MAY 2007
Ergodic Theory and Statistical Mechanics Seminar
Topic:	Circle rotations and the shrinking target properties
Presenter:	Jim Tseng, Brandeis University
Date:	Thursday, May 10, 2007, Time: 2:00 p.m., Location: Fine 401
Abstract:	The shrinking target properties are related to recurrence. We will motivate and present definitions of these properties. We will also give a necessary and sufficient condition for a circle rotation to have the s-exponent monotone shrinking target property (sMSTP), and, thereby we generalize a result for s = 1 that was established by J. Kurzweil and rediscovered by B. Fayad. We will give a detailed sketch of the proof. Finally, we will apply our technique to give a new, very short, proof of the logarithm law for irrational rotations.
Joint Princeton University and IAS Number Theory Seminar
Topic:	The existence of Bessel functionals
Presenter:	Ramin Takloo-Bighash, Princeton University
Date:	Thursday, May 10, 2007, Time: 4:30 p.m., Location: Fine 322
Abstract:	In this talk I will discuss some recent results on the existence of certain unique models related to the Gross-Prasad conjecture. This is joint with Dipendra Prasad.
Symplectic Geometry Seminar
Topic:	Computing cobordism maps in (hat) Heegaard Floer homology
Presenter:	Robert Lipshitz, Columbia University
Date:	Friday, May 11, 2007, Time: 2:00 p.m., Location: Fine 214
Abstract:	Heegaard Floer homology is a package of invariants in low- dimensional topology defined in terms of Lagrangian intersection Floer homology. As such, these invariants have typically been hard to compute. However, a remarkable observation of Sucharit Sarkar last summer led to a revolution in computing Heegaard Floer homology. After reviewing the definition of Heegaard Floer homology we will discuss Sarkar's observation. We will then explain how this extends to allow one to compute the maps on \hat{HF} induced by four-dimensional cobordisms -- joint work of Ciprian Manolescu, Jiajun Wang and the speaker.
Differential Geometry and Geometric Analysis Seminar
Topic:	Regularity of C^{1} smooth solutions to the mean curvature equation in the Heisenberg group
Presenter:	Jih-Hsin Cheng, Academica Sinica
Date:	Friday, May 11, 2007, Time: 3:00 p.m., Location: Fine 314
Abstract:	We consider a C^{1} smooth solution to the p(or H)-mean curvature equation in the 3-dimensional Heisenberg group. Assuming only the p-mean curvature H is C^{0}, we show that any characteristic curve is C^{2} smooth and its curvature equals -H. By introducing special coordinates and invoking the jump formulas along characteristic curves, we can prove that the Legendrian (horizontal) normal gains one more derivative. Therefore the seed curves are C^{2} smooth.