*Office*: Maloney Hall 549, Boston College

Chestnut Hill, MA 02467-3806

*Email*: first name dot last name@bc.edu

I am an Associate Professor at the Mathematics Department, Boston College.

My research field is
Algebraic Geometry, especially the geometry of
Moduli Space.

Research partially supported by NSF grants 1101153, 1200329 and a CAREER award
1350396.

In Spring 2019 I was partially supported by a von Neumann Fellowship.

- Curriculum Vitae (pdf)

- MATH8865: Topics in Algebraic Geometry, Fall 2019. Lecture Notes
- MATH8808: Algebraic Topology, Fall 2018, 2016. Lecture Notes
- MATH8890: Graduate Teaching Seminar I, Fall 2018, 2017, 2016.
- MATH8811: Complex Analysis, Spring 2018, 2017. Lecture Notes
- MATH1105: Calculus II, Fall 2017, 2012, 2011. Syllabus
- MATH2210: Linear Algebra, Spring 2016. Syllabus
- MT845: Riemann Surfaces, Fall 2015. Lecture Notes
- MT460: Complex Variables, Fall 2015. Syllabus
- MT221: Introduction to Abstract Mathematics, Fall 2014. Syllabus
- MT312: Algebra II, Spring 2014. Syllabus
- MT845: Intersection Theory and Enumerative Geometry, Spring 2014. Lecture Notes
- MT311: Algebra I, Fall 2013. Syllabus
- MT845: Algebraic Curves, Spring 2013. Lecture Notes
- MT822: Algebraic Geometry, Spring 2012. Lecture Notes

- Developing Relationships with Experts, Notices of the AMS, Sep 2019.
- Iulia Gheorghita, Ph.D., Boston College, 2017-
- Scott Mullane, Ph.D., Boston College, 2012-16.
- Wantong Wei, Independent Study, Boston College, Summer 2019.
- Mingzhuo Deng, Independent Study, Boston College, Fall 2018.
- Miqiu Ding, Undergraduate Research Fellowship, Boston College, Summer 2017.
- Haoyuan Jiang, Undergraduate Research Fellowship, Boston College, Summer 2017.
- Daniel Conroy, Independent Study, Boston College, Spring 2017.
- Anthony Hernandez, Independent Study, Boston College, Spring 2016.
- Zhangyang Wei, Undergraduate Research Fellowship, Boston College, Spring 2016.

- The moduli space of multi-scale differentials (with M. Bainbridge, Q. Gendron, S. Grushevsky, and M. Möller) (pdf), preprint.
- The WYSIWYG compactification (with A. Wright) (pdf), preprint.
- Masur-Veech volumes and intersection theory on moduli spaces of Abelian differentials (with M. Möller, A. Sauvaget, and D. Zagier) (pdf), preprint.
- Surfaces with big anticanonical class (with C. Schnell) (pdf), preprint.
- Positivity of divisor classes on the strata of differentials (pdf),

*Q. J. Math.*, to appear. - Moduli of differentials (pdf),

*Oberwolfach Rep.*, to appear. - An extremal effective survey about extremal effective cycles in moduli spaces of curves (pdf),

*Abel Symp.*, to appear. - Affine geometry of strata of differentials (pdf),

*J. Inst. Math. Jussieu*18 (2019), no. 6, 1331-1340. - Principal boundary of moduli spaces of abelian and quadratic differentials (with Q. Chen) (pdf),

*Ann. Inst. Fourier*69 (2019), no. 1, 81-118. - Spin and hyperelliptic structures of log twisted differentials (with Q. Chen) (pdf),

*Selecta Math. (N.S.)*25 (2019), no. 2, Art. 20, 42pp. - Tautological ring of strata of differentials (pdf),

*Manuscripta Math.*158 (2019), no. 3-4, 345-351. - Strata of k-differentials (with M. Bainbridge, Q. Gendron, S. Grushevsky, and M. Möller) (pdf),

*Algebr. Geom.*6 (2019), no. 2, 196-233. - Compactification of strata of abelian differentials (with M. Bainbridge, Q. Gendron, S. Grushevsky, and M. Möller) (pdf),

*Duke. Math. J.*167 (2018), no. 12, 2347-2416. - Quasimodularity and large genus limits of Siegel-Veech constants (with M. Möller and D. Zagier) (pdf),

*J. Amer. Math. Soc.*31 (2018), no. 4, 1059-1163. - Degenerations of Abelian differentials (pdf),

*J. Diff. Geom.*107 (2017), no. 3, 395-453. - Teichmüller dynamics in the eyes of an algebraic geometer (pdf),

*Proc. Sympos. Pure Math.*95 (2017), 171-197. - Extremality of loci of hyperelliptic curves with marked Weierstrass points (with N. Tarasca) (pdf),

*Algebra Number Theory*10 (2016), no. 9, 1935-1948. - Loci of curves with subcanonical points in low genus (with N. Tarasca) (pdf),

*Math. Z.*284 (2016), no. 3-4, 683-714. - Extremal effective divisors of Brill-Noether and Gieseker-Petri type in M_{1,n} (with A. Patel) (pdf),

*Adv. Geom.*16 (2016), no. 2, 231-242. - Moduli of generalized line bundles on a ribbon (with J. Kass) (pdf),

*J. Pure Appl. Algebra*220 (2016), no. 2, 822-844. - Extremal higher codimension cycles on moduli spaces of curves (with I. Coskun) (pdf),

*Proc. London Math. Soc. (3)*111 (2015), no. 1, 181-204. - Orbit closures in Teichmüller dynamics and extremal cycles in algebraic geometry (pdf),

*Oberwolfach Rep.*11 (2014), no. 1. - Quadratic differentials in low genus: exceptional and non-varying strata (with M. Möller) (pdf),

*Ann. Sci. Éc. Norm. Supér. (4)*47 (2014), no. 2, 309-369. - Extremal effective divisors on the moduli space of n-pointed genus one curves (with I. Coskun) (pdf),

*Math. Ann.*359 (2014), no. 3-4, 891-908. - Effective divisors on moduli spaces of curves and abelian varieties (with G. Farkas and
I. Morrison) (pdf),

*Clay Math. Proc.*18 (2013), 131-169. - Strata of abelian differentials and the Teichmüller dynamics (pdf),

*J. Mod. Dyn.*7 (2013), no. 1, 135-152. - Covers of the projective line and the moduli space of quadratic differentials (pdf),

*Geom. Dedicata*163 (2013), no. 1, 105-125. - Nonvarying sums of Lyapunov exponents of Abelian differentials in low genus (with M. Möller) (pdf),

*Geom. Topol.*16 (2012), no. 4, 2427-2479. - Detaching embedded points (with S. Nollet) (pdf),

*Algebra Number Theory*6 (2012), no. 4, 731-756. - Towards Mori's program for the moduli space of stable maps (with I. Coskun and an appendix by C. Crissman) (pdf),

*Amer. J. Math.*133 (2011), no. 5, 1389-1419. - Geometry of Teichmüller curves (pdf),

*Oberwolfach Rep.*8 (2011), no. 2. - Square-tiled surfaces and rigid curves on moduli spaces (pdf),

*Adv. Math.*228 (2011), no. 2, 1135-1162. - Hilbert scheme of a pair of codimension two linear subspaces (with I. Coskun and S. Nollet) (pdf),

*Comm. Algebra*39 (2011), no. 8, 3021-3043. - Covers of elliptic curves and the moduli space of stable curves (pdf),

*J. Reine Angew. Math.*649 (2010), 167-205. - Stable base locus decompositions of Kontsevich moduli spaces (with I. Coskun) (pdf),

*Michigan Math. J.*59 (2010), no. 2, 435-466. - Linear series on ribbons (pdf),

*Proc. Amer. Math. Soc.*138 (2010), no. 11, 3797-3805. - On the dimension of the Hilbert scheme of curves (pdf),

*Math. Res. Lett.*16 (2009), no. 6, 941-954. - Mori's program for the Kontsevich moduli space (pdf),

*Int. Math. Res. Not.*(2008), rnn 067, 17 pp. - Covers of elliptic curves and the lower bound for slopes of effective divisors on the moduli space of curves (pdf),

*Ph.D. Thesis*, Harvard University, 2008.

My papers are also available on arXiv. See above for updated versions.

- Dynamics on Flat Surfaces and their Moduli Spaces, Bonn, 4/20-24, 2020.
- Moduli of Curves, Hilbert Schemes, and Tropical Geometry, Tufts University, 3/21-22, 2020.
- Riemann Surfaces and their Moduli Spaces, University of Utah, 2/7-9, 2020.
- Informal Geometry and Dynamics Seminar, Harvard University, 11/20, 2019.
- Algebraic Geometry Seminar, University of Arizona, 11/13, 2019.
- AIM SQuaRE, San Jose, 10/28-11/1, 2019.
- Algebraic Geometry Fall School, Berlin, 9/30-10/4, 2019.
- Algebraic Geometry Northeastern Series, Boston, 9/20-9/22, 2019.