Seminar Calendar
for events the day of Wednesday, March 1, 2017.

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Wednesday, March 1, 2017

Doob Colloquium
3:00 pm   in 243 Altgeld Hall,  Wednesday, March 1, 2017
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Submitted by lescobar.
Ivan Contreras (UIUC)
Quotient spaces, Lie theory and quantization
Abstract: We encounter quotient spaces everywhere in mathematics: circles, cohomology groups, moduli spaces. And sometimes physicists come up with interpretations of such spaces in terms of the symmetries of a given theory. In this talk I will explain how a 2 dimensional topological field theory, called the Poisson sigma model, produce interesting symplectic quotient spaces and its quantization produce deformations of Poisson brackets.

Graduate Student Colloquium
4:00 pm   in 245 Altgeld Hall,  Wednesday, March 1, 2017
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Submitted by hquan4.
William Karr (UIUC Math)
Convexity and curvature in space-time geometry
Abstract: A space-time is said to satisfy $\mathcal{R} \geq K$ if the sectional curvatures of spacelike planes are bounded below by $K$ and the sectional curvatures of timelike planes are bounded above by $K$. Similarly, one can define $\mathcal{R} \leq K$ by reversing the inequalities. These conditions naturally generalize the notion of curvature bounds for Riemannian manifolds to the Lorentzian setting. We describe how these conditions can be used to construct two types of convex functions. We then describe two geometric consequences of space-times supporting these functions. One result establishes geodesic connectedness for a class of space-times satisfying $\mathcal{R} \geq 0$. Another result rules out submanifolds associated with black holes and wormholes in certain domains of space-times satisfying $\mathcal{R} \leq 0$. This is joint work with Stephanie Alexander.