In low-dimensional topology, my work can be broadly divided into two directions. The first uses Khovanov and Khovanov–Rozansky homologies, together with their various extensions and variants, to study different notions of positivity for knots and links. The second is more foundational in nature, focusing on developing new theories and structures. Examples include constructing a more accessible, low-dimensional extension of odd Khovanov homology to tangles and developing oriented skein exact sequences in Khovanov–Rozansky homology.
In symplectic topology, my research focuses on the Siefring's intersection theory for punctured pseudoholomorphic curves. Building on this, I aim to develop an SFT-like framework that counts curves with vanishing self-intersection number, with the broader goal of extending embedded contact homology (ECH) to incorporate richer algebraic structures and interactions.
Publications and preprints:
HOMFLY-PT homology and positivity notions, expected December 2026.
Joint work with Maciej Borodzik and Paula Truöl.
A planar model for odd Khovanov homology and application to functoriality, expected October 2026.
Joint work with Léo Schelstrate and Shun Ming Samuel Lee.
Oriented skein exact sequences in HOMFLY-PT and sl(n) homology, draft available on request, expected September 2026.
Joint work with Marc Kegel.
Reduced even and odd Khovanov homologies of positive and 0-adequate links, draft available on request, expected September 2026.
Torsion in Khovanov homology of positive links, draft available on request, expected September 2026.
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, accepted in The Annali della Scuola Normale Superiore di Pisa, Classe di Scienze.
Joint work with Marc Kegel, Lukas Lewark, Filip Misev, Leo Mousseau and Marithania Silvero.
Khovanov homology of positive links and of L-space knots, arXiv: 2304.13613.
Joint work with Marc Kegel, Leo Mousseau and Marithania Silvero.
On the topology of bi-cyclopermutohedra, arXiv: 1904.12183, accepted in the Indian Journal of Pure and Applied Mathematics.
Joint work with Priyavrat Deshpande and Anurag Singh.
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.