Geometry and Topology Seminar 2019-2020: Difference between revisions
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GIven an n-gon one can join every other vertex with a segment and find the intersection | 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 | of two consecutive segments. We can form a new n-gon with these intersections, and the | ||
map taking the original n-gon to the newly found one is called the pentagram map. | map taking the original n-gon to the newly found one is called the pentagram map. The map's | ||
properties when defined on pentagons are simple to describe (it takes its name from | properties when defined on pentagons are simple to describe (it takes its name from this fact), | ||
but the map turns out to have a unusual number of other properties and applications. | but the map turns out to have a unusual number of other properties and applications. | ||
Revision as of 20:58, 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) | Richard and Tullia | |
| November 18 | Igor Zelenko (Texas A&M University) | 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 these intersections, and the map taking the original n-gon to the newly found one is called the pentagram map. The map's properties when defined on pentagons are simple to describe (it takes its name from this fact), 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