Topology, Geometry and Dynamics Archives - Page 20 of 22

Seminars: Topology, Geometry and Dynamics

Date
Time
Venue

Speaker
Affiliation
Title of Talk

22 Nov 2019
14:00
S17 #04-04 SR3

Brice Loustau
TU Darmstat
Computing harmonic maps between Riemannian manifolds

Computing harmonic maps between Riemannian manifolds

Date/Time : 22 Nov 2019 14:00
Venue : S17 #04-04 SR3
Speaker : Brice Loustau, TU Darmstat

Date/Time:22 Nov 2019 14:00 Venue: S17 #04-04 SR3 Speaker: Brice Loustau , TU Darmstat Computing harmonic maps between Riemannian manifolds The theory of harmonic maps between Riemannian manifolds goes back to the foundational work of Eells-Sampson and Hartman. Using the heat flow method, i.e. the gradient flow for the energy functional, they showed existence and uniqueness of harmonic maps between compact Riemannian manifolds when the target has negative sectional curvature. In order to compute such harmonic maps effectively, we discretize the theory by introducing meshes of the domain manifold, which consist of a geodesic triangulation with vertex and edge weights. By studying the convexity properties of the energy functional, we show that the discrete heat flow method converges to unique discrete harmonic maps. Moreover, under suitable assumptions, the discrete theory converges back to the smooth theory when taking finer and finer meshes. In particular, the smooth harmonic map can be obtained as the limit of discrete harmonic maps, equivalently as the double limit of the discrete heat flow when iterating both the time and space discretization steps. Time permits, we will also discuss center of mass methods to compute harmonic maps. We feature a concrete illustration of these methods withHarmony, a computer software with a graphical user interface that we developed in C++, whose main functionality is to numerically compute and display equivariant harmonic maps between hyperbolic disks. Add to calendar:

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06 Nov 2019
16:00
S17 #06-11

Jonathon Teo
National University of Singapore
Branes in the moduli space of parabolic Higgs bundles

Branes in the moduli space of parabolic Higgs bundles

Date/Time : 06 Nov 2019 16:00
Venue : S17 #06-11
Speaker : Jonathon Teo , National University of Singapore

Date/Time:06 Nov 2019 16:00 Venue: S17 #06-11 Speaker: Jonathon Teo, National University of Singapore Branes in the moduli space of parabolic Higgs bundles In this talk, we will be looking at some constructions of families of branes in the moduli space of stable parabolic Higgs bundles. We will first be introducing the moduli space of rank 2 stable parabolic Higgs bundles over the complex projective curve, which is a hyperkahler manifold and contains the cotangent bundle of the moduli space of stable parabolic bundles. The family of branes are constructed from complex or Lagrangian submanifolds of the moduli space of stable parabolic bundles. Thus, a deformation of the submanifolds in the moduli space of stable parabolic bundles gives us a deformation of branes. We will also show that this deformation space is degenerate. Add to calendar:

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30 Oct 2019
16:00
S17 #06-11

Xu Binbin
University of Luxembourg
Ambartzumian-Pleijel identity in hyperbolic geometry

Ambartzumian-Pleijel identity in hyperbolic geometry

Date/Time : 30 Oct 2019 16:00
Venue : S17 #06-11
Speaker : Xu Binbin , University of Luxembourg

Date/Time:30 Oct 2019 16:00 Venue: S17 #06-11 Speaker: Xu Binbin, University of Luxembourg Ambartzumian-Pleijel identity in hyperbolic geometry Given a convex compact domain in Euclidean plane with C1 boundy, a measure on the space of all straight lines invariant under the isometry group of Euclidean plane induces a distribution on the positive real line, by considering the length of the intersection of straight lines with this domain. Ambartzumian-Pleijel identity is about computing the integral of any real valued C1 function on the positive real line with respect to this distribution. In this talk, we’ll introduce the counterpart of this identity in hyperbolic geometry. Then we will discuss some of its applications. In particular, it can be used to prove Croftin formula and the isoperimetric inequality in hyperbolic geometry. I’ll also discuss some of its generalizations in other context. Add to calendar:

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30 Oct 2019
17:00
S17 #06-11

Xin Nie
Tsinghua University
Planar convex domains and cubic differentials

Planar convex domains and cubic differentials

Date/Time : 30 Oct 2019 17:00
Venue : S17 #06-11
Speaker : Xin Nie , Tsinghua University

Date/Time:30 Oct 2019 17:00 Venue: S17 #06-11 Speaker: Xin Nie, Tsinghua University Planar convex domains and cubic differentials The Cheng-Yau affine sphere construction endows every properly convex domain in the real projective planar with a canonical holomorphic cubic differential. We will first explain this construction and its consequences on the moduli space of convex real projective structures, then we will talk about some recent results and open problems arising from the construction. Add to calendar:

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16 Oct 2019
16:00
S17 #06-11

Yeong Chyuan
Chung Leiden University
Coarse geometry and operator algebras

Coarse geometry and operator algebras

Date/Time : 16 Oct 2019 16:00
Venue : S17 #06-11
Speaker : Yeong Chyuan , Chung Leiden University

Date/Time:16 Oct 2019 16:00 Venue: S17 #06-11 Speaker: Yeong Chyuan Chung, Leiden University Coarse geometry and operator algebras In this talk, we will discuss an aspect of the interplay between coarse geometry of metric spaces, operator algebras, and K-theory of these algebras. Roe algebras are operator algebras designed to encode the coarse geometry of metric spaces. In particular, they are coarse geometric invariants. The question of the extent to which Roe algebras remember the coarse geometry of the metric space is called the rigidity problem. We will describe joint work with Bruno M. Braga and Kang Li relating the rigidity problem to the coarse Baum-Connes conjecture on the K-theory of these and other related algebras. Add to calendar:

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08 Oct 2019
14:00
S17 #05-11 SR5

Chen Xiaoyang
Tongji University
Vanishing theorems of Morse-Novikov cohomology

Vanishing theorems of Morse-Novikov cohomology

Date/Time : 08 Oct 2019 14:00
Venue : S17 #05-11 SR5
Speaker : Chen Xiaoyang , Tongji University

Date/Time:08 Oct 2019 14:00 Venue: S17 #05-11 SR5 Speaker: Chen Xiaoyang, Tongji University Vanishing theorems of Morse-Novikov cohomology We will discuss basic properties of Morse-Novikov cohomology and some vanishing theorems related to almost nonnegative curvature. Add to calendar:

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25 Sep 2019
16:00
S17 #06-11

Foo Wei Guo
Chinese Academy of Sciences
Equivalence problem of CR real hypersurfaces with uniform Levi rank: the degenerate case

Equivalence problem of CR real hypersurfaces with uniform Levi rank: the degenerate case

Date/Time : 25 Sep 2019 16:00
Venue : S17 #06-11
Speaker : Foo Wei Guo , Chinese Academy of Sciences

Date/Time:25 Sep 2019 16:00 Venue: S17 #06-11 Speaker: Foo Wei Guo, Chinese Academy of Sciences Equivalence problem of CR real hypersurfaces with uniform Levi rank: the degenerate case In this talk, we discuss about the Cartan’s equivalence problem of 5-dimensional CR real hypersurfaces of constant Levi rank 1, and which are 2-non-degenerate. An important homogeneous model is the tube over the future light cone which has 10 dimensional Lie algebra of infinitesimal CR automorphisms, isomorphic to so(3,2). In 2015, Samuel Pocchiola in his joint work with Joel Merker produced 2 primary invariants which characterise such a homogeneous model. If time permits, we might discuss about the geometry of PDE for this problem which has relation to third order ODE and the Einstein-Weyl geometry. Add to calendar:

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11 Sep 2019
16:00
S17 #04-04 SR3

Arielle Leitner
Weizmann Institute
Generalized Cusps on Convex Projective Manifolds

Generalized Cusps on Convex Projective Manifolds

Date/Time : 11 Sep 2019 16:00
Venue : S17 #04-04 SR3
Speaker : Arielle Leitner , Weizmann Institute

Date/Time:11 Sep 2019 16:00 Venue: S17 #04-04 SR3 Speaker: Arielle Leitner , Weizmann Institute Generalized Cusps on Convex Projective Manifolds Convex projective manifolds are a generalization of hyperbolic manifolds. Koszul showed that the set of holonomies of convex projective structures on a compact manifold is open in the representation variety. We will describe an extension of this result to convex projective manifolds whose ends are generalized cusps, due to Cooper-Long-Tillmann. Generalized cusps are certain ends of convex projective manifolds. They may contain both hyperbolic and parabolic elements. We will describe their classification (due to Ballas-Cooper-Leitner), and explain how generalized cusps turn out to be deformations of cusps of hyperbolic manifolds. If time permits we will discuss current work on the moduli space of generalized cusps (joint with Ballas and Cooper). Add to calendar:

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18 Jul 2019
14:00
S17 #04-04 SR3

Liu Wenfei
Xiamen University
On the volumes of log canonical surfaces

On the volumes of log canonical surfaces

Date/Time : 18 Jul 2019 14:00
Venue : S17 #04-04 SR3
Speaker : Liu Wenfei , Xiamen University

Date/Time:18 Jul 2019 14:00 Venue: S17 #04-04 SR3 Speaker: Liu Wenfei, Xiamen University On the volumes of log canonical surfaces The geography of singular surfaces acquires more complexity due to their volumes, which are only rational numbers rather than integers. By a fundamental result of Alexeev, the set of volumes of all projective log canonical surfaces satisfies the so-called descending chain condition (DCC), if the coefficients of the boundary divisors belong to a given DCC set. In this talk I will report on some recent progress on accumulation points and the minima of the volume sets for different classes of log canonical surfaces. As an application, one obtains a Noether type inequality for nonnormal stable surfaces. The talk is mostly based on joint work with Valery Alexeev. Add to calendar:

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