Geometry and Topology Seminar 2019-2020: Difference between revisions

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|September 9
|[http://www.math.wisc.edu/~maribeff/ Gloria Mari Beffa] (UW Madison)
|[[#Gloria Mari Beffa (UW Madison)|
''The pentagram map and generalizations: discretizations of AGD flows'']]
|[local]
|-
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|September 16
|September 16
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== Abstracts ==
== Abstracts ==
===Gloria Mari Beffa (UW Madison)===
''The pentagram map and generalizations: discretizations of AGD flows''
GIven an n-gon one can join every other vertex with a segment and find the intersection
of two consecutive segments. We can form a new n-gon with this intersections, and the
map taking the original n-gon to the newly found one is called the pentagram map. This map's
properties when defined on pentagons are simple to describe (it takes its name from there),
but the map turns out to have a unusual  number of other properties and applications.
In this talk I will give a quick review of recent results by Ovsienko, Schwartz and Tabachnikov on the
integrability of the pentagram map and I will describe on-going efforts to generalize the pentagram
map to higher dimensions using possible connections to Adler-Gelfand-Dikii flows. The talk will
NOT be for experts and will have plenty of drawings, so come and join us.


===Ke Zhu (University of Minnesota)===
===Ke Zhu (University of Minnesota)===
''Thin instantons in G2-manifolds and  
''Thin instantons in G2-manifolds and  
Seiberg-Witten invariants''
Seiberg-Witten invariants''
For two nearby disjoint coassociative submanifolds $C$ and $C'$ in a $G_2$-manifold, we construct thin instantons with boundaries lying on $C$
and $C'$ from regular $J$-holomorphic curves in $C$. It is a high dimensional analogue of holomorphic stripes with boundaries on two nearby Lagrangian submanifolds $L$ and $L'$. We explain its relationship with the Seiberg-Witten invariants for $C$. This is a joint work with Conan Leung and Xiaowei Wang.


===David Fisher (Indiana University)===
===David Fisher (Indiana University)===

Revision as of 15:33, 2 September 2011

Fall 2012

The seminar will be held in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm

date speaker title host(s)
September 9 Gloria Mari Beffa (UW Madison)

The pentagram map and generalizations: discretizations of AGD flows

[local]
September 16 Ke Zhu (University of Minnesota)

Thin instantons in G2-manifolds and Seiberg-Witten invariants

Yong-Geun
September 30 Tullia Dymarz's visitor
October 7 David Fisher (Indiana University)

TBA

Richard and Tullia
November 18 Igor Zelenko (Texas A&M University)

TBA

Gloria

Abstracts

Gloria Mari Beffa (UW Madison)

The pentagram map and generalizations: discretizations of AGD flows

GIven an n-gon one can join every other vertex with a segment and find the intersection of two consecutive segments. We can form a new n-gon with this intersections, and the map taking the original n-gon to the newly found one is called the pentagram map. This map's properties when defined on pentagons are simple to describe (it takes its name from there), but the map turns out to have a unusual number of other properties and applications.

In this talk I will give a quick review of recent results by Ovsienko, Schwartz and Tabachnikov on the integrability of the pentagram map and I will describe on-going efforts to generalize the pentagram map to higher dimensions using possible connections to Adler-Gelfand-Dikii flows. The talk will NOT be for experts and will have plenty of drawings, so come and join us.

Ke Zhu (University of Minnesota)

Thin instantons in G2-manifolds and Seiberg-Witten invariants

For two nearby disjoint coassociative submanifolds $C$ and $C'$ in a $G_2$-manifold, we construct thin instantons with boundaries lying on $C$ and $C'$ from regular $J$-holomorphic curves in $C$. It is a high dimensional analogue of holomorphic stripes with boundaries on two nearby Lagrangian submanifolds $L$ and $L'$. We explain its relationship with the Seiberg-Witten invariants for $C$. This is a joint work with Conan Leung and Xiaowei Wang.

David Fisher (Indiana University)

TBA

Igor Zelenko (Texas A&M University)

TBA



Fall-2010-Geometry-Topology