Research
Research interests
Complex and algebraic geometry, in particular vector bundles and principal bundles; stability conditions; Hermitian-Einstein (Yang-Mills) equations; the Kobayashi-Hitchin correspondence and its generalizations, e. g. to “augmented bundles” such as Higgs bundles or parabolic bundles.
PhD thesis
Stability and Hermitian-Einstein metrics for vector bundles on framed manifolds, supervised by Prof. Dr. Georg Schumacher
Marburg, December 2009
PhD thesisPapers
Published papers
Approximate Yang-Mills-Higgs metrics on flat Higgs bundles over an affine manifold (with Indranil Biswas and John Loftin)
Communications in Analysis and Geometry 22 (2014), 737—754
The vortex equation on affine manifolds (with Indranil Biswas and John Loftin)
Transactions of the American Mathematical Society 366 (2014), 3925—3941
Automorphisms and connections on Higgs bundles over compact Kähler manifolds (with Indranil Biswas, Steven B. Bradlow and Adam Jacob)
Differential Geometry and Its Applications 32 (2014), 139—152
Affine Yang-Mills-Higgs metrics (with Indranil Biswas and John Loftin)
Journal of Symplectic Geometry 11 (2013), 377—404
Approximate Hermitian-Einstein connections on principal bundles over a compact Riemann surface (with Indranil Biswas, Steven B. Bradlow and Adam Jacob)
Annals of Global Analysis and Geometry 44 (2013), 257—268
Flat bundles on affine manifolds (with Indranil Biswas and John Loftin)
Arabian Journal of Mathematics 2 (2013), 159—175
Vortex equation and reflexive sheaves (with Indranil Biswas)
Advances in Theoretical and Mathematical Physics 16 (2012), 713—723
Hermitian-Einstein connections on polystable parabolic principal Higgs bundles (with Indranil Biswas)
Advances in Theoretical and Mathematical Physics 15 (2011), 1503—1521
Existence of approximate Hermitian-Einstein structures on semistable principal bundles (with Indranil Biswas and Adam Jacob)
Bulletin des Sciences Mathématiques 136 (2012), 745—751
Stability and Hermitian-Einstein metrics for vector bundles on framed manifolds
International Journal of Mathematics 23 (2012), 1250091
Hermitian-Einstein connections on polystable orthogonal and symplectic parabolic Higgs bundles (with Indranil Biswas)
Journal of Geometry and Physics 62 (2012), 1358—1365
doi:10.4310/CAG.2014.v22.n4.a5
doi:10.1090/S0002-9947-2014-06152-7
doi:10.1016/j.difgeo.2013.11.008
See also: my publications on arXiv.
Cooperations
People with whom I have collaborated:
- Indranil Biswas, Tata Institute of Fundamental Research, Mumbai (India)
- Steven Bradlow, University of Illinois at Urbana-Champaign, Urbana, IL (USA)
- Adam Jacob, Harvard University, Cambridge, MA (USA)
- John Loftin, Rutgers University at Newark, Newark, NJ (USA)
Invited talks
International Conference on Analytic and Algebraic Geometry related to bundles
Kerala School of Mathematics
Kozhikode, March 25—29, 2013International Conference on Complex Analytic Geometry
School of Mathematics, Tata Institute of Fundamental Research
Mumbai, March 26—30, 2012-
School of Mathematics, Tata Institute of Fundamental Research
Mumbai, May 27, 2011 -
Institute of Mathematical Sciences
Chennai, March 24, 2011 -
School of Mathematics, Tata Institute of Fundamental Research
Mumbai, February 10, 2011 Workshop “Lie Theory and Complex Geometry”
Marburg, November 4—6, 2010
Other conferences attended
International Conference on Analytic and Algebraic Geometry related to bundles
School of Mathematics, Tata Institute of Fundamental Research
Mumbai, March 18—22, 2013International Conference on Vector Bundles
Kerala School of Mathematics
Kozhikode, April 2—6, 2012