Research
My doctoral research centers on symplectic and low-dimensional topology. In symplectic topology, my research focusses on understanding the symplectic fillings of contact 3-manifolds using punctured pseudoholomorphic curves. Specifically, I am interested in understanding how surgery like operations on contact 3-manifolds affects the symplectic fillings.
Simultaneously, in low-dimensional topology, my work has been focussed around Knot theory, particularly Khovanov homology, Khovanov--Rozansky homology and their variants.
Publications:
Khovanov-Rozansky homology of positive braids, in preparation.
A stratification of the moduli space using Siefring's intersection theory, draft available on request.
On unknotting fibered positive knot and braids, https://arxiv.org/abs/2312.07339
with Marc Kegel, Lukas Lewark, Filip Misev, Leo Mousseau, Marithania Silvero.
Khovanov homology of positive links and of L-space knots, https://arxiv.org/abs/2304.13613.
with Marc Kegel, Leo Mousseau, Marithania Silvero.
On the topology of bi-cyclopermutohedra, https://doi.org/10.1007/s13226-022-00241-w
with Priyavrat Deshpande, Anurag Singh,
Indian Journal of Pure and Applied Mathematics(2022).
Selected Talks:
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
Khovanov homology of positive links,
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
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:
Hochschild (Co)Homology and Applications workshop at MFO-Mathematisches Forschungsinstitut Oberwolfach.
Apr 14-19, 2024
CAST-2024 at Universität Bochum.
Feb 8-10, 2024
Swiss Knots-2023 at the University of Regensburg, Germany.
Sep 6-8, 2023
Workshop on Symplectic Field theory 10 at Humboldt-Universität zu Berlin, Germany.
Aug 26 - Sep 1, 2023
School on conformal symplectic dynamics and related fields at the Centre International de Rencontres Mathématiques, France.
May 8-12, 2023
Winter school in singularities and low-dimentional topology at Rényi Institute, Hungary.
Jan 20-27, 2023
DMV Annual Meeting 2022 at Freie Universität Berlin.
Sep 12-16, 2022
BMS - BGSMath Junior Meeting at University of Barcelona, Spain.
Sep 05-07, 2022
Frontiers in Geometry and Topology Summer School at The Abdus Salam International Centre for Theoretical Physics, Italy.
Aug 01-05, 2022
X International meeting on Lorentzian geometry (Virtual).
Feb 01-05, 2021
Floer Theory and Hamiltonian Dynamics of Non-Compact Hypersurfaces conference (Virtual).
Jan 18-22 2021