Topology, Geometry and Dynamics Archives - Page 18 of 18

Seminars: Topology, Geometry and Dynamics

Date
Time
Venue

Speaker
Affiliation
Title of Talk

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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14 Jan 2019
15:00
S17 #04-05 SR2

Bao Huanchen
University of Maryland (College Park)
From Schur-Weyl duality to quantum symmetric pairs

From Schur-Weyl duality to quantum symmetric pairs

Date/Time : 14 Jan 2019 15:00
Venue : S17 #04-05 SR2
Speaker : Bao Huanchen , University of Maryland (College Park)

Date/Time:14 Jan 2019 15:00 Venue: S17 #04-05 SR2 Speaker: Bao Huanchen, University of Maryland (College Park) From Schur-Weyl duality to quantum symmetric pairs The classical Schur-Weyl duality relates the representation theory of general linear Lie algebras and symmetric groups. Drinfeld and Jimbo independently introduced quantum groups in their study of exactly solvable models, which leads to a quantization of the Schur duality relating quantum groups of general linear Lie algebras and Hecke algebras of symmetric groups. In this talk, I will explain the generalization of the (quantized) Schur-Weyl duality to other classical types. This new duality leads to a theory of canonical bases arising from quantum symmetric pairs generalizing Lusztig’s canonical bases on quantum groups. Add to calendar:

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