I am a postdoc at UT 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.
Department of Mathematics
The University of Texas at Austin
Austin, TX 78712
Office RLM 9.118
- Derived categories and the genus of space curves, joint with Emanuele Macrì. To appear in Algebraic Geometry. arXiv:1801.02709.
- Stability conditions on threefolds - First wall crossings. arXiv:1509.04608. The mentioned Sage code can be found at stability_library.sage with a short documentation.
- 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.
- Discriminants of stable rank two sheaves on some general type surfaces, joint with Benjamin Sung. arXiv:1812.02735.
- Rank two sheaves with maximal third Chern character in three-dimensional projective space. arXiv:1811.11951.
- 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.
- Bridgeland stability on blow ups and counterexamples, joint with Cristian Martinez, Appendix by Omprokash Das. To appear in Mathematische Zeitschrift. arXiv:1708.08567.
- Lectures on Bridgeland stability, joint with Emanuele Macrì. In Moduli of curves, volume 21 of Lect. Notes Unione Mat. Ital., pages 139-211. Springer, Cham, 2017. arXiv:1607.01262.
- 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.
- A generalized Bogomolov-Gieseker inequality for the smooth quadric threefold, Bull. Lond. Math. Soc. 46 (2014), no. 5, 915-923. arXiv:1309.4265.
- On the birational geometry of Schubert varieties, Bull. Soc. Math. France 143 (2015), no. 3, 489-502. arXiv:1208.5507.
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.
- 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, University of Hannover.
- Winter 2008/09: Probability Theory, University of Hannover.
- Summer 2008: Analysis II, University of Hannover.
- Summer 2008: Linear Algebra II, University of Hannover.
- Winter 2007/08: Analysis I, University of Hannover.
- Winter 2007/08: Linear Algebra I, University of Hannover.
- Spring 2018, Conference (Co-)Organizer: Special Session of the AMS Sectional Meeting at Northeastern University.
- 2017 - 2018: I am mentoring an undergraduate student who has been reading basic algebraic geometry and other advanced topics with me.
- 2017 - 2018, (Co-)Organizer: Geometry Seminar at the University of Texas at Austin.
- 2012 - 2014, (Co-)Organizer: Algebraic geometry reading seminar at the Ohio State University.