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.

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. Here are more interesting facts ;)

Preprints / Publications

1. A^1-Contractibility of Smooth Affine Schemes over Dedekind Schemes - jointly with Adrien Dubouloz and Paul Arne Østvær (in preparation).

Notes / Scripts / Slides*

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

Posters

When topology meets geometry, A^1-Contractibility (2023)

...somewhere in a hyper world, Hyperbolic geometry (2020)

Travel (Past/Future):

BENDZ, Swiss-French joint seminar, Lausanne, April 2025

Motivic homotopy theory, Regensburg, March 2025

Algebraic geometry: a motivic view, Zürich, January 2025

Motivic homotopy in interaction, Luminy, November 2024

Unstable motivic homotopy theory, Mainz, March 2024

EAST, Soestenberg, September 2023

YTM, Lausanne, August 2023

Motivic and non-commutative aspects of enumerative geometry and Homotopy theory, K-theory, and trace methods, Nijmegen, July 2023

Motives in Ratisbona, Regensburg, September 2022

Motivic geometry, Oslo, August 2022

Seminar / Reading Groups

Learning seminar in Dijon on "Smoothability of algebraic cycles" following Kollár-Voisin and Benoist.

Séminaire des doctorants, IMB Dijon

Seminario Matematico Informale, Vario Argomento, UniMi

Seminari di geometria algebrica complessa, Unimi