# Jack Huizenga

E-mail: huizenga at psu dot edu

Office: 324 McAllister

CV (Updated 8/23/20): pdf

I am an assistant professor in the math department at Penn State University. Previously I was a postdoc at UIC, and I completed my Ph.D. under Joe Harris at Harvard. My research focuses on algebraic geometry. In particular, I focus on Hilbert schemes of points, moduli 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.
## Teaching

This semester I am teaching Math 538, Commutative Algebra, at Penn State. Here is the course webpage:
Math 538, Commutative Algebra, Spring 2021.

Here are archived course webpages from past courses I've taught.

Math 435, Basic Abstract Algebra, Fall 2020. (PSU)

Math 435, Basic Abstract Algebra, Spring 2020. (PSU)

Math 436, Linear Algebra, Spring 2020. (PSU)

Math 535, Linear Algebra and its Applications, Fall 2019. (PSU)

Math 465, Number Theory, Spring 2019. (PSU)

Math 538, Commutative Algebra, Spring 2019. (PSU)

Math 497A, Honors MASS Algbra, Fall 2018. (PSU)

Math 436, Linear Algebra, Spring 2018. (PSU)

Math 547, Algebraic Geometry I, Fall 2017. (PSU)

Math 538, Commutative Algebra, Spring 2017. (PSU)

Math 437, Algebraic Geometry, Fall 2016. (PSU)

Math 465, Number Theory, Spring 2016. (PSU)

Math 436, Linear Algebra, Fall 2015. (PSU)

Math 552, Algebraic Geometry I, Fall 2014. (UIC)

Math 320, Linear Algebra I, Fall 2012. (UIC)

Math 21a, Multivariable Calculus, Fall 2010. (Harvard)

Math 21a, Multivariable Calculus, Fall 2009. (Harvard)

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)

## 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.

## Research

Recent papers:
"Ample stable vector bundles on rational surfaces." Joint with John Kopper. Submitted preprint. (2021) pdf
"The cohomology of general tensor products of vector bundles on P^{2}." Joint with Izzet Coskun and John Kopper. Submitted preprint. (2020) 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," to appear. (2020) pdf
"Rationality of Seshadri constants on general blowups of P^{2}." 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. 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 Miró-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 P^{2}." 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 P^{2} 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 P^{3}." 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

Undergraduate research:
"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 writings:
"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 P^{3}." 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
## Past Workshops

I was a co-organizer of the following workshops.
FRG workshop on Moduli Spaces of Sheaves and Bridgeland Stability (UIC, December 7-9, 2018).

FRG Workshop on Moduli of Sheaves and Strange Duality, (PSU, December 8-10, 2017).