RESEARCH INTERESTS
- Differential Geometry, General Relativity, Partial Differential Equations.
- My research has been partly supported by the National Science Foundation, through grants DMS-0707317 and DMS-1207844. You can read a bit them here and here.
- My research was also supported in part by a Simons Collaboration Grant.
PUBLICATIONS
Book review : Curvature of space and time, with an introduction to geometric analysis (by I. Stavrov), Amer. Math. Monthly 128 , no. 8, (2021)
Localized deformation for initial data sets with the dominant energy condition. (Joint with Lan-Hsuan Huang). Calc. Var. Partial Differential Equations 59 , no. 1, 43 pp. (2020)
A short note on the Bartnik mass. Pure and Applied Mathematics Quarterly 15, no. 3, 827-838 (2019)
A Note on the Bartnik Mass. CMSA Series in Mathematics, Vol. 1, Nonlinear Analysis in Geometry and Applied Mathematics, International Press of Boston, (2017), 49-75.
On the P-scalar curvature. (Joint with Farhan Abedin). Journal of Geometric Analysis. 27 , no. 2, 1589-1623 (2017)
Deformation of scalar curvature and volume. (Joint with Michael Eichmair and Penzi Miao). Math. Ann. 357 , 551-584 (2013)
Construction of N-body initial data sets in general relativity. (Joint with Piotr Chrusciel and James Isenberg). Comm. Math. Phys. 304 , 637-647 (2011)
Scalar Curvature and the Einstein Constraint Equations. (Joint with Daniel Pollack). In: H. L. Bray, W. P. Minicozzi, II (eds.), Surveys in Geometric Analysis and Relativity , Adv. Lect. Math. 20 , pp. 145-188 (2011)
Initial data for the relativistic gravitational N-body problem. (Joint with Piotr Chrusciel and James Isenberg). Classical and Quantum Gravity 27 (2010) 222002 (6pp)
Hamiltonian Stationary Tori in Kahler Manifolds. (Joint with Adrian Butscher). Calc. Var. Partial Differential Equations. 45, no. 1-2, 63-100 (2012)
Constructions of time-symmetric N-body initial data sets in general relativity. (Joint with Piotr Chrusciel and James Isenberg). Cont. Math. 554 , 83-92 (2011)
Construction of N-body initial data sets in general relativity. Oberwolfach Reports 6 , no. 4, 2630-2633 (2009)
On Isoperimetric Surfaces in General Relativity, II. (Joint with Farhan Abedin, Shelven Kapita, Haotian Wu.) Journal of Geometry and Physics 59, 1453-1460 (2009)
On the Center of Mass in General Relativity. (Joint with Haotian Wu). Classical and Quantum Gravity 25 (2008)
On Isoperimetric Surfaces and General Relativity. (Joint with 2005 REU group). Pacific J. Math. 231, no. 1, 63-84 (2007)
On the Existence and Stability of the Penrose Compactification. Annales Henri Poincare’ 8, 597-620 (2007)
Some Recent Results on the Einstein Constraint Equations. Oberwolfach Reports 3, no. 1, 83-87 (2006)
On the Asymptotics of the Vacuum Einstein Constraint Equations. (Joint with Richard M. Schoen). Jour. Diff. Geom. 73, no.2, 185-217 (2006)
A Note on Asymptotically Flat Metrics on R^3 which are Scalar-Flat and Admit Minimal Spheres. Proc. Amer. Math. Soc. 133, 3669-3678 (2005)
Constructions of Vacuum Spacetimes Symmetric Near Spatial Infinity. In: V. G. Gurzadyan, et. al. (eds.) Proceedings of the Ninth Marcel Grossmann Meeting on General Relativity (Rome, 2000), pp. 993-994. Singapore: World Scientific, 2002
Scalar curvature deformation and a gluing construction for the Einstein constraint equations. Comm. Math. Phys. 214 , no. 1, 137–189 (2000)
INVITED TALKS
A Celebration of Mathematical Relativity in Miami (Conference in honor of G. J. Galloway on the occasion of his 70th birthday), December 14-16. On Constraint Deformation and the Dominant Energy Condition.
Workshop on Initial Data in General Relativity, University of Alaska, Fairbanks, May 21-23. A survey of localized constraint deformation.
20th School on Differential Geometry. Federal University of Paraíba, Joao Pessoa, Brazil, February 27-March 3, 2018. Deformation and Gluing Constructions for the Einstein Constraint Equations (Plenary Talk)
Between Geometry and Relativity Summer School. Erwin Schrodinger Institute Vienna, Austria, July 2017. Constructing initial data for the Einstein equations (four lecture mini-course)
Banff International Research Station Workshop on Geometric Analysis and General Relativity , July 20, 2016, Deformation and gluing for the Einstein constraints with the dominant energy condition.
Center for Mathematical Sciences and Applications, Workshop on Aspects of General Relativity, May 24, 2016, Harvard University, Cambridge, MA. Scalar curvature deformation and the Bartnik mass.
Static Metrics and Bartnik’s Quasi-local Mass Conjecture, Tubingen, Germany, May 19, 2016, Scalar curvature deformation and the Bartnik mass.
AMS Sectional Meeting, Special Session on Mathematical General Relativity, Stony Brook, March 21, 2016. Deformation of the Einstein constraints with the dominant energy condition.
Tsinghua-Sanya International Mathematics Form on Mathematical Relativity, January 7, 2016, Sanya, China. Deformation and gluing for the Einstein constraints with the dominant energy condition.
40th Ravello Summer School on Mathematical Physics , September 21-26, 2015, Ravello, Italy. Geometric Analysis and the Einstein Constraint Equations. (six-lecture mini-course)
Warwick-Imperial-Cambridge Seminar, July 17, 2015, Imperial College, London. Localized scalar curvature deformation.
General Relativity and Gravitation Einstein Centennial Conference, Penn State University, June 2015. Parallel Session on Mathematical GR. Density and Deformation Theorems for the Constraint Equations.
Geometric Analysis in Geometry and Topology 2014 Workshop, Tokyo University of Science, Tokyo, Japan, October 28-31, 2014. Deformation and gluing constructions for scalar curvature, with applications (three lectures).
ESI-EMP-IAMP Summer School on Mathematical Relativity. Erwin Schrodinger Institute, Vienna, Austria, July 28-August 1, 2014. The Einstein Constraint Equations (five-lecture mini-course).
University of Connecticut Colloquium. Storrs, CT. April 17, 2014. On the scalar curvature and volume of Riemannian manifolds.
2013 Taiwan International Conference on Geometry. National Taiwan University, Taipei. December 17, 2013. Deformation, gluing and density theorems for the Einstein constraint equations.
2013 Taiwan International Conference on Geometry. National Taiwan University, Taipei. December, 2013. Co-taught invited mini-course joint with Pengzi Miao (Miami) Scalar Curvature and the Einstein Constraint Equations
MSRI Workshop: Initial data and Evolution Problems in General Relativity. Berkeley, CA. November 22, 2013. Density and deformation theorems for the Einstein constraint equations.
New York Area General Relativity Seminar. Stony Brook, NY. March 29, 2013. Asymptotics and gluing for the Einstein constraint equations.
ICTP Conference on Geometric Analysis. Trieste, Italy. June 29, 2012. Deformation and gluing constructions for scalar curvature.
University of Pennsylvania Geometry and Topology Seminar. March 22, 2012. Deformation and gluing constructions for scalar curvature.
Lehigh University Colloquium. October 26, 2011. Deformation of Scalar Curvature and Volume.
Beijing Summer Program in Mathematical Relativity. Peking University (Beijing, China). June 10, 2011. Deformation of Scalar Curvature and Volume.
CADS V Workshop on General Relativity and the Einstein Equations (Akko, Israel). May 23, 2011. Deformation of Scalar Curvature and Volume.
PRIMA Conference on Geometric Analysis. Pacific Institute for the Mathematical Sciences, Vancouver. July 25, 2010. Localized Scalar Curvature Gluing.
Columbia University Geometry and Analysis Seminar. November 5, 2009. Geometric Perturbation and Gluing Constructions.
Lehigh University Colloquium. October 29, 2009. Geometric Perturbation and Gluing Constructions.
Oberwolfach Meeting on Mathematical Aspects of General Relativity. October 12, 2009. Construction of N-body initial data sets in general relativity.
Princeton University Differential Geometry and Geometric Analysis Seminar. October 2, 2009. Hamiltonian Stationary Tori in Kahler Manifolds.
CADS IV Workshop on General Relativity and the Einstein Equations (Nahariya, Israel). May 21, 2009. Constructions of N-body solutions of the Einstein constraint equations.
Mittag-Leffler Institute Seminar. December 4, 2008. The center of mass of isolated systems from a geometric point of view.
Banff Workshop. December 13, 2007. Geometry and the Einstein Constraint Equations.
Lehigh University Geometry Seminar. November 28 and December 5, 2006. On the Einstein Constraint Equations.
Oberwolfach Meeting on Mathematical Aspects of General Relativity. January 9, 2006. Some Recent Results on the Einstein Constraint Equations.
Isaac Newton Institute Conference on the Einstein Constraint Equations. December 15, 2005. Some Applications of Scalar Curvature Deformation in General Relativity.
Lafayette College Physics Club/Sigma Xi World Year Physics Seminar. April 15, 2005. On the Structure of Isolated Systems in General Relativity.
Haverford Colloquium. November 8, 2004. Curvature, Topology and General Relativity.
Lafayette-Lehigh Geometry-Topology Seminar. October 19, 2004. The Einstein Constraint Equations.