Seminar Calendar
for events the week of Sunday, May 1, 2016.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, May 2, 2016

Symplectic & Poisson Geometry Seminar
2:00 pm   in 447 Altgeld Hall,  Monday, May 2, 2016
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Submitted by vzh.
Anton Izosimov (University of Toronto)
Lie algebroids and vortex sheets
Abstract: In 1966, V.Arnold suggested a group-theoretic framework for ideal hydrodynamics. In this framework, the motion of an incompressible fluid on a Riemannian manifold is described as the geodesic flow of a right-invariant metric on the group of volume-preserving diffeomorphisms. While Arnold's approach is, in general, not applicable to fluid flows with discontinuities, it has been recently shown by C.Loeschcke and F.Otto that certain discontinuous fluid motions, known as vortex sheets, can also be viewed as geodesics, but on the space of embedded hypersurfaces. In the talk, I will explain how these two pictures (geodesics on a group and geodesics on the space of hypersurfaces) are related to each other via the theory of Lie groupoids and algebroids. In particular, I will describe a large class of discontinuous fluid motions which can be regarded as trajectories of a Hamiltonian system on the dual of a certain infinite-dimensional Lie algebroid. Vortex sheets arise in this setting as solutions lying on a special symplectic leaf. This is joint work with B.Khesin.

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Monday, May 2, 2016
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Submitted by laugesen.
(Department of Mathematics, University of Illinois)
No meeting

Tuesday, May 3, 2016

Topology Seminar
11:00 am   in 345 Altgeld Hall,  Tuesday, May 3, 2016
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Submitted by cmalkiew.
Nathaniel Stapleton (Max Planck Institute)
The infinite prime in chromatic homotopy theory
Abstract: The behavior of the category of E_n-local spectra simplifies in various ways as $p \rightarrow \infty$. For a collection of categories indexed by the prime numbers we construct a category "at the infinite prime" that captures behavior of all but finitely many of the input categories. We then apply this construction to the E_n-local and K(n)-local situations and analyze the resulting categories. This represents joint work with Barthel and Schlank.

Geometry, Groups and Dynamics/GEAR Seminar
12:00 pm   in Altgeld Hall 243,  Tuesday, May 3, 2016
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Submitted by kapovich.
Jérémy Toulisse (University of Southern California)
Hitchin representations in Sp(4,R) and conformally flat space-times
Abstract: Given a closed oriented surface S of genus g>1 and using the isomorphism between Sp(4,R) and SO(2,3), we can associate to a representation from the fundamental group of S to Sp(4,R) an action on the Einstein universe (which is the model space for 3-dimensional conformally flat Lorentz structure). In this talk, we will explain how to realize Hitchin representations in Sp(4,R) as holonomy of conformally flat Lorentz structures on the unit tangent bundle of S. This is a joint work with Nicolas Tholozan.

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, May 3, 2016
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Submitted by jccl.
Laura Escobar (UIUC)
Brick varieties and the toric variety of the associahedron
Abstract: Bott-Samelson varieties are twisted products of CP^1's with a map into G/B. This talk will be about brick varieties which are the general fibers of Bott-Samelson maps. I will describe the moment polytopes of the brick varieties and describe some instances in which these varieties are toric. In particular, I will give a description of the toric variety of the associahedron.

Graduate Algebraic Geometry Seminar
4:00 pm   in 243 Altgeld Hall,  Tuesday, May 3, 2016
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Submitted by jjwen2.
Matej Penciak (UIUC Math)
Noncommutative Algebraic Geometry
Abstract: In this talk I will describe some attempts to study noncommutative rings via analogies with their commutative counterparts in algebraic geometry. First I will explain the Gabriel-Rosenberg reconstruction theorem and the geometry contained in the abelian category of coherent sheaves. I will then define the noncommutative analogues of projective curves and surfaces and describe some results about their classification.

Wednesday, May 4, 2016

Algebra, Geometry and Combinatorics
4:00 pm   in 143 Altgeld Hall,  Wednesday, May 4, 2016
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Submitted by redavid2.
Bridget Tenner   [email] (De Paul University )
Exploiting reduced words
Abstract: Reduced words are strings of positive integers that describe how to write a permutation as a product of adjacent transpositions. They are, at first glance, notably different from the one-line notation that is usually used to depict permutation patterns. However, there is a powerful relationship between these two depictions, allowing us to translate between them and to exploit the most appealing combinatorial properties of each. This yields many algebraic and enumerative results, ranging from structural properties of posets, to tiling criteria, to a bijection between partitions of L and 132-avoiding permutations of length L.

Thursday, May 5, 2016

Analysis Seminar
11:00 am   in 345 Altgeld Hall,  Thursday, May 5, 2016
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Submitted by tumanov.
Luca Capogna (Worcester Polytechnic Institute)
Liouville type theorem for quasiconformal mappings in subRiemannian manifolds
Abstract: In a joint work with Enrico Le Donne (Jyvaskyla) and Alessandro Ottazzi (UNSW), we prove that every $1$-quasiconformal map between domains in an equiregular subRiemannian manifold is smooth if the manifold admits a regularity theorem for the subelliptic $p$-Laplacian operator. We also prove that such regularity holds for any contact subRiemannian manifold, thus in particular including all strictly pseudo-convex CR manifolds. The proofs involve ideas and techniques from analysis in metric spaces, differential geometry and PDE. Our work extends to the subRiemannian setting previous results of Gehring and Reshetnyak in Euclidean spaces, and Ferrand in the Riemannian setting.

Math-Physics Seminar
12:30 pm   in 464 Loomis Laboratory,  Thursday, May 5, 2016
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Submitted by katz.
Arnav Tripathy (Stanford Math)
To Be Announced

Illinois Geometry Lab
1:00 pm   in 239 Altgeld Hall,  Thursday, May 5, 2016
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Submitted by tyson.
IGL Open House
Abstract: The IGL end-of-semester Open House will take place from 1:00 pm to 4:00 pm in Room 239 Altgeld Hall. Come see what the IGL teams have produced this semester!