Van Loo Postdoctoral Fellowship Program

Pengyu Le

Van Loo Post-Doctoral Fellow and Assistant Professor

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

Department of Mathematics
University of Michigan
3827 East Hall
530 Church Street
Ann Arbor, MI 48109-1043

Phone: (734) 764-6442
Email: pengyul@umich.edu

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

Sitai Li

Van Loo Post-Doctoral Fellow and Assistant Professor (beginning 2019)

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

Mathematics Department
1821 East Hall
530 Church Street
Ann Arbor, MI 48109-1043

Phone: 734-615-4413
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.

Education

Diplom, Heidelberg University, Germany (2009)
Ph.D., Stony Brook University, USA (2015)

Contact

Physics Department
3420 Randall Lab
450 Church Street
Ann Arbor, MI 48109-1040

Phone: (734) 615-6428
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)

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/

Jörn Zimmerling

Van Loo Postdoctoral Fellow and Assistant Professor

Research Interest
My research interests lie in the field of numerical methods for partial differential equations.

Currently, my research interests can be mainly summarized within two categories:

  1. Forward problems: Fast and efficient numerical solvers of PDEs with variable coefficients and in complex geometries. These involve reduced-order modeling, Krylov subspace projection methods, computation of resonances, fast numerical linear algebra and scientific computing.
  2. Inverse problems: Estimation of coefficients of PDEs from remote measurements.

Education/Degree

B.Sc., Delft University of Technology (2012)
M.Sc., Delft University of Technology (2014)
Ph.D., Delft University of Technology (2018)

Contact
Mathematics Department
1844 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
Phone: (734) 936-0085
jzimmerl@umich.edu