# 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/