Topology, Geometry and Dynamics Archives - Page 18 of 19

Seminars: Topology, Geometry and Dynamics

Date
Time
Venue

Speaker
Affiliation
Title of Talk

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:

Add to calendar :

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:

Add to calendar :

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:

Add to calendar :

15 May 2019
11:00
S17 #05-11 SR5

Zhong Guolei
National University of Singapore
Totally invariant divisors of amplified endomorphisms of normal projective varieties

Totally invariant divisors of amplified endomorphisms of normal projective varieties

Date/Time : 15 May 2019 11:00
Venue : S17 #05-11 SR5
Speaker : Zhong Guolei , National University of Singapore

Date/Time:15 May 2019 11:00 Venue: S17 #05-11 SR5 Speaker: Zhong Guolei, National University of Singapore Totally invariant divisors of amplified endomorphisms of normal projective varieties This work is encouraged by Professor De-Qi Zhang. We consider an arbitrary int-amplified surjective endomorphism $f$ of a normal projective variety $X$ over $\mathbb{C}$ and its $f^{-1}$-stable prime divisors. We extend the early result for the case of polarized endomorphisms to the case of int-amplified endomorphisms. Assume further that $X$ has at worst Kawamata log terminal singularities. We prove that the total number of $f^{-1}$-stable prime divisors has an optimal upper bound $\dim X+\rho(X)$, where $\rho(X)$ is the Picard number. Also, we give a sufficient condition for $X$ to be rationally connected and simply connected. Finally, by running the minimal model program (MMP), we prove that, under some extra conditions, the end product of the MMP can only be an elliptic curve or a single point. Add to calendar:

Add to calendar :

17 Apr 2019
15:00
S17 #05-11 SR5

Oscar Garcia-Prada
ICMAT, Madrid
Higgs bundles and higher Teichmüller spaces

Higgs bundles and higher Teichmüller spaces

Date/Time : 17 Apr 2019 15:00
Venue : S17 #05-11 SR5
Speaker : Oscar Garcia-Prada , ICMAT, Madrid

Date/Time:17 Apr 2019 15:00 Venue: S17 #05-11 SR5 Speaker: Oscar Garcia-Prada, ICMAT, Madrid Higgs bundles and higher Teichmüller spaces Some connected components of a moduli space are mundane in the sense that they are distinguished only by obvious topological invariants or have no special characteristics. Others are more alluring and unusual either because they are not detected by primary invariants, or because they have special geometric significance, or both. In this talk, I will describe examples of such special components in moduli spaces of G-Higgs bundles on closed Riemann surfaces or, equivalently, moduli spaces of surface group representations into a semisimple Lie group G. These special components are related to higher Teichmüller theory and the notion of positivity for Anosov representations recently introduced by Guichard and Wienhard. Add to calendar:

Add to calendar :

10 Apr 2019
14:00
S17 #05-11 SR5

Li Yunzhe
National University of Singapore
Uniqueness of billiards coding in polygon

Uniqueness of billiards coding in polygon

Date/Time : 10 Apr 2019 14:00
Venue : S17 #05-11 SR5
Speaker : Li Yunzhe, National University of Singapore

Date/Time:10 Apr 2019 14:00 Venue: S17 #05-11 SR5 Speaker: Li Yunzhe, National University of Singapore Uniqueness of billiards coding in polygon The study of mathematical billiards is a rich subject in dynamical systems. It describes the frictionless motion of a mass point in a domain with elastic reflection on the boundary. Among many other variations of mathematical billiards, polygonal billiards concerns the billiard problem in a two dimensional polygonal domain. One particular strategy to study polygonal billiards is to encode the trajectory of a billiard by the sequence of sides of the polygonal domain hit by the billiard along its trajectory. Several questions could be asked regarding this encoding and its relations with the billiard. Especially, we may want to know to what extend this encoding determines the physical trajectory of the billiard in the polygonal domain? In 1993, it has been proven by G. Galperin, T. Krüger and S. Troubetzkoy that for a non periodic trajectory in a simply connected polygon the encoding uniquely determines the physical trajectory. We aims to generalise this result to a wider class of polygons which are not necessarily simply connected but contain a finite number of holes such that the holes have non zero minimal diameter. This result was proven in a research project in 2018 at Aix-Marseille université under the supervision of S. Troubetzkoy. Add to calendar:

Add to calendar :

10 Apr 2019
15:00
S17 #05-11 SR5

Wang Dong
National University of Singapore
Phase transition related to Lyapunov exponents in the model of product of complex Ginibre matrices

Phase transition related to Lyapunov exponents in the model of product of complex Ginibre matrices

Date/Time : 10 Apr 2019 15:00
Venue : S17 #05-11 SR5
Speaker : Wang Dong , National University of Singapore

Date/Time:10 Apr 2019 15:00 Venue: S17 #05-11 SR5 Speaker: Wang Dong, National University of Singapore Phase transition related to Lyapunov exponents in the model of product of complex Ginibre matrices In this talk we consider the product of M independent complex Ginibre matrices, each of size N x N. The singular values of the product random matrix as M goes to infinity, under proper scaling, are Lyapunov exponents of a toy dynamical system model. In this talk we consider the model as (1) M goes to infinity and N is fixed, (2) N goes to infinity and M is fixed, or (3) M, N both goes to infinity, and find the behaviour of the largest singular eigenvalues. We observe a phase transition as M/N is O(1). Add to calendar:

Add to calendar :

03 Apr 2019
15:00
S17 #05-11 SR5

Sichen Li
NUS and East China Normal University
A note on a smooth projective surface with Picard number 2

A note on a smooth projective surface with Picard number 2

Date/Time : 03 Apr 2019 15:00
Venue : S17 #05-11 SR5
Speaker : Sichen Li , NUS and East China Normal University

Date/Time:03 Apr 2019 15:00 Venue: S17 #05-11 SR5 Speaker: Sichen Li, NUS and East China Normal University A note on a smooth projective surface with Picard number 2 We characterize the integral Zariski decomposition of a smooth projective surface with Picard number 2 to partially solve a problem of B. Harbourne, P. Pokora, and H. Tutaj-Gasinska [Electron. Res. Announc. Math. Sci. 22 (2015), 103–108]. Add to calendar:

Add to calendar :

20 Mar 2019
14:00
S17 #06-11

Huan Zhen
Sun Yat-Sen University
Quasi-elliptic cohomology

Quasi-elliptic cohomology

Date/Time : 20 Mar 2019 14:00
Venue : S17 #06-11
Speaker : Huan Zhen , Sun Yat-Sen University

Date/Time:20 Mar 2019 14:00 Venue: S17 #06-11 Speaker: Huan Zhen, Sun Yat-Sen University Quasi-elliptic cohomology Quasi-elliptic cohomology is constructed as an object both reflecting the geometric nature of elliptic curves and more practicable to study than most ellipitc cohomology theories. Quasi-elliptic cohomology is closely related to Tate K-theory. It can be interpreted by orbifold loop spaces and expressed in terms of equivariant K-theories. We formulate the complete power operation of this theory. Applying that we prove the finite subgroups of Tate curve can be classified by the Tate K-theory of symmetric groups modulo a certain transfer ideal. Moreover, we construct an orthogonal G-spectrum representing quasi-elliptic cohomology. This construction leads to the birth of a new global homotopy theory. Add to calendar:

Add to calendar :