Matt Larson

I am an Associate Research Scholar at Princeton University and a Bourgain fellow at the Institute for Advanced Study. I graduated from Stanford University in 2024, where I was advised by June Huh and Ravi Vakil.

I'm mostly interested in combinatorial algebraic geometry, especially toric varieties, moduli of curves, and applications of algebraic geometry to matroid theory.

My email is mattlarson AT princeton DOT edu. My offices are 112 Simonyi Hall at the IAS and 1010 Fine Hall at Princeton.

CV  /  arXiv  /  Scholar  

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Preprints
  1. Fine multidegrees of matrix Schubert varieties (with D. Huang).
  2. Determinants of Hodge-Riemann forms (with I. Novik and A. Stapledon).
  3. Rigidity matroids and linear algebraic matroids with applications to matrix completion and tensor codes (with J. Brakensiek, M. Dhar, J. Gao, and S. Gopi).
  4. Straightening laws for Chow rings of matroids.
  5. Kapranov degrees (with J. Brakensiek, C. Eur, and S. Li).
  6. Rank functions and invariants of delta-matroids.
  7. The local motivic monodromy conjecture for simplicial nondegenerate singularities (with S. Payne and A. Stapledon).
  8. The Bergman fan of a polymatroid (with C. Crowley, J. Huh, C. Simpson, and B. Wang).

Publications
  1. K-theoretic positivity for matroids (with C. Eur). To appear in Alg. Geom.
  2. K-classes of delta-matroids and equivariant localization (with C. Eur and H. Spink). To appear in Trans. Amer. Math. Soc.
  3. Signed permutohedra, delta-matroids, and beyond (with C. Eur, A. Fink, and H. Spink). Proc. Lond. Math. Soc. 3 (2024). Paper No. e12592, 54pp.
  4. Intersection theory of polymatroids (with C. Eur). Int. Math. Res. Not. IMRN. 5 (2024), 4207-4241
  5. K-rings of wonderful varieties and matroids (with S. Li, S. Payne, and N. Proudfoot). Adv. Math. 441 (2024). Paper No. 109554, 43pp.
  6. Kazhdan-Lusztig polynomials of braid matroids (with L. Ferroni). Comm. Amer. Math. Soc. 4 (2024), 64-79.
  7. Stellahedral geometry of matroids (with C. Eur and J. Huh). Forum Math. Pi 11 (2023). 48pp.
  8. Resolutions of local face modules, functoriality, and vanishing of local h-vectors (with S. Payne and A. Stapledon). Algebr. Comb. 6 (2023). 15pp.
  9. Theorem of the base (with R. Cheng, L. Ji, and N. Olander). Stacks Project Expository Collection, 163-193, London Math. Soc. Lecture Note Ser., 480, Cambridge Univ. Press (2022).
  10. The Arakelov-Zhang pairing and Julia sets (with A. Bridy). Proc. Amer. Math. Soc. 149 (2021). 14pp.
  11. Inverse problems for minimal complements and maximal supplements (with N. Alon and N. Kravitz). J. Number Theory (2021). 18pp.
  12. Unions of Random Trees and Applications (with A. James, D. Montealegre, and A. Salmon). Disc. Math. 344 (2021). 13pp.
  13. Power maps in finite groups. Integers 19 (2019). 15pp.

Slides
  1. Geometry of polymatroids
  2. Algebraic geometry of delta-matroids
  3. Nonvanishing criteria for local h-polynomials

Upcoming travel
  1. Algecom, November 9 2024, Ann Arbor, MI
  2. Matroids, rigidity, and algebraic statistics, March 17-21 2025, ICERM, Providence, RI

Other

I gave a talk about invariants of delta-matroids. The talk was aimed at experts.

My thesis, titled "K-theoretic positivity for wonderful varieties and matroids." It is based on the papers K-rings of wonderful varieties and matroids (with S. Li, S. Payne, and N. Proudfoot) and K-theoretic positivity for matroids (with C. Eur), although with a different exposition and some different proofs.

I've written some code in Sage to compute certain intersection numbers on the Deligne-Mumford-Knudsen moduli space of stable curves of genus 0 with marked points, which we called "Kapranov degrees" and studied in this paper. The code can be found here.

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