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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 models of 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

Posters

  • When topology meets geometry, A^1-Contractibility (2023)
  • ...somewhere in a hyper world, Hyperbolic geometry (2020)
  • Travel (Past/Future):

  • YTM, Stockholm, June 2025
  • 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

  • Organizing member of PhDdays, April 14-16, 2025.
  • 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
  • * The materials presented here are not completely immune from errors; if you have found any/some, please do not hesitate to let me know :)