalizing the Verlinde formu la) for the moduli space of G-bundles on a closed Riemann surface. I will describe an approach to reformulating and generalizing their theorem to th e smooth setting.\n LOCATION:https://stable.researchseminars.org/talk/analysisgeometryNE/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Vladimir E. Nazaikinskii (Ishlinsky Institute for Problems in Mech anics\, Moscow) DTSTART:20201016T161500Z DTEND:20201016T171500Z DTSTAMP:20260404T092654Z UID:analysisgeometryNE/5 DESCRIPTION:Title: Partial spectral flow and the Aharonov-Bohm effect in gr aphene\nby Vladimir E. Nazaikinskii (Ishlinsky Institute for Problems in Mechanics\, Moscow) as part of Analysis and Geometry Seminar\n\n\nAbstr act\nWe study the Aharonov-Bohm effect in an open-ended tube made of a gra phene sheet whose dimensions are much larger than the interatomic distance in graphene. An external magnetic field\nvanishes on and in the vicinity of the graphene sheet\, and its flux through the tube is adiabatically swi tched on. It is shown that\, in the process\, the energy levels of the tig ht-binding Hamiltonian of π-electrons unavoidably cross the Fermi level\, which results in the creation of electron-hole pairs. The number of pairs is proven to be equal to the number of magnetic flux quanta of the extern al field. The proof is based on the new notion of partial spectral flow\, which generalizes the ordinary spectral flow already having well-known app lications (such as the Kopnin forces in superconductors and superfluids) i n condensed matter physics. (joint work with Mikhail I. Katsnelson)\n LOCATION:https://stable.researchseminars.org/talk/analysisgeometryNE/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Simone Cecchini (University of Goettingen) DTSTART:20201030T161500Z DTEND:20201030T171500Z DTSTAMP:20260404T092654Z UID:analysisgeometryNE/6 DESCRIPTION:Title: A long neck principle for Riemannian spin manifolds with positive scalar curvature\nby Simone Cecchini (University of Goettin gen) as part of Analysis and Geometry Seminar\n\n\nAbstract\nWe present re sults in index theory on compact Riemannian spin manifolds with boundary i n the case when the topological information is encoded by bundles which ar e supported away from the boundary.\nAs a first application\, we establish a ``long neck principle'' for a compact Riemannian spin n-manifold with b oundary X\, stating that if scal(X) ≥ n(n-1) and there is a nonzero degr ee map f into the n-sphere which is area decreasing\, then the distance be tween the support of the differential of f and the boundary of X is at mos t π/n. This answers\, in the spin setting\, a question recently asked by Gromov.\nAs a second application\, we consider a Riemannian manifold X obt ained by removing a small n-ball from a closed spin n-manifold Y. We show that if scal(X) ≥ σ >0 and Y satisfies a certain condition expressed in terms of higher index theory\, then the width of a geodesic collar neighb orhood Is bounded from above from a constant depending on σ and n.\nFinal ly\, we consider the case of a Riemannian n-manifold V diffeomorphic to Nx [-1\,1]\, with N a closed spin manifold with nonvanishing Rosenebrg index .\nIn this case\, we show that if scal(V) ≥ n(n-1)\, then the distance b etween the boundary components of V is at most 2π/n. This last constant i s sharp by an argument due to Gromov.\n LOCATION:https://stable.researchseminars.org/talk/analysisgeometryNE/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Misha Karpukhin (Irvine) DTSTART:20201106T171500Z DTEND:20201106T181500Z DTSTAMP:20260404T092654Z UID:analysisgeometryNE/7 DESCRIPTION:Title: Eigenvalues of the Laplacian and min-max for the energy functional\nby Misha Karpukhin (Irvine) as part of Analysis and Geomet ry Seminar\n\n\nAbstract\nThe Laplacian is a canonical second order ellipt ic operator defined on any Riemannian manifold. The study of optimal upper bounds for its eigenvalues is a classical problem of spectral geometry go ing back to J. Hersch\, P. Li and S.-T. Yau. It turns out that the optimal isoperimetric inequalities for Laplacian eigenvalues are closely related to minimal surfaces and harmonic maps. In the present talk we survey recen t developments in the field. In particular\, we will discuss a min-max con struction for the energy functional and its applications to eigenvalue ine qualities\, including the regularity theorem for optimal metrics. The talk is based on the joint work with D. Stern.\n LOCATION:https://stable.researchseminars.org/talk/analysisgeometryNE/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Hadrian Quan (Urbana-Champaign) DTSTART:20201113T171500Z DTEND:20201113T181500Z DTSTAMP:20260404T092654Z UID:analysisgeometryNE/8 DESCRIPTION:Title: Sub-Riemannian Limit of the differential form heat kerne ls of contact manifolds\nby Hadrian Quan (Urbana-Champaign) as part of Analysis and Geometry Seminar\n\n\nAbstract\nWe present work investigatin g the behavior of the heat kernel of the Hodge Laplacian on a contact mani fold endowed with a family of Riemannian metrics that blow-up the directio ns transverse to the contact distribution. We apply this to analyze the be havior of global spectral invariants such as the η-invariant and the dete rminant of the Laplacian. In particular we prove that contact versions of the relative η-invariant and the relative analytic torsion are equal to t heir Riemannian analogues and hence topological. (Joint work with Pierre A lbin)\n LOCATION:https://stable.researchseminars.org/talk/analysisgeometryNE/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Laura Fredrickson (U. of Oregon) DTSTART:20201120T171500Z DTEND:20201120T181500Z DTSTAMP:20260404T092654Z UID:analysisgeometryNE/9 DESCRIPTION:Title: The asymptotic geometry of the Hitchin moduli space\ nby Laura Fredrickson (U. of Oregon) as part of Analysis and Geometry Semi nar\n\n\nAbstract\nHitchin's equations are a system of gauge theoretic equ ations on a Riemann surface that are of interest in many areas including r epresentation theory\, Teichm\\"uller theory\, and the geometric Langlands correspondence. The Hitchin moduli space carries a natural hyperk\\"ahler metric. An intricate conjectural description of its asymptotic structure appears in the work of Gaiotto-Moore-Neitzke and there has been a lot of progress on this recently. I will discuss some recent results using tools coming out of geometric analysis which are well-suited for verifying thes e extremely delicate conjectures. This strategy often stretches the limits of what can currently be done via geometric analysis\, and simultaneously leads to new insights into these conjectures.\n LOCATION:https://stable.researchseminars.org/talk/analysisgeometryNE/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Charles Ouyang (U. Mass Amherst) DTSTART:20201204T171500Z DTEND:20201204T181500Z DTSTAMP:20260404T092654Z UID:analysisgeometryNE/10 DESCRIPTION:Title: Length spectrum compactification of the SL(3\,R)-Hitchi n component\nby Charles Ouyang (U. Mass Amherst) as part of Analysis a nd Geometry Seminar\n\n\nAbstract\nHitchin components are natural generali zations of the classical\nTeichmüller space. In the setting of SL(3\,R)\, the Hitchin component\nparameterizes the holonomies of convex real projec tive structures. By\nstudying Blaschke metrics\, which are Riemannian metr ics associated to such\nstructures\, along with their limits\, we obtain a compactification of the\nSL(3\,R) Hitchin component. We show the boundary objects are hybrid\nstructures\, which are in part flat metric and in par t laminar. These\nhybrid objects are natural generalizations of measured l aminations\, which\nare the boundary objects in Thurston's compactificatio n of Teichmüller\nspace. (joint work with Andrea Tamburelli)\n LOCATION:https://stable.researchseminars.org/talk/analysisgeometryNE/10/ END:VEVENT END:VCALENDAR