My doctoral 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.
In Preparation:
Khovanov-Rozansky homology of positive braids.
Publications:
A stratification of the moduli space using Siefring's intersection theory, arXiv: 2412.11897,
submitted.
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.
Poincare duality 4-complexes, Oberwolfach report, MFO - Webpage
with Daniel Galvin, Mark Pencovitch and Arunima Ray.
Selected Talks:
Strip shrinking isomorphism in Lagrangian intersection theory, European Kylerec at Oppdal, Norway. Mar 2025.
Khovanov stable homotopy type: Flow categories and Khovanov stable homotopy type: Cube resolutions and Burnside category, Symplectic geometry research seminar at Humboldt-Universität zu Berlin. Jul 2024.
Khovanov homology of positive links,
Institut Fourier summer school on low dimentional topology, Université Grenoble Alpes. Jun 27, 2024
Berlin Brandenburg Workshop II: Knot theory and its applications at Freie Universität Berlin. Nov 17, 2023
School on conformal symplectic dynamics and related fields at the Centre International de Rencontres Mathématiques (Lightning talk). May 8, 2023
the DMV Annual Meeting 2022 at Freie Universität Berlin. Sep 12-16, 2022
Chromatic graph homology and its relation to Hochschild homology, at MFO-Mathematisches Forschungsinstitut Oberwolfach, Hochschild (Co)Homology and Applications workshop (Lightning talk). Apr 2024
A vanishing theorem in Siefring's intersection theory, Symplectic geometry seminar at Universität Heidelberg. Jan 22, 2024
Homotopy IBL structure on DeRham Complex and its applications to String topology, Symplectic geometry research seminar at Humboldt-Universität zu Berlin. Jul 17, 2023
A very short introduction to Stein fillings, Symplectic geometry research seminar at Humboldt-Universität zu Berlin. Jun 27, 2022
Conferences/Workshops (2025):
Categorification in Low Dimensional Topology workshop + research conference} at Universität Bochum, Germany. Jul 2025
Swiss Knots 2025 at Université de Genève, Switzerland. Jun 2025
European Kylerec: Lagrangian Correspondences and quilts at Oppdal, Norway. Mar 2025.