Benjamin Dodson (Johns Hopkins) Global well-posedness and scattering for the 3D cubic nonlinear wave equation Sponsored by the Meyer Fund

Apr. 20, 2017 2pm (Math 220)

Lie Theory

Steve Butler (Iowa State) Parking functions and parking functions on trees

Apr. 20, 2017 3pm (MATH 220)

Probability

Miklos Z. Racz (Microsoft Research, Redmond) Braess's paradox for the spectral gap in random graphs and delocalization of eigenvectors

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In this talk we will discuss global well-posedness and scattering for the defocusing, cubic 3D problem with radial data. To prove this it is useful to use hyperbolic coordinates.

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We give an introduction to parking functions, give basic counts, and discuss a generalization to trees. In this latter setting we look at using generating functions to help efficiently count the number of these parking functions.

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If you add an edge to a random graph, do its conductance properties almost always get better? Perhaps surprisingly the answer is no, and I will discuss how this is connected to delocalization properties of eigenvectors. This is based on joint work with Ronen Eldan and Tselil Schramm.