My research centers on symplectic and low-dimensional topology. In low dimentional topology, I work on developing obstructions for various notions of positivity of links using Khovanov homology and its related theories.
In symplectic topology, my research focusses on understanding the symplectic fillings of contact manifolds using punctured pseudoholomorphic curves. Specifically, I am interested in understanding how surgery-type operations on contact manifolds affects the symplectic fillings.
Publications:
A vanishing theorem in Siefring's intersection theory, arXiv: 2412.11897,
accepted in the International Journal of Mathematics.
On unknotting fibered positive knot and braids, arXiv: 2312.07339
with Marc Kegel, Lukas Lewark, Filip Misev, Leo Mousseau and Marithania Silvero,
accepted in The Annali della Scuola Normale Superiore di Pisa, Classe di Scienze.
Khovanov homology of positive links and of L-space knots, arXiv: 2304.13613
with Marc Kegel, Leo Mousseau and Marithania Silvero,
submitted.
On the topology of bi-cyclopermutohedra, arXiv: 1904.12183, Journal
with Priyavrat Deshpande and Anurag Singh,
Indian Journal of Pure and Applied Mathematics(2022).
Other publications:
Algorithms in 4-Manifold topology, arXiv: 2411.08775
Collaborative work with 30 other authors; the complete list can be found in the ArXiv link provided above.
accepted in Algebraic and Geometric Topology.
Poincare duality 4-complexes, Oberwolfach report, MFO - Webpage
with Daniel Galvin, Mark Pencovitch and Arunima Ray.