Oscar Kivinen

I am a researcher at EPFL. Before, I was a postdoctoral fellow at the University of Toronto and an Olga Taussky & John Todd Instructor at the California Institute of Technology (Caltech). I completed my Ph.D. at the University of California, Davis (UC Davis) in 2019. Prior to that, I received an M.Sc. degree in engineering physics from Aalto University. I am also a Fulbright grantee.

research

I am interested in algebraic geometry, representation theory, low-dimensional topology, number theory and mathematical physics.

Currently, the main focus of my research is in harmonic analysis on p-adic groups and how it is influenced by so called braid homology theories. I also care about the related arithmetic geometry. This comes close to some "physical mathematics" like 3d SUSY QFTs and string theory, sometimes featuring in my research. Some other (math) things I'm thinking about are double affine Hecke algebras, elliptic cohomology, and three-manifold invariants.

links:

- AIM research community on link homology (2021-). A continuation of this will be the AIM Workshop at AIM/Caltech July 31-August 4, 2023.
- Categorified Enumerative Geometry and Representation Theory at the Bernoulli Center, EPFL, September 11-15, 2023.
- Quantum Topology Biennial at the SwissMAP Research Station, Les Diablerets, January 14-18, 2024.

writing

articles:

- (with Cheng-Chiang Tsai) Shalika germs for tamely ramified elements in GL(n). Submitted, available at arXiv:2209.02509. (Video 1, Video 2, slides.)
- (with Eugene Gorsky and Alexei Oblomkov) The affine Springer fiber-sheaf correspondence. Submitted, available at arXiv:2204.00303. (Video, slides.)
- (with Nicolas Hemelsoet and Anna Lachowska) On the affine Springer fibers inside the invariant center of the small quantum group. Submitted, available at arXiv:2205.09700. (Video.)
- (with Pablo Boixeda Alvarez and Ivan Losev) Appendix to: Affine Springer fibers, Procesi bundles, and Cherednik algebras. Submitted, available at arXiv:2104.09543.
- (with Niklas Garner) Generalized affine Springer theory and Hilbert schemes on planar curves. arXiv:2004.15024,
*IMRN, rnac038 (2022)*. - Unramified affine Springer fibers and isospectral Hilbert schemes. arXiv:1808.02278,
*Selecta Mathematica (New Series) 26, 61 (2020)*. - Hecke correspondences for Hilbert schemes of reducible locally planar curves. arXiv:1711.06444,
*Algebraic Geometry (Foundation Compositio Mathematica) 6.5 (2019)*. - (with Yuzhe Bai and Eugene Gorsky) Quadratic ideals and Rogers-Ramanujan recursions. arXiv:1805.01593,
*The Ramanujan Journal (2018): 1-23*.

other:

- Sage code to compute Shalika germs, orbital integrals, etc. for GL(n).
- Some hand-written notes on Maulik's proof of the OS/DHS conjecture.
- (with Eugene Gorsky and José Simental Rodríguez) IHÉS notes on Algebra and geometry of link homology. arXiv:2108:10356.
*Bulletin of the LMS (2022)*. - (with Gurbir Dhillon) Proof of the hard Lefschetz theorem. Chapter 20 of Introduction to Soergel Bimodules,
*RSME Springer Series (2020)*. - Koszul algebras and resolutions. M.Sc. thesis, Aalto University, May 2014. Available on request. See also arXiv:1412:3542.
- Steady states in chemical reaction networks. B.Sc. thesis, Aalto University, January 2014. Available on request.
- Lecture notes from the course "Combinatorics" at Aalto University, 2014. Taught by Alexander Engström. (Warning: typos)

teaching

fall 2022 (EPFL):

- TA for MATH-563 "Student Seminar in Pure Mathematics" (Topic: Knot theory)
*Instructor:*Dimitri Wyss.