Van Loo Postdoctoral Fellowship Program

Thomas Bothner

Van Loo Post-Doctoral Fellow and Assistant Professor

Research Interest
My research focuses on asymptotical questions in the modern theory of integrable systems. This theory belongs to the field of mathematical physics and I am foremost interested in problems of random matrix theory, in particular problems which display intimate connections to statistical physics (exactly solvable models) and the field of integrable differential equations (Painleve and nonlinear wave type equations). The application of asymptotic methods, special function theory and the theory of orthogonal polynomials is central to this work. My papers can be found on the arXiv and on MathSciNet.

Education/Degree
B.Sc., Ulm University (2007)
M. Sc., Ulm University (2009)
Ph. D., Purdue University (2013)

Contact
Mathematics Department
4823 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
phone: (734) 763-1181
bothner@umich.edu

Eduardo Corona

Van Loo Post-Doctoral Assistant Professor

Research Interest
Fast algorithms, numerical methods for integral equations, randomized linear algebra, high performance scientific computing (HPC), computational fluid dynamics (CFD), computational electromagnetics (CEM), and finite element methods (FEM).

Research Goals
Development of optimal complexity fast algorithms for hierarchical compression and inversion of linear operators – Fast Multipole Methods, HSS matrices and Tensor Train decomposition- and their application to Integral operators arising in diverse areas of scientific computing, such as particulate and granular flow, material science, and electromagnetic and accoustic scattering.

Development of novel integral equation formulations and singular quadrature methods which, coupled with fast algorithm and collision detection technology, allow for the efficient simulation of large scale multibody, multiphysics problems. Ongoing work includes simulation of rigid body suspensions in the context of microscopic swimming and magnetorheological flows, and simulation of granular flow for high-fidelity, large scale terramechanics problems.

Education/Degree
B.S., Instituto Tecnologico Autonomo de Mexico (2007)
M.S., New York University (2010)
Ph. D., New York University (2014)

Contact
Department of Mathematics
4860 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
E-mail: coronae(at)umich.edu
Phone: (734) 763-1357

John Golden

Van Loo Research Fellow

Research Interest: Theoretical Elementary Particle Physics
My research is focused on scattering amplitudes, which are mathematical functions predicting what will happen when subatomic particles collide. These functions frequently involve a class of functions known as polylogarithms, which are generalizations of the logarithm. Unexpectedly, scattering amplitudes also appear intricately related to cluster algebras, a class of commutative rings introduced by Sergey Fomin and collaborators here at UMich. I am trying to understand how these worlds of particle physics, polylogarithms, and cluster algebras intersect, and hopefully gain some physical understanding of the role that these branches of mathematics play in the structure of our universe.

Ph.D. Topic: Cluster Polylogarithms and Scattering Amplitudes
Current Field(s) of Interest: High Energy Theoretical Physics
Research Group: Michigan Center for Theoretical Physics

Education/Degree
Brown University

Contact
Department of Physics
3429 Randall
450 Church Street
Ann Arbor, MI 48109-1040
E-mail: jkgolden(at)umich.edu
Phone: (734) 763-4313

Howard Levinson

Van Loo Post-Doctoral Fellow and Assistant Professor

Research Interest
My research focuses on inverse problems and its imaging applications. In particular, I am interested in developing robust and efficient algorithms and computational methods for solving various types of inverse scattering problems. Specific topics of interest include nonlinear scattering, sparse reconstructions, and fluorescence microscopy.

Education/Degree
B.A., Tufts University (2011)
Ph. D., University of Pennsylvania (2016)

Contact
Mathematics Department
1830 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
Phone: (734) 936-0145
levh@umich.edu

Ian Tobasco

Van Loo Post-Doctoral Fellow and Assistant Professor

Research Interest
I am a mathematical analyst specializing in the calculus of variations and partial differential equations. My work comes from physics and more specifically from solid mechanics and fluid dynamics. I have also worked on problems from statistical mechanics and the mean field theory of spin glasses. Regarding mechanics, I work on problems from nonlinear elasticity theory involving the wrinkling and crumpling of thin elastic sheets. Regarding fluids, I work on optimal design problems such as the design of optimal heat transport by an incompressible fluid. Both areas concern the study of highly non-convex optimization problems which possess many local optimizers. The challenge, therefore, is to understand what makes test functions globally optimal, and to reject those which are not.

Education/Degree
B.S.E., University of Michigan (2011)
Ph. D., Courant Institute, New York University (2016)

Contact
Mathematics Department
1833 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
itobasco@umich.edu
personal website: http://www-personal.umich.edu/~itobasco/