Topology & Geometry Archives - Page 13 of 14

Seminars: Topology & Geometry

Date
Time
Venue

Speaker
Affiliation
Title of Talk

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:

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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:

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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:

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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:

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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:

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20 Mar 2019
15:00
S17 #06-11

John Loftin
Rutgers University-Newark
Coordinates along neck pinches for moduli of convex real projective structures

Coordinates along neck pinches for moduli of convex real projective structures

Date/Time : 20 Mar 2019 15:00
Venue : S17 #06-11
Speaker : John Loftin , Rutgers University-Newark

Date/Time:20 Mar 2019 15:00 Venue: S17 #06-11 Speaker: John Loftin, Rutgers University-Newark Coordinates along neck pinches for moduli of convex real projective structures It is well-known that the boundary of the Deligne-Mumford compactification of the moduli space of hyperbolic structures on a surface of genus at least 2 can be described in terms of Fenchel-Nielsen coordinates for a pants decomposition of the surface for which the necks to be pinched are boundaries of the pants. Along each loop which is pinched, the length parameter goes to zero, while the twist parameter disappears. These coordinates can be used to form orbifold coordinates for the Deligne-Mumford compactification. I will discuss the analogous degenerations for convex real projective structures, and how to extend a version of Goldman’s Fenchel-Nielsen type coordinates to degenerations along necks. This involves some new classes of geometric limits, and involves a version of Goldman’s interior parameters due to Zhang. I will also discuss how this relates to the complex structure on the moduli space as described via cubic differentials. This is based on joint work with Tengren Zhang. Add to calendar:

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12 Mar 2019
15:00
S17 #05-11 SR5

Zhe Sun
University of Luxembourg
McShane identities for higher Teichmüller theory and the Goncharov-Shen potential

McShane identities for higher Teichmüller theory and the Goncharov-Shen potential

Date/Time : 12 Mar 2019 15:00
Venue : S17 #05-11 SR5
Speaker : Zhe Sun , University of Luxembourg

Date/Time:12 Mar 2019 15:00 Venue: S17 #05-11 SR5 Speaker: Zhe Sun, University of Luxembourg McShane identities for higher Teichmüller theory and the Goncharov-Shen potential We describe a family of Mcshane-type identities for simple root length on positive surface group representations into PGL(n, R). It looks very similar to Mirzakhani’s generalized McShane identity for bordered surfaces which is used to again prove Witten-Kontsevich theorem, except new parameters appear. We find nice properties for these new parameters. Our techniques are based on a family of “generalized horocycle lengths” (called Goncharov-Shen potential), on the positive representation with parabolic monodromy around each boundary component. These horocycle lengths were introduced by Goncharov and Shen, who used their tropical versions to define positive integral points for parametrizing certain canonical bases and to formulate a homological mirror symmetry picture that provides a compactification of the character variety. This is joint work with Yi Huang. Add to calendar:

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05 Mar 2019
15:00
S17 #05-12 SR4

Alan McLeay
University of Luxembourg
Mapping class groups, covers, and braids

Mapping class groups, covers, and braids

Date/Time : 05 Mar 2019 15:00
Venue : S17 #05-12 SR4
Speaker : Alan McLeay , University of Luxembourg

Date/Time:05 Mar 2019 15:00 Venue: S17 #05-12 SR4 Speaker: Alan McLeay, University of Luxembourg Mapping class groups, covers, and braids The mapping class group of a surface is the group of isotopy classes of boundary preserving homeomorphisms of the surface. Given a finite sheeted covering space between surfaces, we may ask what relationship, if any, exists between the two mapping class groups? In joint work with Tyrone Ghaswala we investigate this question for surfaces with non-empty boundary. I will discuss a classical theorem of Birman-Hilden and give new insight into a family of covering spaces related to the Burau representation of braid groups. Add to calendar:

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26 Jan 2019
15:00
S17 #04-04 SR3

Hsin-Ku Chen
National Taiwan University
Threefolds of Kodaira dimension one

Threefolds of Kodaira dimension one

Date/Time : 26 Jan 2019 15:00
Venue : S17 #04-04 SR3
Speaker : Hsin-Ku Chen , National Taiwan University

Date/Time:26 Jun 2019 15:00 Venue: S17 #04-04 SR3 Speaker: Hsin-Ku Chen, National Taiwan University Threefolds of Kodaira dimension one We prove that for any smooth complex projective threefold of Kodaira dimension one, the m-th pluricanonical map is birational to the Iitaka fibration for every m >= 5868 and divisible by 12. Add to calendar:

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