Seminar Calendar
for events the day of Tuesday, March 13, 2012.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, March 13, 2012

Topology Seminar
11:00 am   in 243 Altgeld Hall,  Tuesday, March 13, 2012
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Submitted by franklan.
 Gabriel Drummond-Cole (Northwestern University)Homotopically trivializing the circle in the framed little disksAbstract: An action of the space of framed little disks on a target space induces a circle action on the target space. Kontsevich suggested that an action of the framed little disks along with a trivialization of the circle action could be encapsulated as follows: this data should be the same as an action of the Deligne-Mumford-Knudsen compactified genus zero moduli space. I'll present a rigorous formulation of this statement in the category of topological operads. There will be many pictures.

Harmonic Analysis and Differential Equations
1:00 pm   in 347 Altgeld Hall,  Tuesday, March 13, 2012
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Submitted by ekirr.
 Christof Sparber (UIC Math)High frequency interactions in nonlinear Schroedinger equations and applicationsAbstract: We consider the cubic nonlinear Schroedinger equation in a weakly nonlinear semiclassical scaling and analyze the interaction of highly oscillatory waves within this context. An extension to the Davey-Stewartson system will be discussed, as well as applications in proving ill-posedness of NLS in Sobolev spaces of negative order. This is based joint works with R. Carles and E. Dumas.

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, March 13, 2012
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Submitted by ssolecki.
 Christian Rosendal (UIC)Global and local boundedness of Polish groupsAbstract: We present a comprehensive theory of boundedness properties for Polish groups developed with a main focus on Roelcke precompactness (precompactness of the lower uniformity) and Property (OB) (boundedness of all isometric actions on separable metric spaces). In particular, these properties are characterised by the orbit structure of isometric or continuous affine representations on separable Banach spaces or Hilbert space.

Geometry Seminar
2:00 pm   in 243 Altgeld Hall,  Tuesday, March 13, 2012
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Submitted by sba.
 Stephanie Alexander (Department of Mathematics, University of Illinois at Urbana-Champaign)The unit sphere in flat space-time, anti-deSitter space, and modeling particle interactions.Abstract: We introduce the geometry of the unit spheres'' in the flat space-time $\mathbf{R^4_-}$, as well as in $\mathbf{R^4_{--}}$. These unit spheres may be called hyperbolic - de Sitter space'' and $\pm$ anti-deSitter space''. We explain how these spaces, and a realization theorem of Schlenker on convex surfaces, are used to model particle interactions. This is an expository talk, emphasizing visualization.

Algebraic Geometry
3:00 pm   in 243 Altgeld Hall,  Tuesday, March 13, 2012
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Submitted by schenck.
 Tom Nevins   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)Derived equivalence of quantum symplectic varietiesAbstract: Singular symplectic varieties and their resolutions of singularities lie at the crossroads of algebraic and symplectic geometry, representation theory, and integrable systems. Central examples include the nilpotent cone of a complex semisimple Lie algebra and its resolution by the cotangent bundle of the flag variety (the Springer resolution); the nth symmetric product of the affine plane and its resolution by the Hilbert scheme of points; and a Kleinian surface singularity and its minimal resolution. A singular variety and its resolution never have equivalent geometry (as encoded, for example, in their derived categories). Replacing a symplectic variety by a quantization, however---an algebro-geometric analog of passing to a Fukaya-type category---one miraculously finds that such equivalences are common. I'll discuss singular symplectic varieties and their resolutions, examples, quantization, and a general criterion for such geometric equivalences that extends classical results (for example, Beilinson-Bernstein localization). Time permitting, I'll also discuss some additional features of these quantizations that parallel emerging structures in the (much more complicated) world of Fukaya categories. This is based on joint work with K. McGerty.

Graph Theory and Combinatorics
3:00 pm   in 241 Altgeld Hall,  Tuesday, March 13, 2012
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Submitted by west.
 Jeffrey Paul Wheeler (University of Pittsburgh)The Polynomial Method of Alon, Ruzsa, and NathansonAbstract: We will explore a particular method of tackling problems in Additive Combinatorics, namely the Polynomial Method of Noga Alon, Imre Ruzsa, and Melvyn Nathanson.  Additive Combinatorics can be described as the study of additive structures of sets.   This area is attractive in that it has numerous connections with other areas of mathematics, including Number Theory, Ergodic Theory, Graph Theory, Finite Geometry, and Group Theory and has drawn the attention of many good mathematicians, including Fields Medalist Terence Tao (2006).