# Former Van Loo Post-Doctoral Fellows

#### 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**

bothner@umich.edu

**First placement after postdoc: **Lecturer

King’s College

#### 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**

coronae@umich.edu

**First placement after postdoc: **Assistant Professor

New York Institute of Technology

#### 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**

jkgolden@umich.edu

#### David Goluskin

Van Loo Research Fellow

**Research Interest:** My research is in the broad area of applied nonlinear dynamics and incorporates both computation and analysis. Much of my work concerns fluid dynamics, but I also study simpler ordinary and partial differential equations. Recently I have been developing ways to use polynomial optimization to study dynamics, for instance to estimate time averages and other properties of attractors. A lecture for the public relating generally to some of my fluid dynamical research can be found here. I currently have funding for another PhD or MSc student to join my research group; a strong mathematical background and computational skills are required.

**Education/Degree**PhD Applied Mathematics, Columbia University, 2013

MS Applied Mathematics, Columbia University, 2009

BS Applied Mathematics, University of Colorado Boulder, 2007

BS Aerospace Engineering, University of Colorado Boulder, 2007

**Contact: **goluskin@uvic.ca

#### Pengyu Le

Van Loo Research Fellow

**Research Interest: **My research fields are differential geometry and general relativity. I am especially interested in Lorentzian geometry and their applications to specific problems in general relativity. I have studied the surface theory in Lorentzian manifolds and contributed to the criteria of the existence of trapped surfaces which is closely related to black holes in general relativity. I am also interested in the connections between Lorentzian geometry and other kinds of geometries.

Another focus of my research is the geometry of null hypersurfaces, which plays important roles in understanding the geometry of spacetimes. An application is the Penrose’s inequality relating the total mass of the spacetime and the mass of a black hole in it. In the future, I want to continue exploring these fields and broaden our knowledge about them.

**Education/Degree**

B.Sc., Tsinghua University (2013)

Ph.D., ETH Zurich (2018)

**Contact**

pengyul@umich.edu

**First placement after postdoc:**Beijing Institute of Mathematical Sciences and Applications (BIMSA)

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#### Howard Levinson

Van Loo Research Fellow

**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**

levh@umich.edu

**First placement after postdoc:**Santa Clara University Tenure Track Assistant Professor

#### Sitai Li

Van Loo Research Fellow

**Research Interest**My main research interests are integrable nonlinear partial differential equations and their applications. These equations possess a remarkably deep mathematical structure and are also important from a practical point of view. They appear as the governing equations to many concrete physical situations, such as acoustics, Bose-Einstein condensates, optics, plasmas, and water waves. In particular, I apply analytic methods, including inverse scattering transform and long-time asymptotics, and numerical simulations to study the nonlinear Schrödinger-type systems and the Maxwell-Bloch systems and their solutions.

**Education/Degree**

B.Sc., Nankai University (2010)

Ph.D., University at Buffalo, SUNY (2018)

**Contact**

Email: sitaili@umich.edu

Personal website: http://www-personal.umich.edu/~sitaili/

#### Jun Nian

Van Loo Research Fellow

**Research Interest:**I am broadly interested in theoretical physics and mathematical physics. More specifically, I study quantum field theories, gravity theories, integrable models and their correspondences inspired by string theory.

Currently I am using supersymmetric localization to compute some physical quantities exactly with full quantum effects, which allows us to study the conjectured relations among different quantum theories as well as black hole entropies with quantum corrections. This also provides a physical way of obtaining some mathematical quantities, such as some topological invariants.

I am also working on quantum fluid, in particular Bose-Einstein condensate, by mapping it into an effective string theory and applying string theory techniques.

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**Education/Degree**Diplom, Heidelberg University, Germany (2009)

Ph.D., Stony Brook University, USA (2015)

**Contact**nian@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)