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BEGIN:VEVENT
SUMMARY:Xuwen Zhu (Northeastern)
DTSTART;VALUE=DATE-TIME:20200925T161500Z
DTEND;VALUE=DATE-TIME:20200925T171500Z
DTSTAMP;VALUE=DATE-TIME:20240328T083657Z
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;VALUE=DATE-TIME:20201002T161500Z
DTEND;VALUE=DATE-TIME:20201002T171500Z
DTSTAMP;VALUE=DATE-TIME:20240328T083657Z
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;VALUE=DATE-TIME:20201009T161500Z
DTEND;VALUE=DATE-TIME:20201009T171500Z
DTSTAMP;VALUE=DATE-TIME:20240328T083657Z
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;VALUE=DATE-TIME:20201023T161500Z
DTEND;VALUE=DATE-TIME:20201023T171500Z
DTSTAMP;VALUE=DATE-TIME:20240328T083657Z
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;VALUE=DATE-TIME:20201016T161500Z
DTEND;VALUE=DATE-TIME:20201016T171500Z
DTSTAMP;VALUE=DATE-TIME:20240328T083657Z
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;VALUE=DATE-TIME:20201030T161500Z
DTEND;VALUE=DATE-TIME:20201030T171500Z
DTSTAMP;VALUE=DATE-TIME:20240328T083657Z
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;VALUE=DATE-TIME:20201106T171500Z
DTEND;VALUE=DATE-TIME:20201106T181500Z
DTSTAMP;VALUE=DATE-TIME:20240328T083657Z
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;VALUE=DATE-TIME:20201113T171500Z
DTEND;VALUE=DATE-TIME:20201113T181500Z
DTSTAMP;VALUE=DATE-TIME:20240328T083657Z
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;VALUE=DATE-TIME:20201120T171500Z
DTEND;VALUE=DATE-TIME:20201120T181500Z
DTSTAMP;VALUE=DATE-TIME:20240328T083657Z
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;VALUE=DATE-TIME:20201204T171500Z
DTEND;VALUE=DATE-TIME:20201204T181500Z
DTSTAMP;VALUE=DATE-TIME:20240328T083657Z
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/
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