Events Calendar

November 2009
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Events for November 2009:

6 (Friday)	Analysis Seminar Renormalization in the Kondo problem Sarada Rajeev, University of Rochester 2:00 pm - 3:00 pm, Hylan 1106A When electrons in a metal encounter an impurity of small size, the zero temperature resistance is predicted to be infinite by the usual methods of quantum theory. Experimentally, the resistance grows at low temperatures, but remains finite. This contradiction was resolved by Wilson using his celebrated Numerical Renormalization Group method. I will discuss another approach which has the potential of being mathematically rigorous. Some toy models of renormalization with a rigorous mathematical formulation will also be discussed. Tea served at 3:00pm, in the Math Lounge, 9th floor Hylan Bldg.
	Geometry Seminar Scalar Curvature and Connected Sums Of Self-Dual 4-Manifolds Mustafa Kalafat, University of Wisconsin-Madison 4:00 pm - 5:00 pm, Hylan 1106A Under a vanishing hypothesis, Donaldson and Friedman proved that the connected sum of two self-dual Riemannian 4-Manifolds is again self-dual. We prove that the same result can be extended over to the positive scalar curvature case. Tea will be served starting at 3:00pm in the Math Lounge, 9th Floor, Hylan Bldg.
12 (Thursday)	Special Lecture TBA Karen Rhea, University of Michigan 2 pm - 3 pm, Hylan 1106B
	Colloquium Twist & Shout: Maximal enstrophy production in the 3D Navier-Stokes Charles Doering 3:30 pm - 4:30 pm, Computer Studies Building 209 It is still not known whether solutions to the 3D Navier-Stokes equations for incompressible flows in a finite periodic box can become singular in finite time. (This question is the subject of one of the $1M Clay Prize problems.) It is known that a solution remains smooth as long as the enstrophy, i.e., the mean-square vorticity, of the solution is finite. The generation rate of enstrophy is given by a functional that can be bounded using elementary functional estimates. Those estimates establish short-time regularity but do not rule out finite-time singularities in the solutions. In this work we formulate and solve the variational problem for the maximal growth rate of enstrophy and display flows that generate enstrophy at the greatest possible rate. Implications for questions of regularity or singularity in solutions of the 3D Navier-Stokes equations are discussed. This is joint work with Lu Lu, Indiana University Mathematics Journal Vol. 57, pp. 2693-2727 (2008).
13 (Friday)	Analysis Seminar Eventual regularization of the slightly supercritical fractional Burgers equation. Magdalena Czuback of the University of Toronto. 2 pm - 3 pm, Hylan 1106A We prove that a weak solution of a slightly supercritical fractional Burgers equation becomes H\"older continuous for large time. Tea served at 1:30pm, Math Lounge, Hylan Bldg., 9th floor.