Joe J Perez
 joe_j_perez @

Teaching Portfolio
Mathematical Genealogy
Activity and Prospects
Research - Levi Problem
My current mathematical research is in several complex variables and invariant, subelliptic operators on principal bundles.
First Paper
Second Paper
Third Paper
Research Statement
Dissertation Defense Announcement
Dissertation Abstract
Talks and Meetings
Analysis Seminar, Montana State University, April 14, 2006

UMass Boston, October 29, 2007 - Slides

Analysis Seminar, NEU, Dec. 13, 2007, On Feynman's derivation of the Navier-Stokes equation.

Departmental Seminar, Texas A & M University - Kingsville, April 18, 2008 - Write-Up

South Texas Mathematics Consortium, UTPA, Edinburg, Texas, Saturday, Feb. 21, 2009. Talk: $L^2$-holomorphic functions on $G$-complexifications of manifolds.

Texas A & M University -- Kingsville's Annual High School-College Interface, Feb. 27, 2009. Talk: The Advanced Math and Science Academy Charter School -- An experiment in accelerated secondary education.

Several Complex Variables Seminar, Texas A&M University (College Station), April 9, 2009. Talk: $L^2$-holomorphic functions on strongly pseudoconvex $G$-manifolds.

Spectral Theory and Geometric Analysis (meeting in honor of M A Shubin's 65th birthday) Jul. 29--Aug. 2, 2009

$\bar\partial$-Neumann Problem special program at ESI, Vienna, Oct. 27--Dec. 23rd, 2009.

Math Kolloquium, U Bern, 22 March 2010

Other Projects
Bocksteins in Mathematica. Functions were written in Mathematica to compute nontrivial Bockstein homomorphisms in the Z/2Z cohomology of SO(n).

Random triangulations of surfaces in Mathematica. Functions were written in Mathematica to randomly generate simplicial complexes of closed, orientable surfaces. These are being checked against those in the list here and statistics are being computed. Our method is similar to that of Brooks-Makover, but we ignore nonsimplicial complexes their method generates. Translations of available triangulations of surfaces are available here.

Asymmetric features of an icosahedral virus. Reovirus is a nonenveloped virus with an icosahedral protein capsid enclosing a segmented dsRNA genome. While the structure of the capsid is known in great detail, the arrangement of the genetic material, which does not have icosahedral symmetry, is unknown. Cryo-electron micrographs of reovirus particles were analyzed to search for asymmetric features.
Laboratory Experience
The first real jobs I had were in R A Kenefick's Laboratory at Texas A & M University. In the last bit of my undergraduate period and the beginning of my graduate, I worked on the antimatter trapping and cooling project in this lab. This was enormously stimulating and Professor Kenefick was and still is an important influence and inspiration. I was given the responsibility of designing and building a GaAs-FET preamplifier to operate in a 4K, UHV, 8T environment. I designed, built, and maintained cryogenic ultrahigh vacuum systems. I designed and machined various scientific instruments, including an entire Penning trap. I then became enamored of quantum field theory. This led me (predictably) to mathematics, where I have worked since.

Below, I link to two papers in which I am acknowledged for my work in the lab.