Joe J Perez
joe_j_perez @ yahoo.com

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2008 Creative Accomplishments -- Joe J Perez, TAMUK
Completed Research
Completed and submitted article: The G-Fredholm property of the -Neumann problem. In press at Journal of Geometric Analysis (v19, no 1). The journal reports an impact factor of 0.846 (2007).

Wrote and submitted article: The Levi Problem On Strongly Pseudoconvex G-Bundles.

Both these papers are available here.
Scholarly Service to the University
Served on Masters thesis committee of R G Hanus, L H Thurston chairman.
Advanced Undergraduate Education
STEP program mentor (student Albert Velasquez). Taught implementation of algorithms for approximate solution of partial differential equations of physics and integral curves in Mathematica using Fourier analytic techniques. Also taught techniques for producing high-quality graphics and animations. Some of the results can be seen at the following links: General, Heat equation, Fourier, and Integral Curves. These topics were chosen because the student was to enter TAMU's Aerospace Engineering Department. Student has maintained frequent contact. Already has found Fourier analysis he learned here helpful in his physics course.
Service to Mathematics Community
Provided illustrations of Bockstein Homomorphisms for Allen Hatcher's website. Joint work with M A Agosto.
Pending Research Projects
Initiated (with M A Agosto) computer investigation of the statistical character of the topology of random triangulations of closed surfaces without boundary. Here are some preliminary results and a lot of code.


Five papers in preparation: Will submit the first two this semester. The third probably next semester. The fourth and fifth are begun but serious mathematical difficulties still need be overcome.

i) (Review) Rellich's Compactness Theorem on Noncompact G-Spaces
ii) The G-Fredholm Property of Kohn's Boundary Laplacian
iii) The Bergman kernel and holomorphic functions on G-bundles (joint with Miroslav Engliš)
iv) Levi's Singular Functions and their Convolutions
v) Holomorphic Extensions of Boundary Values on Strictly Pseudoconvex G-bundles