Temple-Rutgers Global Analysis Seminar
Current contacts: Gerardo Mendoza (Temple) and Siqi Fu and Howard Jacobowitz (Rutgers)
The seminar takes place Friday 3:00 - 3:50 pm in Wachman 527 for talks at Temple, or 319 Cooper, Rm 110, for talks at Rutgers-Camden. Click on title for abstract.
Sönmez Şahutoğlu, University of Toledo
TBA
Stephen McKeown, Princeton University
TBA
Purvi Gupta, Rutgers University
Starting with the observation that every continuous complex-valued function on the unit circle can be approximated by rational combinations of one function and polynomial combinations of two functions, we will discuss analogous approximation phenomena for compact manifolds of higher dimensions. On a related note, we will discuss some questions regarding the minimum embedding (complex) dimension of real manifolds within the context of polynomial convexity. In the special case of even-dimensional manifolds, we will present a technique that improves previously known bounds. This is joint work with Rasul Shafikov.
Siqi Fu, Rutgers University
In this talk, I will explain the proof of the following result due to C. Laurent-Thiebault, M.-C. Shaw and myself: Let $\Omega=\widetilde{\Omega}\setminus \overline{D}$ where $\widetilde{\Omega}$ is a bounded domain with connected complement in $\mathbb C^n$ and $D$ is relatively compact open subset of $\widetilde{\Omega}$ with connected complement in $\widetilde{\Omega}$. If the boundaries of $\widetilde{\Omega}$ and $D$ are Lipschitz and $C^2$-smooth respectively, then both $\widetilde{\Omega}$ and $D$ are pseudoconvex if and only if $0$ is not in the spectrum of the $\bar\partial $-Neumann Laplacian on $(0, q)$-forms for $1\le q\le n-2$ when $n\ge 3$; or $0$ is not a limit point for the spectrum of the $\bar\partial $-Neumannn Laplacian on $(0, 1)$-forms when $n=2$.