Ricci flow through singularities

Speaker: 

Professor Dan Knopf

Institution: 

UT Austin

Time: 

Monday, May 17, 2010 - 4:00pm

Location: 

RH 340N

We construct smooth forward Ricci flow evolutions of singular initial metrics resulting from rotationally symmetric neckpinches, without performing an intervening surgery. In the restrictive context of rotational symmetry, the construction gives evidence in favor of Perelman's hope for a "canonically defined Ricci flow through singularities". This is joint work with Sigurd Angenent and Cristina Caputo.

Rigorous Bounds on the Critical Temperature of Dilute Bose Gases

Speaker: 

Daniel Ueltschi

Institution: 

University of Warwick, UK

Time: 

Thursday, April 1, 2010 - 2:00pm

Location: 

RH 306

Predicted by Einstein in 1924, the Bose-Einstein condensation is a
striking phase transition that takes place in certain systems of
quantum bosonic particles. The dependence of the critical
temperature on the interparticle interactions has been a controversial
issue in the physics community. I will review the mathematical setting
and the literature, and I will describe rigorous upper bounds for the
critical temperature of dilute systems. This upper bound is expected
to be sharp in 2D but not in 3D. (This is joint work with R. Seiringer.)

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