Difference between revisions of "Colloquia"
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− | |Monday, November 7 at 4:30 ( | + | |Monday, November 7 at 4:30 ([http://www.ams.org/meetings/lectures/maclaurin-lectures AMS Maclaurin lecture]) |
| [http://www.massey.ac.nz/massey/expertise/profile.cfm?stref=339830 Gaven Martin] (New Zealand Institute for Advanced Study) | | [http://www.massey.ac.nz/massey/expertise/profile.cfm?stref=339830 Gaven Martin] (New Zealand Institute for Advanced Study) | ||
|Siegel's problem on small volume lattices | |Siegel's problem on small volume lattices | ||
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Abstract: Initiated by Erdos, Graham, Montgomery and others in the 1970's, geometric Ramsey theory studies geometric configurations, determined up to translations, rotations and possibly dilations, which cannot be destroyed by finite partitions of Euclidean spaces. Later it was shown by ergodic and Fourier analytic methods that such results are also possible in the context of sets of positive upper density in Euclidean spaces or the integer lattice. We present a new approach, motivated by developments in arithmetic combinatorics, which provide new results as well new proofs of some classical results in this area. | Abstract: Initiated by Erdos, Graham, Montgomery and others in the 1970's, geometric Ramsey theory studies geometric configurations, determined up to translations, rotations and possibly dilations, which cannot be destroyed by finite partitions of Euclidean spaces. Later it was shown by ergodic and Fourier analytic methods that such results are also possible in the context of sets of positive upper density in Euclidean spaces or the integer lattice. We present a new approach, motivated by developments in arithmetic combinatorics, which provide new results as well new proofs of some classical results in this area. | ||
+ | |||
+ | ===November 7: Gaven Martin (New Zealand Institute for Advanced Study) === | ||
+ | Title: Siegel's problem on small volume lattices | ||
+ | |||
+ | Abstract: We outline in very general terms the history and the proof of the identification | ||
+ | of the minimal covolume lattice of hyperbolic 3-space as the 3-5-3 | ||
+ | Coxeter group extended by the involution preserving the symmetry of this | ||
+ | diagram. This gives us the smallest regular tessellation of hyperbolic 3-space. | ||
+ | This solves (in three dimensions) a problem posed by Siegel in 1945. Siegel solved this problem in two dimensions by deriving the | ||
+ | signature formula identifying the (2,3,7)-triangle group as having minimal | ||
+ | co-area. | ||
+ | |||
+ | There are strong connections with arithmetic hyperbolic geometry in | ||
+ | the proof, and the result has applications in the maximal symmetry groups | ||
+ | of hyperbolic 3-manifolds in much the same way that Hurwitz's 84g-84 theorem | ||
+ | and Siegel's result do. | ||
== Past Colloquia == | == Past Colloquia == |
Revision as of 13:23, 9 September 2016
Mathematics Colloquium
All colloquia are on Fridays at 4:00 pm in Van Vleck B239, unless otherwise indicated.
Fall 2016
date | speaker | title | host(s) | |||
---|---|---|---|---|---|---|
September 9 | ||||||
September 16 | Po-Shen Loh (CMU) | TBA | Ellenberg | |||
September 23 | Gheorghe Craciun (UW-Madison) | TBA | Street | |||
September 30 | Akos Magyar (University of Georgia) | Geometric Ramsey theory | Cook | |||
October 7 | Mark Andrea de Cataldo (Stony Brook) | TBA | Maxim | |||
October 14 | Ling Long (LSU) | TBA | Yang | |||
October 21 | No colloquium this week | |||||
October 28 | Linda Reichl (UT Austin) | TBA | Minh-Binh Tran | |||
November 4 | Steve Shkoller (UC Davis) | TBA | Feldman | |||
Monday, November 7 at 4:30 (AMS Maclaurin lecture) | Gaven Martin (New Zealand Institute for Advanced Study) | Siegel's problem on small volume lattices | Marshall | |||
November 11 | Reserved for possible job talks | |||||
November 18 | Reserved for possible job talks | |||||
November 25 | Thanksgiving break | |||||
December 2 | Reserved for possible job talks | |||||
December 9 | Reserved for possible job talks |
Spring 2017
date | speaker | title | host(s) | |
---|---|---|---|---|
January 20 | Reserved for possible job talks | |||
January 27 | Reserved for possible job talks | |||
February 3 | ||||
February 6 (Wasow lecture) | Benoit Perthame (University of Paris VI) | TBA | Jin | |
February 10 | No Colloquium | |||
February 17 | ||||
February 24 | ||||
March 3 | Ken Bromberg (University of Utah) | Dymarz | ||
Tuesday, March 7, 4PM (Distinguished Lecture) | Roger Temam (Indiana University) | Smith | ||
Wednesday, March 8, 2:25PM | Roger Temam (Indiana University) | Smith | ||
March 10 | No Colloquium | |||
March 17 | ||||
March 24 | Spring Break | |||
Wednesday, March 29 (Wasow) | Sylvia Serfaty (NYU) | TBA | Tran | |
March 31 | No Colloquium | |||
April 7 | Hal Schenck | Erman | ||
April 14 | Wilfrid Gangbo | Feldman & Tran | ||
April 21 | ||||
April 28 | Thomas Yizhao Hou | TBA | Li |
Abstracts
September 30: Akos Magyar (University of Georgia)
Title: Geometric Ramsey theory
Abstract: Initiated by Erdos, Graham, Montgomery and others in the 1970's, geometric Ramsey theory studies geometric configurations, determined up to translations, rotations and possibly dilations, which cannot be destroyed by finite partitions of Euclidean spaces. Later it was shown by ergodic and Fourier analytic methods that such results are also possible in the context of sets of positive upper density in Euclidean spaces or the integer lattice. We present a new approach, motivated by developments in arithmetic combinatorics, which provide new results as well new proofs of some classical results in this area.
November 7: Gaven Martin (New Zealand Institute for Advanced Study)
Title: Siegel's problem on small volume lattices
Abstract: We outline in very general terms the history and the proof of the identification of the minimal covolume lattice of hyperbolic 3-space as the 3-5-3 Coxeter group extended by the involution preserving the symmetry of this diagram. This gives us the smallest regular tessellation of hyperbolic 3-space. This solves (in three dimensions) a problem posed by Siegel in 1945. Siegel solved this problem in two dimensions by deriving the signature formula identifying the (2,3,7)-triangle group as having minimal co-area.
There are strong connections with arithmetic hyperbolic geometry in the proof, and the result has applications in the maximal symmetry groups of hyperbolic 3-manifolds in much the same way that Hurwitz's 84g-84 theorem and Siegel's result do.