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.

In my thesis, I studied the relationship of affine Springer fibers to various things, such as Hilbert schemes of points on plane curve singularities/smooth surfaces, and knot homology. Historically, I have been interested in commutative algebra as well.

Currently, I am trying to understand the mathematics of some 3d field theories and the relationship of braid invariants to affine Springer fibers/orbital integrals (see e.g. this talk.) Some other things I'm thinking about are double affine Hecke algebras, elliptic cohomology, and three-manifold invariants.

other:

Here is a link to the AIM research community on link homology.

writing

articles:

- (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*. - (with Eugene Gorsky and Alexei Oblomkov) The affine Springer fiber-sheaf correspondence. arXiv:2204.00303. (Video, slides.)
- (with Pablo Boixeda Alvarez and Ivan Losev) Appendix to: Affine Springer fibers, Procesi bundles, and Cherednik algebras. arXiv:2104.09543, April 2021.
- (with Nicolas Hemelsoet and Anna Lachowska) The invariant part of the center of the small quantum group. In preparation. (Video.)
- (with Cheng-Chiang Tsai) Shalika germs and weight polynomials for tamely ramified elements in GL(n). In preparation. (Video, slides.)

other:

- 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, August 2021.
- (with Gurbir Dhillon) Proof of the hard Lefschetz theorem. Chapter 20 of Introduction to Soergel Bimodules.
- 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

spring 2022:

- MATH-535 "Topics in Algebraic Geometry"

fall 2020-spring 2021:

- MAT 133Y "Calculus and Linear Algebra for Commerce"

winter 2020:

fall 2019:

fall 2018:

- MAT 21A "Calculus"

fall 2016:

- MAT 150A "Algebra".
*Instructor:*Albert Schwarz.

spring 2016:

- MAT 22B "ODEs".
*Instructor:*James Bremer.

winter 2016:

- MAT 21C "Calculus".
*Instructor:*Francesco Rubini.

fall 2015:

- MAT 21A "Calculus".
*Instructor:*Brian Osserman.