Xinliang (Adam) An
Department of Mathematics I am a Postdoctoral Fellow in Mathematics at University of Toronto. I got my PhD from Princeton University in 2014. My advisor is Professor Sergiu Klainerman. ## Research Interests:I am interested in geometric PDEs. My main research direction is singularity formation in general relativity. With tools from hyperbolic PDE, quasilinear elliptic equations, geometric analysis, dynamical system and numerical approach, I am working to answer questions arising from physics. Together with my co-authors, we have worked on and provided answers for the following four physical questions:- Can “black holes” form dynamically in vacuum? (link)
- To form a “black hole”, what is the least size of initial data? (link)
- Can we find the boundary of a “black hole” region? Can we show that a “black hole region” is emerging from a point? (link)
- For Einstein vacuum equations, could singularities other than black hole type form in gravitational collapse? (link)
## Papers and Preprints:- Polynomial blow-up upper bounds for Einstein-scalar field system, in preparation
- (with Willie Wong ) Warped product space-times, 31 pages
- Emergence of apparent horizon in gravitational collapse, 51 pages
- An iteration scheme in gravitational collapse II, 120 pages, preprint
- An iteration scheme in gravitational collapse I, 60 pages, preprint
- (with Avy Soffer ) Fermi’s golden rule and H^1 scattering for nonlinear Klein-Gordon equations with metastable states, 36 pages
- (with Xuefeng Zhang and Hong Lu) Examples of naked singularity formation in higher-dimensional Einstein-vacuum spacetimes, 16 pages
- (with Xuefeng Zhang) Naked singularity and black hole formation in self-similar Einstein-scalar fields with exponential potentials, 24 pages
- (with Jonathan Luk ) Trapped surfaces in vacuum arising dynamically from mild incoming radiation, 93 pages
- Formation of trapped surfaces in General Relativity, PhD thesis, 309 pages
- Formation of trapped surfaces from past null infinity, 125 pages
## Selected Conference Talks:- International Conference on Nonlinear Waves and General Relativity, The Chinese University of Hong Kong, December 11-17, 2017
- 27th Midwest Relativity Meeting, University of Michigan, October 12-14, 2017
- The IV Applied Mathematics, Modeling and Computational Science (AMMCS) International Conference, University of Waterloo, August 20-25, 2017
- International Conference on Evolution Equations (in conjunction with the 31st annual Shanks Lecture), Vanderbilt University, May 16-20, 2016
- Tsinghua Sanya International Mathematics Forum, Mathematical Sciences Center, Tsinghua University, January 5-9, 2016
- Nonlinear Wave equations and their numerical study, Fields Institute, June 22-26, 2015
- Focus Program on 100 Years of General Relativity (Black Hole Stability), Fields Institute, June 8-12, 2015
- General Relativity and Gravitation: A Centennial Perspective, Pennsylvania State University, June 7-12, 2015
- Rutgers-CUNY Symposium on Geometric Analysis, CUNY-Rutgers, March 27-29, 2015
- Mathematical Problems in General Relativity, Simons Center for Geometry and Physics, January 21, 2015
## Selected Seminar Talks:- Black Hole Initiative Colloquium, Harvard University, November 14, 2017
- Mathematical Physics Seminar, University of Vienna, April 26, 2017
- Montreal Analysis Seminar, McGill University, April 7, 2017
- PDE Seminar, Peking University, May 30, 2016
- Calderon-Zygmund Analysis Seminar, University of Chicago, Feb 29, 2016
- New York Area Mathematical General Relativity Seminar, Stony Brook University, December 12, 2014
- Analysis/PDE Seminar, Johns Hopkins University, January 27, 2014
- General Relativity Seminar, Columbia University, November 30, 2012
## Past Teaching:- Fall 2014: Partial Differential Equations
- Spring 2015: Advanced Calculus I and Honors Calculus III
- Fall 2015: Advanced Calculus I and Honors Calculus III
- Spring 2016: Differential Equations for Engineering and Physics
- Fall 2016: Calculus I
- Spring 2017: Calculus II
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