Biography

Joe Po-Chou Chen is a/an Faculty/Staff in the University Of Connecticut department at University Of Connecticut

University of Connecticut - Mathematics

Assistant Professor of Mathematics at Colgate University
Joe P.
Chen
Syracuse, New York Area
I am an NSF-funded principal investigator who studies and teaches probability, analysis, and mathematical physics. In particular I am most interested in problems surrounding the scaling limits of various particle systems, especially on rough geometries that do not possess spatial symmetries. While some physical intuition guides my research, ultimately I utilize tools from probability theory, (stochastic) PDEs, and discrete harmonic analysis to prove theorems that justify the phenomena.

Some of my best mathematical results to date are as follows:
*Proved a new, optimal functional inequality for the exclusion process on any finite connected weighted graph, using the monotonicity of the Dirichlet energy under electric network reduction. This paves the way for proving scaling limits of particle systems with microscopic interactions on non-translationally-invariant state spaces, such as trees, fractals, and random graphs.
*Solved the magnetic spectrum on the Sierpinski gasket under uniform magnetic field, thereby establishing the Sierpinski gasket version of Hofstadter's butterfly.
*Established limit shape universality of discrete Laplacian growth models on the Sierpinski gasket, including the complete exact solution of the abelian sandpile growth problem.
*Discovered a simple random walk model on the integer half-line which exhibits purely singularly continuous spectrum (that is, neither has point mass nor has density with respect to Lebesgue measure)---the simplest such model currently known.
*Generalized Niels Bohr's asymptotic semiclassical formula for Schrodinger operators to abstract metric measure spaces.

I have delivered 5x 90-min research minicourses at Universität Bielefeld, Germany (twice) and Instituto Superior Técnico Lisboa, Portugal; been invited to give hour-long seminars or colloquia at: Brown, UChicago, Colby, Cornell, CUNY Graduate Center, Delft, Düsseldorf, Graz, Leiden, Montréal (CRM), SUNY Albany; and co-organized 4+ int'l conferences.