Research
My research interests include birational geometry, the theory of moduli spaces, derived categories in algebraic geometry, and higher codimension cycles. This includes using methods from many areas including the minimal model program, representation theory, combinatorics, and homological algebra.
An illustration of the lines of the two rulings of a smooth quadric surface.
By Theon at French Wikipedia -Public Domain.
Preprints
Tim Ryan, Anna Brosowsky, Haoyu Du, Madhav Krishna, Sandra Nair, and Janet Page, "Maximal skew sets of lines on a Hermitian surface and a modified Bron-Kerbosch algorithm", In preparation, Available upon request
Tim Ryan, Anna Brosowsky, Janet Page, and Karen Smith, "The geometry of smooth extremal surfaces", Submitted -arxiv:2110.15908, 2021
Tim Ryan, Manuel Leal, and César Lozano Huerta, "Minimal free resolutions of sheaves on the plane and the stable base locus decomposition of their moduli spaces", Submitted - arxiv:2110.15346, 2021.
Tim Ryan, "The geometry of Hilbert schemes of two points on projective space", Submitted - arxiv:2103.12674, 2021.
Publications
Tim Ryan and Gregory Taylor, "Irreducibility and singularities of some nested Hilbert schemes", Journal of Algebra. Volume 609, 2022, Pages 380-406.
Joseph Donato, Monica Lewis, Tim Ryan, Faustas Udrenas, and Zhijian Zhang, "The sum of Betti numbers of Smooth Hilbert schemes", Journal of Algebraic Combinatorics. Volume 55, 2022, Pages 393–411.
Tim Ryan and Alexander Stathis, "Higher codimension cycles on the Hilbert scheme of three points on the projective plane", Journal of Pure and Applied Algebra, Volume 225, Issue 10, 2021.
Tim Ryan and César Lozano Huerta, "On the position of nodes of plane curves", Bulletin of the Australian Mathematical Society. Volume 103, Number 1, 2021, Pages 62-68.
Tim Ryan and César Lozano Huerta, "On the birational geometry of Hilbert schemes of points and Severi divisors", Communications in Algebra. Volume 48, Number 11, 2020, Pages 4596-4614.
Tim Ryan and Ruijie Yang, "Nef Cones of Nested Hilbert Schemes of Points on Surfaces", International Mathematical Research Notices. Volume 2020, Issue 11, June 2020, Pages 3260–3294.
Tim Ryan, "The effective cone of moduli spaces of sheaves on a smooth quadric surface", Nagoya Mathematical Journal, Volume 232, 2018, Pages 151-215. This is the article version of my thesis.
Tim Ryan, "The effective cone of moduli spaces of sheaves on a smooth quadric surface", (2016) This is the version of my thesis submitted to UIC.