E-mail: huizenga at psu dot edu
Office: 324 McAllister
CV (Updated 8/25/21): pdf
I am an associate professor in the math department at Penn State University. My research focuses on algebraic geometry. In particular, I focus on Hilbert schemes of points, moduli spaces of vector bundles, and various interpolation-type problems that arise in algebraic geometry.
I am a co-organizer of the Algebra and Number Theory Seminar at Penn State.
Lecture Notes
In 2018 I designed a course which uses linear algebra to study interpolation problems and begin a serious study of algebraic geometry without needing the more advanced machinery of commutative algebra. These notes should be suitable for advanced undergraduates.
Polynomial interpolation: an introduction to algebraic geometry.
Here are some exercises given for various minicourses.
Exercises on the birational geometry of moduli spaces of sheaves (ELGA3, Mexico, 2017)
Exercises on moduli spaces (VIASM, Vietnam, 2013)
Research
- Interpolation and moduli spaces of vector bundles on very general blowups of P2.
Joint with Izzet Coskun. Submitted preprint. (2023) pdf - The Brill-Noether theory of moduli spaces of sheaves on surfaces.
Joint with Izzet Coskun and Howard Nuer. Submitted preprint. (2023) pdf - Stability and cohomology of kernel bundles on projective space.
Joint with Izzet Coskun and Geoffrey Smith, Michigan Math Journal, to appear. (2023) pdf - Disconnected moduli spaces of stable bundles on surfaces.
Joint with Izzet Coskun and John Kopper. Bull. London Math. Society. (2022) pdf - Ample stable vector bundles on rational surfaces.
Joint with John Kopper. Comm. Algebra. (2022) pdf - The cohomology of general tensor products of vector bundles on P2.
Joint with Izzet Coskun and John Kopper. Selecta Math. (2021) pdf - Existence of semistable sheaves on Hirzebruch surfaces.
Joint with Izzet Coskun. Advances in Mathematics. (2021) pdf - Brill-Noether problems, Ulrich bundles and the cohomology of moduli spaces of sheaves.
Joint with Izzet Coskun. Proceedings of the ICM 2018 Satellite Meeting “Moduli spaces in algebraic geometry and applications.” (2020) pdf - Rationality of Seshadri constants on general blowups of P2.
Joint with Lucja Farnik, Krishna Hanumanthu, David Schmitz, and Tomasz Szemberg. J. Pure Appl. Algebra. (2020) pdf - The moduli spaces of sheaves on surfaces, pathologies and Brill-Noether problems.
Joint with Izzet Coskun. Geometry of Moduli, Abel Symposia Book Series. (2018) pdf - Brill-Noether theorems and globally generated vector bundles on Hirzebruch surfaces.
Joint with Izzet Coskun. Nagoya Math Journal. (2018) pdf - Weak Brill-Noether for rational surfaces.
Joint with Izzet Coskun. Local and Global Methods in Algebraic Geometry, Contemporary Math Book Series. (2018) pdf - Negative curves on symmetric blowups of the projective plane, resurgences and Waldschmidt constants.
Joint with Thomas Bauer, Sandra Di Rocco, Brian Harbourne, Alexandra Seceleanu, and Tomasz Szemberg. Int. Math. Res. Not. (2018) pdf - Birational geometry of moduli spaces of sheaves and Bridgeland stability.
Surveys on Recent Developments in Algebraic Geometry, Proceedings of Symposia in Pure Mathematics. (2017) pdf - The nef cone of the moduli space of sheaves and strong Bogomolov inequalities.
Joint with Izzet Coskun. Israel J. Math. (2018). pdf - Nef cones of Hilbert schemes of points on surfaces.
Joint with B. Bolognese, Y. Lin, E. Riedl, B. Schmidt, M. Woolf, and X. Zhao. Algebra & Number Theory. (2016) pdf - Ulrich Schur bundles on flag varieties.
Joint with Izzet Coskun, Laura Costa, Rosa Maria Miro-Roig and Matthew Woolf. Journal of Algebra. (2017) pdf - The ample cone of moduli spaces of sheaves on the plane.
Joint with Izzet Coskun. Algebraic Geometry. (2016) pdf - The effective cone of the moduli space of sheaves on the plane.
Joint with Izzet Coskun and Matthew Woolf. Journal of the European Mathematical Society. (2017) pdf - The birational geometry of the moduli spaces of sheaves on P2.
Joint with Izzet Coskun. Survey article for the Proceedings of the Gökova Geometry-Topology Conference. (2014) pdf - Bounded negativity and arrangements of lines.
Joint with Th. Bauer, S. Di Rocco, B. Harbourne, A. Lundman, P. Pokora, and T. Szemberg. International Math Research Notices. (2015) pdf - Interpolation, Bridgeland stability, and monomial schemes in the plane.
Joint with Izzet Coskun. Journal de Mathématiques Pures et Appliquées. (2014) pdf - Effective divisors on the Hilbert scheme of points in the plane and interpolation for stable bundles.
Journal of Algebraic Geometry. (2016) pdf - The minimal model program for the Hilbert scheme of points on P2 and Bridgeland stability.
Joint with Daniele Arcara, Aaron Bertram, and Izzet Coskun. Advances in Mathematics. (2013) pdf - Restrictions of Steiner bundles and divisors on the Hilbert scheme of points in the plane.
Article version of my thesis. International Math Research Notices. (2012) pdf - Interpolation on surfaces in P3.
Transactions of the American Mathematical Society. (2011) pdf - Restrictions of Steiner bundles and divisors on the Hilbert scheme of points in the plane.
Harvard Ph.D. thesis. (2012) pdf - Invariant metrics with nonnegative curvature on SO(4) and other Lie groups.
Joint work with Kristopher Tapp, conducted at Williams College in 2006. Michigan Math Journal. (2007) pdf - The minimum size of complete caps in (Z/nZ)2.
Work done in the summer of 2005 at the University of Minnesota, Duluth. Electronic Journal of Combinatorics. (2006) pdf - Chromatic capacity and graph operations.
Work done in the summer of 2004 at the University of Minnesota, Duluth. Discrete Mathematics. (2007) pdf
Expository writing
- Steiner bundles and divisors on the Hilbert scheme of points in the plane.
Poster presented at Joe Harris’ 60th birthday conference. pdf - Interpolation on surfaces in P3.
Slides from New Orleans talk, Jan. 2011. pdf - Rationally connected varieties.
This was my minor thesis at Harvard. pdf - The Noether-Lefschetz Theorem.
This is an expository article on the Noether-Lefschetz theorem. pdf