Colloquia/Fall18: Difference between revisions
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which entirely avoids some color. The unusual function log^* is the | which entirely avoids some color. The unusual function log^* is the | ||
inverse function of the tower function (iterated exponentiation). | inverse function of the tower function (iterated exponentiation). | ||
=== September 23: Gheorghe Craciun (UW-Madison) === | |||
Title: Toric Differential Inclusions and a Proof of the Global Attractor Conjecture | |||
Abstract: The Global Attractor Conjecture says that a large class of polynomial dynamical systems, called toric dynamical systems, have a globally attracting point within each linear invariant space. In particular, these polynomial dynamical systems never exhibit multistability, oscillations or chaotic dynamics. | |||
The conjecture was formulated by Fritz Horn in the early 1970s, and is strongly related to Boltzmann's H-theorem. | |||
We discuss the history of this problem, including the connection between this conjecture and the Boltzmann equation. Then, we introduce toric differential inclusions, and describe how they can be used to prove this conjecture in full generality. | |||
=== September 30: Akos Magyar (University of Georgia) === | === September 30: Akos Magyar (University of Georgia) === | ||
Revision as of 19:33, 13 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) | Directed paths: from Ramsey to Pseudorandomness | Ellenberg | |||
| September 23 | Gheorghe Craciun (UW-Madison) | Toric Differential Inclusions and a Proof of the Global Attractor Conjecture | Street | |||
| September 30 | Akos Magyar (University of Georgia) | Geometric Ramsey theory | Cook | |||
| October 7 | ||||||
| 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 | Mark Andrea de Cataldo (Stony Brook) | TBA | Maxim | |
| April 28 | Thomas Yizhao Hou | TBA | Li |
Abstracts
September 16: Po-Shen Loh (CMU)
Title: Directed paths: from Ramsey to Pseudorandomness
Abstract: Starting from an innocent Ramsey-theoretic question regarding directed paths in graphs, we discover a series of rich and surprising connections that lead into the theory around a fundamental result in Combinatorics: Szemeredi's Regularity Lemma, which roughly states that every graph (no matter how large) can be well-approximated by a bounded-complexity pseudorandom object. Using these relationships, we prove that every coloring of the edges of the transitive N-vertex tournament using three colors contains a directed path of length at least sqrt(N) e^{log^* N} which entirely avoids some color. The unusual function log^* is the inverse function of the tower function (iterated exponentiation).
September 23: Gheorghe Craciun (UW-Madison)
Title: Toric Differential Inclusions and a Proof of the Global Attractor Conjecture
Abstract: The Global Attractor Conjecture says that a large class of polynomial dynamical systems, called toric dynamical systems, have a globally attracting point within each linear invariant space. In particular, these polynomial dynamical systems never exhibit multistability, oscillations or chaotic dynamics.
The conjecture was formulated by Fritz Horn in the early 1970s, and is strongly related to Boltzmann's H-theorem.
We discuss the history of this problem, including the connection between this conjecture and the Boltzmann equation. Then, we introduce toric differential inclusions, and describe how they can be used to prove this conjecture in full generality.
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.