I study various different topics in algebraic geometry, representation theory and low-dimensional topology. Sometimes I also study number theory and mathematical physics.

I am particularly interested in the local theory of automorphic forms, especially (weighted) orbital integrals. Relatedly, I study moduli spaces of sheaves supported on singular curves. Recently, I have been getting more into Floer theory as well.

My research is supported by a Väisälä project grant from the the Finnish Academy of Science and Letters.

articles:

• A Lie-theoretic generalization of some Hilbert schemes. Submitted, available at arXiv:2512:08532.
• (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 Alexei Oblomkov and Dimitri Wyss) Discriminants and motivic integration. Recommended for publication in Compositio Mathematica, available at arXiv:2503:18449.
• (with Nicolas Hemelsoet and Anna Lachowska) On the affine Springer fibers inside the invariant center of the small quantum group. Submitted to Representation Theory. Available at arXiv:2205.09700. (Video.)
• (with Minh-Tam Trinh) The Hilb-vs-Quot conjecture. arXiv:2310:19633. J. Reine Angew. Math. (Crelle's Journal) (2025).
• (with Eugene Gorsky and Alexei Oblomkov) The affine Springer fiber-sheaf correspondence. arXiv:2204.00303. Advances in Math. 464 (2025). (Video, slides.)
• (with Pablo Boixeda Alvarez and Ivan Losev) Appendix to: Affine Springer fibers, Procesi bundles, and Cherednik algebras. arXiv:2104.09543. Duke Math. J. 173.5 (2024).
• (with Eugene Gorsky and José Simental Rodríguez) IHÉS notes on Algebra and geometry of link homology. arXiv:2108:10356. Bulletin of the LMS 55.2 (2023): 537-591.
• (with Niklas Garner) Generalized affine Springer theory and Hilbert schemes on planar curves. arXiv:2004.15024, IMRN, 8, 6402-6460 (2023).
• Unramified affine Springer fibers and isospectral Hilbert schemes. arXiv:1808.02278, Selecta Mathematica (New Series) 26, 61 (2020).
• (with Yuzhe Bai and Eugene Gorsky) Quadratic ideals and Rogers-Ramanujan recursions. arXiv:1805.01593, The Ramanujan Journal 52 (2020): 67-89.
• Hecke correspondences for Hilbert schemes of reducible locally planar curves. arXiv:1711.06444, Algebraic Geometry (Foundation Compositio Mathematica) 6.5 (2019).

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 Gurbir Dhillon) Proof of the hard Lefschetz theorem. Chapter 20 of Introduction to Soergel Bimodules. RSME Springer Series (2020).

postdocs:

• GyeongHyeon Nam (Postdoc, 2025-).
• Ikshu Neithalath (Postdoc based at the University of Helsinki, jointly with Kari Vilonen, 2024-).
• Lizao Ye (Postdoc, 2024-).

phd students:

• Emilia Takanen (PhD student, 2024-): Emilia is working on sheaf-theoretic Floer homology.
• Miika Rankaviita (PhD student, 2024-): Miika is working on Poisson and birational geometry.

undergraduate students and summer trainees:

• Oscar Escartin (BSc student & summer trainee, 2026)
• Ville Uotila (MSc student based at the University of Helsinki, 2025)
• Corentin Vogin (Visiting MSc student from Université de Rennes, 2025)
• Mikko Palojärvi (BSc student & summer trainee, 2025): Gromov-Witten theory and virtual localization.
• Michael Yang (Summer trainee, 2024)
• Lassi Virtanen (MSc student, 2024)
• Lauri Karanko (BSc student, 2023): Cyclic sieving in rational q,t-Catalan combinatorics.
• Susanna Terron (MSc student, 2023): Dynamical Quantum Groups.
• Hana Ephremidze (BSc student, 2023): Algebraic closure of local fields in characteristic p>0. Hana's thesis won the Prix Junior Maryam Mirzakhani 2023.

spring 2026 (Aalto):

• Algebraic Geometry II (Period IV)

fall 2025 (Aalto):

• Algebraic Geometry I (Period I-II)

spring 2025 (Aalto):

• Advanced topics in algebra: Modern Representation Theory (Period IV)