*Associate Professor*

*Office*: Maloney Hall 549, Boston College

Chestnut Hill, MA 02467-3806

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

I am the Assistant Chair for Graduate Programs at the Mathematics Department, Boston College.

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

My research is partially supported by NSF grants 1101153, 1200329 and a CAREER award
1350396.

- Curriculum Vitae (pdf)

- MT8811: Complex Analysis, MWF 1-1:50, Maloney 560, Spring 2017. Lecture Notes
- MT8808: Algebraic Topology, MWF 2-2:50, Gasson 208, Fall 2016. Syllabus
- MT8890: Graduate Teaching Seminar I, M 3-3:50, Maloney 536, Fall 2016.
- MT2210: 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.
- MT105: Calculus II, Fall 2011, 2012. Syllabus.
- MT822: Algebraic Geometry, Spring 2012. Lecture Notes.

- Scott Mullane, Ph.D., Boston College, 2012-16.
- Daniel Conroy, Independent Study, Boston College, Spring 2017.
- Miqiu Ding, Undergraduate Research Fellowship, Boston College, Summer 2017.
- Anthony Hernandez, Independent Study, Boston College, Spring 2016.
- Haoyuan Jiang, Undergraduate Research Fellowship, Boston College, Summer 2017.
- Zhangyang Wei, Undergraduate Research Fellowship, Boston College, Spring 2016.

- Tautological ring of strata of differentials (pdf), preprint.
- Principal boundary of moduli spaces of abelian and quadratic differentials (with Q. Chen) (pdf), preprint.
- Strata of k-differentials (with M. Bainbridge, Q. Gendron, S. Grushevsky, and M. Möller) (pdf), preprint.
- Spin and hyperelliptic structures of log twisted differentials (with Q. Chen) (pdf), preprint.
- Quasimodularity and large genus limits of Siegel-Veech constants (with M. Möller and D. Zagier) (pdf), preprint.
- Compactification of strata of abelian differentials (with M. Bainbridge, Q. Gendron, S. Grushevsky, and M. Möller) (pdf), preprint.
- Surfaces with big anticanonical class (with C. Schnell) (pdf), preprint.
- Affine geometry of strata of differentials (pdf),

*J. Inst. Math. Jussieu*, to appear. - Degenerations of Abelian differentials (pdf),

*J. Diff. Geom.*, to appear. - 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.

- Moduli Spaces: Birational Geometry and Wall Crossings, Banff, 10/7-12, 2018.
- Algebraic Geometry Northeastern Series, Northeastern University, 10/13-15, 2017.
- AIM SQuaRE, San Jose, 9/18-22, 2017.
- The Hamilton Geometry and Topology Workshop, Dublin, 8/22-26, 2017.
- The Abel Symposium, Lofoten, 8/7-11, 2017.
- The First China Algebraic Geometry Conference, Beijing, 7/3-7, 2017.