Faculty Biography


  Aghil Alaee Khangha

  Assistant Professor
  Department of Mathematics
  Clark University
  Worcester, MA 01610-1477

  Phone: 508-793-7129
  Email: aalaeekhangha

  Research Website

 


 Education

Professor Aghil Alaee Khangha joined the Mathematics department at Clark University in fall 2020. Before joining Clark University, he was a Black Hole Initiative fellow at Harvard University (2019-2020); a postdoctoral fellow at the Center of Mathematical Sciences and Applications at Harvard University (2018-2019); a Natural Sciences and Engineering Research Council postdoctoral fellow at the University of Toronto (2017-2018); and a Pacific Institute for the Mathematical Sciences postdoctoral fellow at the University of Alberta (2015-2017). He received his doctorate in mathematics, with distinction, from Memorial University in December 2015.

 

Current Teaching and Research

Professor Alaee's research focuses on geometric analysis and mathematical relativity. He investigates conjectures in general relativity — such as existence, uniqueness, and stability — and the formation of black holes using geometric analysis, which lies at the intersection of developments in differential geometry, partial differential equations, and modern physics. He has proved several geometric inequalities involving total energy, quasi-local energy, area of horizon, angular momentum, and charges of black holes.

Professor Alaee taught a variety of undergraduate mathematics courses at Clark University, Harvard University, University of Toronto, University of Alberta, and Memorial University.

 

Selected Publications

"A localized spacetime Penrose inequality and horizon detection with quasi-local mass", with Martin Lesourd and Shing-Tung Yau, To appear in Journal of Differential Geometry.

"Positive mass theorem for initial data sets with corners along a hypersurface", with Shing-Tung Yau, To appear in Communications in Analysis and Geometry.

"Cosmic cloaking of rich extra dimensions", with Marcus Khuri and Hari Kunduri, International Journal of Modern Physics D (2021), Honorable Mention - in the Gravity Research Foundation 2021 Awards for Essays on Gravitation.

"Stable surfaces and free boundary marginally outer trapped surfaces", with Martin Lesourd and Shing-Tung Yau, Calculus of Variations and Partial Differential Equations 60, 186, (2021).

"Stability of a quasi-local positive mass theorem for graphical hypersurfaces of Euclidean space", Armando Cabrera-Pacheco and Stephen McCormick, Transactions of the American Mathematical Society 374 , 3535-3555 (2021).

"Geometric inequalities for quasi-local masses", with Marcus Khuri and Shing-Tung Yau, Communications in Mathematical Physics 378, 467–505 (2020).

"Existence and uniqueness of near-horizon geometries for five-dimensional black holes", with Marcus Khuri and Hari Kunduri, Journal of Geometry and Physics 144, 370-387 (2019).

"Mass-angular momentum inequality for black rings", Marcus Khuri and Hari Kunduri, Physical Review Letters 119, 7, 071101 (2017).

"Proof of the mass-angular momenta inequality for bi-Axisymmetric black holes with spherical topology", Marcus Khuri and Hari Kunduri,  Advances in Theoretical and Mathematical Physics 20, 6, 1397-1441 (2017).