Jack Huizenga

photo

E-mail: huizenga at psu dot edu
Office: 324 McAllister
CV (Updated 2/5/17): pdf

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

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

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 the 2013 minicourse on moduli spaces at VIASM.

Exercises on moduli spaces

Research

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.


Recent papers:

"Brill-Noether theorems and globally generated vector bundles on Hirzebruch surfaces." Joint with Izzet Coskun. Preprint. pdf

"Weak Brill-Noether for rational surfaces." Joint with Izzet Coskun. To appear in Contemp. Math. 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. Preprint. pdf

"Birational geometry of moduli spaces of sheaves and Bridgeland stability." Survey article for the 2015 Bootcamp in Algebraic Geometry at the University of Utah. To appear in Proceedings of Symposia in Pure Mathematics. pdf

"The nef cone of the moduli space of sheaves and strong Bogomolov inequalities." Joint with Izzet Coskun. Preprint. 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 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


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 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

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