Szegő Assistant Professor at the Department of Mathematics at Stanford University.
450 Serra Mall, Building 380
Stanford, CA 94305, USA
Tel: (650) 721-6799
Moduli theory: particularly moduli spaces of curves, stable maps, K3 surfaces or Abelian varieties.
Commutative algebra: in particular syzygies of coordinate rings of varieties.
I am particularly excited by the two-way interaction between the above two topics.
I am supported by NSF grant DMS-1701245.
My CV is available here. (Note that I am no longer on the job market).
The Resolution of Paracanonical Curves of Odd Genus, joint with
G. Farkas. To appear in Geometry and Topology.
Syzygies of Curves beyond Green's Conjecture. To appear in Proceedings of the Abel Symposium 2017. [arXiv:1711.04463]
The Prym-Green Conjecture for torsion line bundles of high order, joint with
Duke Math. J. (2017) 166 (6): 1103-1124.
The extremal Secant Conjecture for curves of arbitrary gonality.
Compositio Math. (2017) 153 (2): 347-357.
The generic Green-Lazarsfeld secant conjecture, joint with
Invent. Math. (2016) 203 (1): 265-301
The moduli of singular curves on K3 surfaces.
J. Math. Pures. Appl. (2015) 104 (5): 882-920.
Stable maps and Chow groups, joint with
Doc. Math. (2013) 18: 507-517.
The universal Severi variety of rational curves on K3 surfaces.
Bull. London Math. Soc. (2013) 45 (1): 159-174.
- Stable maps and singular curves on K3 surfaces.
PhD thesis at Universität Bonn (June 2015). Supervised by Daniel Huybrechts.
Seminar Talk. MIT. March, 2018.
Seminar Talk. Boston College. February, 2018.
Seminar Talk. Stony Brook University. February, 2018.
Seminar Talk. University of California, Davis. February, 2018.
Colloquium Talk. University of Cambridge. January 2018.
Colloquium Talk. University of North Carolina, Chapel Hill. December 2017.
Colloquium Talk. University of Wisconsin Madison. November 2017.
Colloquium Talk. EPFL, Lausanne. February 2017.
Colloquium Talk. University of Vienna. January 2017.
Syzygies of curves via K3 surfaces, Syzygies in Algebra and Geometry. Busan, Korea. August 2015 *Slides*
Syzygies of curves, Motivic invariants related to K3 and abelian geometries. Berlin, Germany. February 2015.
The moduli space of singular curve on K3 surfaces, Brill-Noether methods in the study of Hyperkähler and Calabi-Yau manifolds. Bonn, Germany. March 2014.
Chow groups and stable maps, GAeL XX. Grenoble, France. June 2012.
- Some new directions in the study of syzygies of curves, Workshop on Topics in Algebraic Geometry. Chapel Hill, November 2017.
- The Prym-Green conjecture for curves of odd genus, WAGS Fall 2017. LA, October 2017.
- On the possible Betti tables of a canonical curve, The Abel Symposium. Svolvaer, Norway. July 2017.
- Degenerations of projective K3 surfaces and paracanonical curves, Higgs Bundles, K3 Surfaces and Moduli. Berlin, July 2017.
- Schreyer's Conjecture and Hurwitz Spaces, Geometry of Moduli Spaces. San Diego, May 2017.
- Effective bounds for Green-Lazarsfeld's Gonality Conjecture, Conference On Moduli and Birational geometry (COMB V). Jeju, Korea. December 2016.
- Betti numbers of canonical curves and Hurwitz spaces, Geometry at the ANU: Conference. Canberra, Australia. August 2016.
- Hurwitz spaces and extremal Betti numbers, Advanced School and Workshop on Moduli Spaces, Mirror Symmetry and Enumerative Geometry. Trieste, Italy. August 2016.*Notes*
- The Prym-Green Conjecture, School on Moduli of Curves. Guanajuato, Mexico. Feb-March 2016.
- Extremal cases of the Secant conjecture for curves of arbitrary gonality, German-Israeli Workshop in
Algebraic and Tropical Geometry. Ramat Gan, Israel. January 2016.
- Syzygies of curves and K3 surfaces, Mini-Workshop: Singular Curves on K3 Surfaces and Hyperkähler Manifolds. Oberwolfach, Germany. November 2015. Oberwolfach Report
- Torsion bundles on K3 sections and the Prym-Green Conjecture, Geometry of Algebraic Varieties. Berlin, Germany. October 2015.