Research

I am spending time to learn tools and techniques from algebraic and differential topology towards solving problems in the realm of algebraic geometry. Particular focus is on exploring connections between motivic homotopy theory, topology at infinity, and affine geometry. In a broader perspective, this includes various cohomology theories, vector bundle classification, algebraic K-theory and birational geometry.

In my Master thesis, I studied the fundamentals of the homotopy theory of schemes and the dichotomous behaviour of vector bundles in algebraic geometry. Out of curiosity, I also indulge in various texts on biology, physics and psychology.

$Ant on a Klein bottle$

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

3. Relative A^1-Contractibility of Smooth Schemes - with Adrien Dubouloz and Paul Arne Østvær (coming soon) - early version available upon request.

2. Relative A^1-Contractibility, Koras-Russell Prototypes and Exotic Motivic Spheres, Ph.D. Dissertataion (2026), Hosted in arXiv:2603.04167, HAL Science, IRIS AIR.

1. Relative A^1-Contractibility of Koras-Russell Prototypes and Exotic Motivic Spheres (2025), Available in arXiv:2510.21594.

Notes / Scripts / Slides*

11. 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

10. Relative A^1-Contractibility over Dedekind Schemes - Motivic Homotopy in Interaction, CIRM Marseille, November 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