Research

Interests

My research centers on complex dynamics and several complex variables. I am especially interested in connections with other fields of mathematics.

Short bio

I received my Ph.D. in mathematics from the University of Michigan under the direction of Prof. Berit Stensønes.

After graduating, I held postdoctoral positions at Purdue University in West Lafayette, Indiana, the Institut Henri Poincaré in Paris, and Universidade Federal Fluminense in Rio de Janeiro.

I have also been fortunate to have visiting positions at SL Math (formerly MSRI) in Berkeley, California, Centre de Recherches Mathematiques in Montreal, Canada and at the Institute for Advance Study; in Princeton, New Jersey.

Curriculum vitae (PDF)

Publications and preprints

An arithmetic approach to parabolic multiplicity in complex dynamics With Xavier Buff and Valentin Hughin. Submitted. arXiv
A Non-Autonomous Model for Parabolic Implosion With Katelynn Huneycutt and Samantha Sandberg-Clark. Submitted. arXiv
On the dimension of bundle-valued Bergman spaces on compact Riemann surfaces With Anne-Katrin Gallagher and Purvi Gupta. Indiana Univ. Math. J. 73 (2024), no. 4, 1541–1549.arXiv
On the dimension of Bergman spaces on ℙ¹ With Anne-Katrin Gallagher and Purvi Gupta. La Matematica 1 (2022), 666–684. arXiv
Stable manifolds of biholomorphisms in ℂⁿ asymptotic to formal curves With Lorena López-Hernanz, Javier Ribón and Fernando Sanz Sánchez. Proc. Lond. Math. Soc. (3) 125 (2022), no. 2, 277–317. arXiv
Hardy spaces for a class of singular domains With Anne-Katrin Gallagher, Purvi Gupta and Loredana Lanzani. Math. Z. 299 (2021), no. 3–4, 2171–2197. arXiv
Parabolic implosion With Han Peters. Notices Amer. Math. Soc. 67 (2020), no. 8, 1095–1103. PDF
Non-autonomous parabolic bifurcation Proc. Amer. Math. Soc. 148 (2020), no. 6, 2525–2537. arXiv
Local dynamics of parabolic skew-products Pro Mathematica Vol. 31 Num. 61 (2020). arXiv
Parametrization of unstable manifolds for parabolic skew-products Complex Anal. Synerg. 4 (2018), no. 1. arXiv
A polynomial skew-product with a wandering Fatou disk With Han Peters. Math. Z. 283 (2016), no. 1–2, 349–366. arXiv
A survey on non-autonomous basins in several complex variables With co-authors (2014). arXiv
Dynamics of two-resonant biholomorphisms With Jasmin Raissy. Math. Res. Lett. 20 (2013), no. 4, 757–771. arXiv
Basins of attraction of automorphisms in ℂ³ With Berit Stensønes. Ergodic Theory Dynam. Systems 34 (2014), no. 2, 689–692. arXiv
Bounding the rank of Hermitian forms and rigidity for CR mappings of hyperquadrics With Jiří Lebl and Dusty Grundmeier. Math. Ann. 358 (2014), no. 3–4, 1059–1089. arXiv
Geodesics in the space of Kähler metrics With László Lempert. Duke Math. J. 162 (2013), no. 7, 1369–1381. arXiv
Degenerate characteristic directions for maps tangent to the identity Indiana Univ. Math. J. 61 (2012), no. 6, 2019–2040. Preprint
Fatou–Bieberbach domains as basins of attraction of automorphisms tangent to the identity J. Geom. Anal. 22 (2012), no. 2, 352–382. arXiv
Fatou–Bieberbach domains associated to maps tangent to the identity Ph.D. thesis, University of Michigan.
Remarks on automorphisms of ℂ^* × ℂ^* and their basins Complex Var. Elliptic Equ. 54 (2009), no. 3–4, 401–407. arXiv
Attracting basins of volume preserving automorphisms of ℂ^k With Han Peters and Erlend Fornæss Wold. Internat. J. Math. 19 (2008), no. 7, 801–810. arXiv