I am a postdoc in the Institute of Algebraic Geometry at Leibniz Universität Hannover. Between Fall 2016 and Spring 2019 I was an R. H. Bing Fellow at the University of Texas at Austin. Between Fall 2012 and Spring 2016 I have been a graduate student at the Ohio State University. I finished a Ph.D. with Emanuele Macrì. More information about me can be found on my CV.
My main area of interest is Algebraic Geometry. I am primarily interested in relations between classical algebraic geometry, and derived categories. My research focuses on Bridgeland stability conditions, moduli spaces of sheaves, Hilbert schemes of curves, and birational geometry. These topics have also led me to study exceptional collections, moduli of quiver representations, and geometric invariant theory.
Institut für Algebraische Geometrie
Leibniz Universität Hannover
The desingularization of the theta divisor of a cubic threefold as a moduli space, joint with Arend Bayer, Sjoerd Beentjes, Soheyla Feyzbakhsh, Georg Hein, Diletta Martinelli, Fatemeh Rezaee. arXiv:2011.12240.
Discriminants of stable rank two sheaves on some general type surfaces, joint with Benjamin Sung. To appear in Mathematical Research Letters. arXiv:1812.02735.
Rank two sheaves with maximal third Chern character in three-dimensional projective space. To appear in Proceedings of the ICM 2018 satellite conference "Moduli Spaces in Algebraic Geometry and Applications". arXiv:1811.11951.
Bridgeland stability on blow ups and counterexamples, joint with Cristian Martinez, Appendix by Omprokash Das. Math. Z., 292(3-4):1495-1510, 2019. arXiv:1708.08567.
Families of elliptic curves in P^3 and Bridgeland stability, joint with Patricio Gallardo and César Lozano Huerta. Michigan Math. J. 67 (2018), no. 4, 787-813. arXiv:1609.08184. M2-Code.
Bridgeland stability conditions on Fano threefolds, joint with Marcello Bernardara, Emanuele Macrì, and Xiaolei Zhao. Épijournal Geom. Algébrique 1 (2017), Art. 2, 24 pp. arXiv:1607.08199.
Counterexample to the generalized Bogomolov-Gieseker inequality for threefolds, Int. Math. Res. Not. IMRN 2017, no. 8, 2562–2566. arXiv:1602.05055.
Nef cones of Hilbert schemes of points on surfaces, joint with Barbara Bolognese, Jack Huizenga, Yinbang Lin, Eric Riedl, Matthew Woolf, and Xiaolei Zhao. Algebra Number Theory 10 (2016), no. 4, 907-930. arXiv:1509.04722.
Stability conditions on threefolds - First wall crossings. J. Algebraic Geom., 29(2):247-283, 2020. arXiv:1509.04608. The mentioned Sage code can be found at stability_library.sage with a short documentation.
A generalized Bogomolov-Gieseker inequality for the smooth quadric threefold, Bull. Lond. Math. Soc. 46 (2014), no. 5, 915-923. arXiv:1309.4265.
These are various notes in more or less polished form. They certainly contain numerous mistakes and inaccuracies. Let me know if you find any mistakes.
What has Algebraic Geometry to do with Geometry? Notes from a talk given at the graduate student seminar of the Ohio State University in April 2016.
Constructing Stability Conditions on Threefolds. Notes from a talk given at Yau's student seminar at Harvard in March 2016.
Introduction to Deformation Theory. Notes from a talk given at a graduate student seminar joint between MIT and NEU in March 2016.
Winter 2020/21: Toric Varieties, Leibniz Universität Hannover.
Summer 2020: Analysis II, Leibniz Universität Hannover.
Winter 2019/20: Analysis I, Leibniz Universität Hannover.
Spring 2019: Bridgeland Stability Conditions, The University of Texas at Austin.
Fall 2018: Applied Number Theory, The University of Texas at Austin.
Fall 2017: Calculus 1, The University of Texas at Austin.
Spring 2017: Complex Analysis, The University of Texas at Austin.
Fall 2016: Elementary Number Theory, The University of Texas at Austin.
Fall 2014: Calculus 1, The Ohio State University.
Spring 2014: Calculus 1, The Ohio State University.
Fall 2013: Calculus 1, The Ohio State University.
Summer 2009: Probability Theory, Leibniz Universität Hannover.
Winter 2008/09: Probability Theory, Leibniz Universität Hannover.
Summer 2008: Analysis II, Leibniz Universität Hannover.
Summer 2008: Linear Algebra II, Leibniz Universität Hannover.
Winter 2007/08: Analysis I, Leibniz Universität Hannover.
Winter 2007/08: Linear Algebra I, Leibniz Universität Hannover.