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. F-rationality of multiplicity-free subvarieties.
  2. Matroid flat counts can have many peaks (with A. Divoux, C. Lowen, and S. Wang).
  3. Kazhdan-Lusztig polynomials of Dowling geometries (with L. Ferroni).
  4. Hodge theory for combinatorial projective bundles (with E. Partida).
  5. Cohomological aspects of power ideals (with C. Crowley).
  6. Absolute incidence theorems and tilings (with L. Kühne).
  7. A decomposition theorem for Lefschetz modules (with O. Amini and J. Huh).
  8. Vanishing theorems for combinatorial geometries (with C. Eur and A. Fink).
  9. Complementary vectors of simplicial complexes (with A. Stapledon).
  10. Determinants of Hodge-Riemann forms (with I. Novik and A. Stapledon).

Publications
  1. Fine multidegrees, universal Grobner bases, and matrix Schubert varieties (with D. Huang). J. Lond. Math. Soc. 114 (2026), 39pp.
  2. Differential operators, anistropy, and simplicial spheres (with K. Karu and A. Stapledon). Int. Math. Res. Not. IMRN. 13 (2026), 15pp.
  3. The local motivic monodromy conjecture for simplicial nondegenerate singularities (with S. Payne and A. Stapledon). Comm. Amer. Math. Soc. 6 (2026), 424-491.
  4. The Bergman fan of a polymatroid (with C. Crowley, J. Huh, C. Simpson, and B. Wang). Trans. Amer. Math. Soc. 379 (2026), 3239-3256.
  5. Rigidity matroids and linear algebraic matroids with applications to matrix completion and tensor codes (with J. Brakensiek, M. Dhar, J. Gao, and S. Gopi). Combinatorica. 46 (2026), 29pp.
  6. K-theoretic positivity for matroids (with C. Eur). Algebr. Geom. 13 (2026), 241-265.
  7. Lefschetz properties of local face modules (with A. Stapledon). Algebr. Comb. 8 (2026), 1473-1491.
  8. Kapranov degrees (with J. Brakensiek, C. Eur, and S. Li). Int. Math. Res. Not. IMRN. (2025), 16pp.
  9. Rank functions and invariants of delta-matroids. Electron. J. Combin. 32 (2025), 17pp.
  10. Combinatorial Hodge theory (with C. Eur). Notices Amer. Math. Soc. 72 (2025), 261-270.
  11. Straightening laws for Chow rings of matroids. J. Algebra 672 (2025), 50-70.
  12. K-classes of delta-matroids and equivariant localization (with C. Eur and H. Spink). Trans. Amer. Math. Soc. 378 (2025), 731-750.
  13. Signed permutohedra, delta-matroids, and beyond (with C. Eur, A. Fink, and H. Spink). Proc. Lond. Math. Soc. 128 (2024), 54pp.
  14. Intersection theory of polymatroids (with C. Eur). Int. Math. Res. Not. IMRN. (2024), 4207-4241.
  15. K-rings of wonderful varieties and matroids (with S. Li, S. Payne, and N. Proudfoot). Adv. Math. 441 (2024), 43pp.
  16. Kazhdan-Lusztig polynomials of braid matroids (with L. Ferroni). Comm. Amer. Math. Soc. 4 (2024), 64-79.
  17. Stellahedral geometry of matroids (with C. Eur and J. Huh). Forum Math. Pi 11 (2023), 48pp.
  18. Resolutions of local face modules, functoriality, and vanishing of local h-vectors (with S. Payne and A. Stapledon). Algebr. Comb. 6 (2023), 15pp.
  19. 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).
  20. The Arakelov-Zhang pairing and Julia sets (with A. Bridy). Proc. Amer. Math. Soc. 149 (2021), 14pp.
  21. Inverse problems for minimal complements and maximal supplements (with N. Alon and N. Kravitz). J. Number Theory (2021), 18pp.
  22. Unions of Random Trees and Applications (with A. James, D. Montealegre, and A. Salmon). Disc. Math. 344 (2021), 13pp.
  23. Power maps in finite groups. Integers 19 (2019). 15pp.

Recorded talks
  1. Matrix completion and tensor codes (the first three minutes of video are missing)
  2. K-theory of Bergman fans
  3. Geometry of delta-matroids
  4. Invariants of delta-matroids (aimed at experts)

Slides
  1. Matrix completion and tensor codes
  2. Kapranov degrees
  3. Geometry of polymatroids
  4. Algebraic geometry of delta-matroids
  5. Nonvanishing criteria for local h-polynomials

Upcoming travel
  1. Algebra and Geometry of Matroids, September 28-October 2 2026, Oaxaca MX
  2. University of Toronto algebraic geometry seminar, October 21 2026, Toronto CA
  3. ROB-AG, October 28-30 2026, Stony Brook NY

Other writing
  1. Some notes on K-theoretic positivity can be found here.
  2. Counterexamples to two conjectures about matroids.
  3. 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.

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