research interests


My research interests center around Complex Dynamics and Several Complex Variables. I am specially interested on connections with other fields of Mathematics.

At the moment I am thinking of Parabolic Implosion, Orthogonal Polynomials, Hardy Spaces and Hartogs Triangles.



preprints/publications


On the dimension of bundle-valued Bergman spaces on compact Riemann surfaces. arxiv. With Anne-Katrin Gallagher, Purvi Gupta. Submitted.

On the dimension of Bergman spaces on P^1. arxiv. With Anne-Katrin Gallagher, Purvi Gupta. La Matematica 1 (2022), 666–684.

Stable manifolds of biholomorphisms in C^n asymptotic to formal curves arxiv. With Lorena Lopez-Hernanz, Javier Ribon and Fernando Sanz Sanchez. Proc. Lond. Math. Soc. (3) 125 (2022), no. 2, 277–317.

Hardy Spaces for a Class of Singular Domainsarxiv. With Anne-Katrin Gallagher, Purvi Gupta and Loredana Lanzani. Math. Z. 299 (2021), no. 3-4, 2171--2197.

Parabolic Implosion (2020) at the Notices of the AMS. With Han Peters. Notices Amer. Math. Soc. 67 (2020), no. 8, 1095–1103.

Non-autonomous Parabolic Bifurcation arxiv. Proc. Amer. Math. Soc. 148 (2020), no. 6, 2525--2537.

Local dynamics of parabolic skew-products (2018) arxiv, to appear in Pro Mathematica.

Parametrization of unstable manifolds for parabolic skew-products arxiv. Complex Anal. Synerg. 4 (2018), no. 1.

A polynomial skew-product with a wandering Fatou-disk. With Han Peters. arxiv. Math. Z. 283 (2016), no. 1-2, 349--366.

A survey on non-autonomous basins in several complex variables. With co-authors. (2014) arxiv.

Dynamics of two-resonant biholomorphisms. With Jasmin Raissy. arxiv. Math. Res. Lett. 20 (2013), no. 4, pp. 757--771.

Basins of attraction of automorphisms in C^3. With Berit Stensones. arxiv. Ergodic Theory Dynam. Systems 34 (2014), no. 2, pp. 689--692.

Bounding the rank of positiver hermitian forms and rigidity for CR mappings of hyperquadrics. With Jiri Lebl and Dusty Grundmeier. arxiv. Math. Ann. 358 (2014), no. 3--4, pp. 1059--1089.

Geodesics in the space of Kahler metrics. With Laszlo Lempert. arxiv. Duke Math. J. 162 (2013), no. 7, pp. 1369--1381

Degenerate characteristic directions for maps tangent to the identity. arxiv. Indiana Univ. Math. J. 61 (2012), no. 6, pp. 2019--2040.

Fatou-Bieberbach domains as basins of attraction of automorphisms tangent to the identity. arxiv. J. Geom. Anal. 22 (2012), no. 2, pp. 352--382.

Fatou-Bieberbach domains associated to maps tangent to the identity. Ph.D. Thesis: University of Michigan.

Remarks on automorphisms of C* x C* and their basins. arxiv. Complex Var. Elliptic Equ., Vol. 54 (2009), no.3--4, pp. 401--407.

Attracting Basins of Volume Preserving Automorphisms of C^k. With Han Peters and Erlend Fornaess Wold. arxiv. Internat. J. Math., Vol. 19 (2008), no. 7, pp. 801--810.



short bio


I received my Ph.D. in mathematics from the University of Michigan under the direction of Prof. Berit Stensones.
After graduating, I had postdoctoral positions at Purdue University at Lafayette, IN, Institute Henri Poincaré at Paris, and Universidad Federal Fluminense at Rio de Janeiro.
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