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:20260422T212752Z UID:analysisgeometryNE/1 DESCRIPTION:Title: Spectral properties of spherical conical metrics\nby Xuwen Zhu (Northeastern) as part of Analysis and Geometry Seminar\n\n\nAbstract \nThis talk will focus on the recent works on the spectral properties of c onstant curvature metrics with conical singularities on surfaces. The moti vation comes from earlier works joint with Rafe Mazzeo on the study of def ormation of such spherical metrics with large cone angles\, which suggests that there is a deep connection between the geometric properties of the m oduli space and the analytical properties of the associated singular Lapla ce operator. In this talk I will talk about a joint work with Bin Xu on sp ectral characterization of the monodromy of such metrics\, and work in pro gress with Mikhail Karpukhin on the relation of spectral properties with h armonic maps.\n LOCATION:https://researchseminars.org/talk/analysisgeometryNE/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Marina Prokhorova (Technion) DTSTART:20201002T161500Z DTEND:20201002T171500Z DTSTAMP:20260422T212752Z UID:analysisgeometryNE/2 DESCRIPTION:Title: Family index for self-adjoint elliptic operators on surfaces wi th boundary\nby Marina Prokhorova (Technion) as part of Analysis and G eometry Seminar\n\n\nAbstract\nAn index theory for elliptic operators on a closed manifold was developed by Atiyah and Singer. For a family of such operators parametrized by points of a compact space X\, they computed the $K^0(X)$-valued analytical index in purely topological terms. An analog of this theory for self-adjoint elliptic operators on closed manifolds was d eveloped by Atiyah\, Patodi\, and Singer\; the analytical index of a famil y in this case takes values in the $K^1$ group of a base space.\n If a m anifold has non-empty boundary\, then boundary conditions come into play\, and situation becomes much more complicated. The integer-valued index 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\, however\, r emained open.\n In the talk I shall present a family index theorem for s elf-adjoint elliptic operators on a surface with boundary. I consider such operators with self-adjoint elliptic local boundary conditions. Both op erators and boundary conditions are parametrized by points of a compact sp ace $X$. I compute the $K^1(X)$-valued analytical index of such a family i n terms of the topological data of the family over the boundary. A particu lar case of this result is the spectral flow formula for one-parameter fam ilies of boundary value problems.\n LOCATION:https://researchseminars.org/talk/analysisgeometryNE/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Shu Shen (Jussieu) DTSTART:20201009T161500Z DTEND:20201009T171500Z DTSTAMP:20260422T212752Z UID:analysisgeometryNE/3 DESCRIPTION:Title: Complex-valued analytic torsion and the dynamical zeta function \nby Shu Shen (Jussieu) as part of Analysis and Geometry Seminar\n\n\n Abstract\nThe relation between the spectrum of the Laplacian and the close d geodesics on a closed Riemannian manifold is one of the central themes i n differential geometry. Fried conjectured that the analytic torsion\, whi ch is an alternating product of regularized determinants of the Laplacians \, equals the zero value of the dynamical zeta function. In this talk\, I will explain a recent work on a relation between the complex valued analy tic torsion and the dynamical zeta function with arbitrary twist on locall y symmetric space\, which generalises the previous result of myself for un itary twists\, and the results of Müller and Spilioti on hyperbolic manif olds.\n LOCATION:https://researchseminars.org/talk/analysisgeometryNE/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Yiannis Loizides (Cornell) DTSTART:20201023T161500Z DTEND:20201023T171500Z DTSTAMP:20260422T212752Z UID:analysisgeometryNE/4 DESCRIPTION:Title: Hamiltonian loop group spaces and a theorem of Teleman-Woodward \nby Yiannis Loizides (Cornell) as part of Analysis and Geometry Semin ar\n\n\nAbstract\nUsing algebro-geometric methods\, Teleman and Woodward p roved an interesting index formula (generalizing the Verlinde formula) for the moduli space of G-bundles on a closed Riemann surface. I will describ e an approach to reformulating and generalizing their theorem to the smoot h setting.\n LOCATION:https://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:20260422T212752Z UID:analysisgeometryNE/5 DESCRIPTION:Title: Partial spectral flow and the Aharonov-Bohm effect in graphene< /a>\nby Vladimir E. Nazaikinskii (Ishlinsky Institute for Problems in Mech anics\, Moscow) as part of Analysis and Geometry Seminar\n\n\nAbstract\nWe study the Aharonov-Bohm effect in an open-ended tube made of a graphene s heet whose dimensions are much larger than the interatomic distance in gra phene. An external magnetic field\nvanishes on and in the vicinity of the graphene sheet\, and its flux through the tube is adiabatically switched o n. It is shown that\, in the process\, the energy levels of the tight-bind ing Hamiltonian of π-electrons unavoidably cross the Fermi level\, which results in the creation of electron-hole pairs. The number of pairs is pro ven to be equal to the number of magnetic flux quanta of the external fiel d. The proof is based on the new notion of partial spectral flow\, which g eneralizes the ordinary spectral flow already having well-known applicatio ns (such as the Kopnin forces in superconductors and superfluids) in conde nsed matter physics. (joint work with Mikhail I. Katsnelson)\n LOCATION:https://researchseminars.org/talk/analysisgeometryNE/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Simone Cecchini (University of Goettingen) DTSTART:20201030T161500Z DTEND:20201030T171500Z DTSTAMP:20260422T212752Z UID:analysisgeometryNE/6 DESCRIPTION:Title: A long neck principle for Riemannian spin manifolds with positi ve scalar curvature\nby Simone Cecchini (University of Goettingen) as part of Analysis and Geometry Seminar\n\n\nAbstract\nWe present results i n index theory on compact Riemannian spin manifolds with boundary in the c ase when the topological information is encoded by bundles which are suppo rted away from the boundary.\nAs a first application\, we establish a ``lo ng neck principle'' for a compact Riemannian spin n-manifold with boundary X\, stating that if scal(X) ≥ n(n-1) and there is a nonzero degree map f into the n-sphere which is area decreasing\, then the distance between t he support of the differential of f and the boundary of X is at most π/n. This answers\, in the spin setting\, a question recently asked by Gromov. \nAs a second application\, we consider a Riemannian manifold X obtained b y 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 neighborhood Is bounded from above from a constant depending on σ and n.\nFinally\, 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 t his case\, we show that if scal(V) ≥ n(n-1)\, then the distance between the boundary components of V is at most 2π/n. This last constant is sharp by an argument due to Gromov.\n LOCATION:https://researchseminars.org/talk/analysisgeometryNE/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Misha Karpukhin (Irvine) DTSTART:20201106T171500Z DTEND:20201106T181500Z DTSTAMP:20260422T212752Z UID:analysisgeometryNE/7 DESCRIPTION:Title: Eigenvalues of the Laplacian and min-max for the energy functio nal\nby Misha Karpukhin (Irvine) as part of Analysis and Geometry Semi nar\n\n\nAbstract\nThe Laplacian is a canonical second order elliptic oper ator defined on any Riemannian manifold. The study of optimal upper bounds for its eigenvalues is a classical problem of spectral geometry going bac k to J. Hersch\, P. Li and S.-T. Yau. It turns out that the optimal isoper imetric inequalities for Laplacian eigenvalues are closely related to mini mal surfaces and harmonic maps. In the present talk we survey recent devel opments in the field. In particular\, we will discuss a min-max constructi on for the energy functional and its applications to eigenvalue inequaliti es\, including the regularity theorem for optimal metrics. The talk is bas ed on the joint work with D. Stern.\n LOCATION:https://researchseminars.org/talk/analysisgeometryNE/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Hadrian Quan (Urbana-Champaign) DTSTART:20201113T171500Z DTEND:20201113T181500Z DTSTAMP:20260422T212752Z UID:analysisgeometryNE/8 DESCRIPTION:Title: Sub-Riemannian Limit of the differential form heat kernels of c ontact manifolds\nby Hadrian Quan (Urbana-Champaign) as part of Analys is and Geometry Seminar\n\n\nAbstract\nWe present work investigating the b ehavior of the heat kernel of the Hodge Laplacian on a contact manifold en dowed with a family of Riemannian metrics that blow-up the directions tran sverse to the contact distribution. We apply this to analyze the behavior of global spectral invariants such as the η-invariant and the determinant of the Laplacian. In particular we prove that contact versions of the rel ative η-invariant and the relative analytic torsion are equal to their Ri emannian analogues and hence topological. (Joint work with Pierre Albin)\n LOCATION:https://researchseminars.org/talk/analysisgeometryNE/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Laura Fredrickson (U. of Oregon) DTSTART:20201120T171500Z DTEND:20201120T181500Z DTSTAMP:20260422T212752Z UID:analysisgeometryNE/9 DESCRIPTION:Title: The asymptotic geometry of the Hitchin moduli space\nby Lau ra Fredrickson (U. of Oregon) as part of Analysis and Geometry Seminar\n\n \nAbstract\nHitchin's equations are a system of gauge theoretic equations on a Riemann surface that are of interest in many areas including represen tation theory\, Teichm\\"uller theory\, and the geometric Langlands corres pondence. The Hitchin moduli space carries a natural hyperk\\"ahler metric . An intricate conjectural description of its asymptotic structure appear s in the work of Gaiotto-Moore-Neitzke and there has been a lot of progres s on this recently. I will discuss some recent results using tools coming out of geometric analysis which are well-suited for verifying these extre mely delicate conjectures. This strategy often stretches the limits of wha t can currently be done via geometric analysis\, and simultaneously leads to new insights into these conjectures.\n LOCATION:https://researchseminars.org/talk/analysisgeometryNE/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Charles Ouyang (U. Mass Amherst) DTSTART:20201204T171500Z DTEND:20201204T181500Z DTSTAMP:20260422T212752Z UID:analysisgeometryNE/10 DESCRIPTION:Title: Length spectrum compactification of the SL(3\,R)-Hitchin compo nent\nby Charles Ouyang (U. Mass Amherst) as part of Analysis and Geom etry Seminar\n\n\nAbstract\nHitchin components are natural generalizations of the classical\nTeichmüller space. In the setting of SL(3\,R)\, the Hi tchin component\nparameterizes the holonomies of convex real projective st ructures. By\nstudying Blaschke metrics\, which are Riemannian metrics ass ociated to such\nstructures\, along with their limits\, we obtain a compac tification of the\nSL(3\,R) Hitchin component. We show the boundary object s are hybrid\nstructures\, which are in part flat metric and in part lamin ar. These\nhybrid objects are natural generalizations of measured laminati ons\, which\nare the boundary objects in Thurston's compactification of Te ichmüller\nspace. (joint work with Andrea Tamburelli)\n LOCATION:https://researchseminars.org/talk/analysisgeometryNE/10/ END:VEVENT END:VCALENDAR