Research Interests
Broadly speaking, my research interests lie at the intersection of homotopy theory and algebraic geometry.
I am especially interested in questions relating to mixed-characteristic singulatity theory. I've also worked in foundational questions developing the theory of algebraic geometry over semirings, where homotopy theory appears to play a more vital role than that of classical algebraic geometry.
More recently, I've become interested in the applications of AI to mathematical research. In my experience, even the most abstract mathematical questions can boil down to a difficult computation, and I want to use AI tools to help with these computations. Of course, the question of how AI can learn to do mathematical research is profound, and I plan on exploring this soon enough.
If any of the above sounds interesting, please feel free to reach out at ivan [dot] zelich [at] columbia [dot] edu!
Workshops Attended/Organized
- Fundamental Uses of AI in Math: Research, February 2026 (Organized) Workshop Page
- The Legacy of John Tate and Beyond, March 2025
- Special Year on p-adic Arithmetic Geometry, March 2024
- Algebraic Geometry and Cohomology in Mixed Characteristic, May 2023
- Periods, motives, and differential equations: between arithmetic and geometry, on the occasion of Yves Andre's 60th++ birthday, June 2022
Research
- I. Zelich (2025), 'Affineness of the complement of the ramification locus in mixed characteristic', in preparation.
- I. Zelich (2025), 'Algebraic Geometry and Tor-dimension over Semirings', in preparation.
- I. Zelich (2024), 'Indivisible Sequences and Descendability', arxiv:2411.19944, (to appear in Journal of Algebra).
- I. Zelich (2024), 'Faithfully flat ring maps are not descendable', arXiv:2405.08124 (Proceedings, AMS).
- I. Zelich (2022), 'Almost Witt Vectors' arXiv:2205.14745.
- I. Zelich and X. Liang (2019), 'Triangles with Vertices Equidistant to a Pedal Triangle', to be published in Forum Geometricorum, Vol. 19, arXiv:2012.05485.
- I. Zelich and X. Liang (2015), 'Generalisations of the Properties of the Neuberg Cubic to the Euler pencil of Isopivotal Cubics', International Journal of Geometry, Vol. 4, No. 2, p5-25.