Research

My recent time is being spent in learning tools and techniques from algebraic and differential topology that can help solve problems in algebraic geometry. Currently, I am interested in the connection between motivic homotopy theory and affine fibration theory. In a broader perspective, this also includes various cohomology theories and birational geometry. From time to time, I also indulge in various texts on physics and psychology. In my Master thesis, I studied the fundamentals of the homotopy theory of schemes and the dichotomous behaviour of vector bundles in algebraic geometry.

$Ant on a Klein bottle$

OK! but what's so special about this bottle? This bottle has no inside or outside and the total volume = Zero! It originally resides in 4-D but when viewed as a 2-D surface, we see an intersection through itself that leaves anyone who travels on it confused. Click here for more interesting facts ;)

Preprints / Publications

2. Exotic affine threefolds and motivic spheres over Dedekind schemes (in preparation).
1. A^1-Contractibility of Smooth Schemes over Dedekind Schemes - jointly with Adrien Dubouloz and Paul Arne Østvær (in preparation).

Notes / Scripts / Slides*

12. A^1-Contractibility of Smooth schemes over a Dedekind base - Géométrie algébrique et Théorie des nombres en Bourgogne Franche-Comté, IMB Dijon, March 2025 - Schedule
11. Relative A^1-Contractibility over Dedekind Schemes - Motivic Homotopy in Interaction, CIRM Marseille, November 2024 - Slides, Schedule
10. Torsors are pointless actions, but learning them is not - Séminaire des doctorants, IMB Dijon, October 2024 - Slides, Schedule
9. Contractibility in algebraic geometry - Journée de l'Ecole Doctorale, Besançon, June 2024 - Script, Schedule
8. Tannaka duality for locally Noetherian stacks - SeMIVA, June 2024 - Script, Video
7. The world of Spectral Algebraic Geometry - SeMIVA, May 2024 - Script, Video
6. On shrinking algebro-geometric entities - PhD^2ays, Milan, March 2024 - Script, Schedule
5. K-theory, Chow groups and the cycle class map - eCHT, October 2023 - Notes, Syllabus
4. Elliptic curves over arithmetic fields - SeMIVA, June 2023 - Script, Video
3. Serre's problem on projective modules - Graduate course, Milan, 2022 - Notes
2. Covering Spaces - Galois Groups and Fundamental Groups, Regensburg, 2021 - Notes, Schedule
1. Class Formations - Local Fields and Class Field Theory, Regensburg, 2020 - Notes, Schedule