Oscar Kivinen

I am an Olga Taussky & John Todd Instructor at Caltech. My mentors here are Eric Rains, Xinwen Zhu, and Tom Graber. I completed my Ph.D. at the Department of Mathematics at the University of California, Davis (UC Davis) under the supervision of Eugene Gorsky. I received the M.Sc. degree in engineering physics from Aalto University in June 2014, majoring in mathematics with a minor in computer science. 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. Some other things I'm thinking about are double affine Hecke algebras, elliptic cohomology, and three-manifold invariants.

writing

articles:

- 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*. - Unramified affine Springer fibers and isospectral Hilbert schemes. arXiv:1808.02278, August 2018. Submitted.
- (with Niklas Garner) Hilbert schemes on planar curve singularities are generalized affine Springer fibers. March 2020. Submitted.

other:

- (with Gurbir Dhillon) Proof of the hard Lefschetz theorem. Chapter 18 of "Soergel Bimodules", To appear in the Springer RSME Series.
- 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

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.