## Past Seminars- Analysis

• Jie Xiao
Tue Dec 4, 2012
3:00 pm
Based on a paper joint with David R. Adams, we will address quasi-continuities of Morrey potentials and their applications to fine properties of weak solutions of two p-Laplace systems: (p,q)-type harmonic map and Lane-Emden systems, whence getting that any local singular set of the minimizing p-harmonic maps from a bounded domain to the unit...
• Xiaodong Wang
Fri Nov 9, 2012
3:00 pm
I will discuss a sharp lower bound for the first positive eigenvalue of the sublaplacian on a closed, strictly pseudoconvex pseudo-hermitian manifold of dimension \$2m+1\geq 5\$. We prove that the equality holds iff the manifold is equivalent to the CR sphere up to a scaling. The essential step is a characterization of the CR sphere when there is a...
• Xianghong Gong
Tue Oct 23, 2012
3:00 pm
Let M be a smooth hypersurface in R^{2n}. Suppose that on each side of M, there is a complex structure which is smooth up to M. Assume that the difference of the two complex structures is sufficiently small on M. We show that if a continuous function is holomorphic with respect to both complex structures, the function must be smooth from both...
• Bernard Russo
Tue Oct 16, 2012
2:00 pm
A quantum Banach space (operator space for short) is a linear subspace of Hilbert space operators together with its induced matrix norm structure. It is said to be a quantum operator algebra (operator algebra for short) if it is closed under multiplication. In a joint work with Matt Neal, a necessary and sufficient condition is given for a...
• Yuan Zhang
Tue May 29, 2012
3:00 pm
In this talk, we study Cauchy-Riemann equation on some smooth convex domains of in nite type in C2. In detail, we show that supnorm estimates hold for those infi nite exponential type domains provided the exponent is less than 1. This is a joint work with John Erik Fornaess and Lina Lee.
• Bernard Russo
Tue Apr 17, 2012
3:00 pm
I will present elementary (classical) proof(s) that every derivation of a finite dimensional semisimple algebra (associative, Lie, or Jordan) is inner, and state what is known in infinite dimensions for operator algebras. Then I will do the same for the corresponding triple systems. The purpose is to set the stage for the study of continuous...
• Professor Sagun Chanillo
Thu Apr 12, 2012
3:00 pm
We consider the global embedding problem for compact, three dimensional CR manifolds. Sufficient conditions for embeddability are obtained from assumptions on the CR Yamabe invariant and the non-negativity of a certain conformally invariant fourth order operator called the CR Paneitz operator. The conditions are shown to be necessary for small...