Geometry and Topology Seminar 2019-2020: Difference between revisions
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|October 18 | |October 18 | ||
| [http://www.math.uiuc.edu/~jathreya/ Jayadev Athreya] (Illinois) | | [http://www.math.uiuc.edu/~jathreya/ Jayadev Athreya] (Illinois) | ||
|[[#Jayadev Athreya (Illinois)| '' | |[[#Jayadev Athreya (Illinois)| ''Gap Distributions and Homogeneous Dynamics'']] | ||
| [http://www.math.wisc.edu/~rkent/ Kent] | | [http://www.math.wisc.edu/~rkent/ Kent] | ||
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Abstract: | Abstract: | ||
For a compact surface S, the associated pants graph P(S) consists of vertices corresponding to pants decompositions of S and edges corresponding to elementary moves between pants decompositions. Motivated by the Weil-Petersson geometry of Teichmüller space, Aramayona, Parlier, and Shackleton conjecture that the full subgraph G of P(S) determined by fixing a multicurve is totally geodesic in P(S). We resolve this conjecture in the case that G is a product of Farey graphs. This is joint work with Sam Taylor. | For a compact surface S, the associated pants graph P(S) consists of vertices corresponding to pants decompositions of S and edges corresponding to elementary moves between pants decompositions. Motivated by the Weil-Petersson geometry of Teichmüller space, Aramayona, Parlier, and Shackleton conjecture that the full subgraph G of P(S) determined by fixing a multicurve is totally geodesic in P(S). We resolve this conjecture in the case that G is a product of Farey graphs. This is joint work with Sam Taylor. | ||
===Jayadev Athreya (Illinois)=== | |||
''Gap Distributions and Homogeneous Dynamics'' | |||
Abstract: | |||
We discuss the notion of gap distributions of various lists of numbers in [0, 1], in particular focusing on those which are associated to certain low-dimensional dynamical systems. We show how to explicitly compute some examples using techniques of homogeneous dynamics, generalizing earlier work on gaps between Farey Fractions. This works gives some possible notions of `randomness' of special trajectories of billiards in polygons, and is based partly on joint works with J. Chaika, J. Chaika and S. Lelievre, and with Y.Cheung. This talk may also be of interest to number theorists. | |||
===Neil Hoffman (Melbourne)=== | ===Neil Hoffman (Melbourne)=== | ||
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Hidetoshi Masai, Shin'ichi Oishi, and Akitoshi Takayasu. | Hidetoshi Masai, Shin'ichi Oishi, and Akitoshi Takayasu. | ||
== Spring 2014 == | == Spring 2014 == | ||
Revision as of 16:58, 28 August 2013
The Geometry and Topology seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.
For more information, contact Richard Kent.
Fall 2013
| date | speaker | title | host(s) |
|---|---|---|---|
| September 6 | |||
| September 13 | Alex Zupan (Texas) | Totally geodesic subgraphs of the pants graph | Kent |
| September 20 | |||
| September 27 | |||
| October 4 | |||
| October 11 | |||
| October 18 | Jayadev Athreya (Illinois) | Gap Distributions and Homogeneous Dynamics | Kent |
| October 25 | |||
| November 1 | |||
| November 8 | Neil Hoffman (Melbourne) | Verified computations for hyperbolic 3-manifolds | Kent |
| November 15 | |||
| November 22 | |||
| Thanksgiving Recess | |||
| December 6 | |||
| December 13 | |||
Fall Abstracts
Alex Zupan (Texas)
Totally geodesic subgraphs of the pants graph
Abstract: For a compact surface S, the associated pants graph P(S) consists of vertices corresponding to pants decompositions of S and edges corresponding to elementary moves between pants decompositions. Motivated by the Weil-Petersson geometry of Teichmüller space, Aramayona, Parlier, and Shackleton conjecture that the full subgraph G of P(S) determined by fixing a multicurve is totally geodesic in P(S). We resolve this conjecture in the case that G is a product of Farey graphs. This is joint work with Sam Taylor.
Jayadev Athreya (Illinois)
Gap Distributions and Homogeneous Dynamics
Abstract: We discuss the notion of gap distributions of various lists of numbers in [0, 1], in particular focusing on those which are associated to certain low-dimensional dynamical systems. We show how to explicitly compute some examples using techniques of homogeneous dynamics, generalizing earlier work on gaps between Farey Fractions. This works gives some possible notions of `randomness' of special trajectories of billiards in polygons, and is based partly on joint works with J. Chaika, J. Chaika and S. Lelievre, and with Y.Cheung. This talk may also be of interest to number theorists.
Neil Hoffman (Melbourne)
Verified computations for hyperbolic 3-manifolds
Abstract: Given a triangulated 3-manifold M a natural question is: Does M admit a hyperbolic structure?
While this question can be answered in the negative if M is known to be reducible or toroidal, it is often difficult to establish a certificate of hyperbolicity, and so computer methods have developed for this purpose. In this talk, I will describe a new method to establish such a certificate via verified computation and compare the method to existing techniques.
This is joint work with Kazuhiro Ichihara, Masahide Kashiwagi, Hidetoshi Masai, Shin'ichi Oishi, and Akitoshi Takayasu.
Spring 2014
| date | speaker | title | host(s) |
|---|---|---|---|
| January 24 | |||
| January 31 | |||
| February 7 | |||
| February 14 | |||
| February 21 | |||
| February 28 | |||
| March 7 | |||
| March 14 | |||
| Spring Break | |||
| March 28 | |||
| April 4 | |||
| April 11 | |||
| April 18 | |||
| April 25 | |||
| May 2 | |||
| May 9 |
Spring Abstracts
Archive of past Geometry seminars
2012-2013: Geometry_and_Topology_Seminar_2012-2013
2011-2012: Geometry_and_Topology_Seminar_2011-2012
2010: Fall-2010-Geometry-Topology