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Christianson, Hans P

Hans Christianson

Director of Graduate Studies
Phillips Hall 304B

Research Interests

Partial differential equations, spectral geometry, microlocal analysis, quantum chaos

Professional Background

B.S., University of Minnesota, Twin Cities, 2002; Ph.D. University of California, Berkeley, 2007; CLE Moore Instructor, MIT 2007-2010; MSRI Postdoc, 2008; Assistant Professor, UNC, Chapel Hill, 2010-2016; Associate Professor, UNC, Chapel Hill, 2016-present

Research Synopsis

My research interests are based on the idea of classical-quantum correspondence. Differential geometry describes a classical system, such as Newtonian Mechanics, geodesic flow. The classical system tells us how the related quantum system, such as drum vibrations, quantum particle distribution, should behave. The machinery used to make this connection is called microlocal analysis, which means we study solutions of Partial Differential Equations living in a classical phase space, varying both in position and frequency of oscillation. I am mostly interested in chaotic and singular classical systems, which lead to quantum systems exhibiting equidistribution of waves or unstable scattering.

Representative Publications

Equidistribution of Neumann Data Mass on Simplices and a Simple Inverse Problem
H. Christianson,
Mathematical Research Letters, 26, 2, 421-445, 2019

Imperfect Geometric Control and Overdamping for the Damped Wave Equation
N. Burq and H. Christianson,
Communications in Mathematical Physics, 336,1, 101-130, 2015

Local Smoothing for the Schrödinger Equation With a Prescribed Loss
H Christianson and J. Wunsch,
American Journal of Mathematics, 135, 6, 1601-1632, 2011