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Office: Root Hall A-128

About me:

I am an associate professor in the Department of Math and Computer Science at Indiana State University. My research interests include complex dynamics, Teichmüller space, self-similar groups, and Thurston's theorem for postcritically finite rational maps. My doctoral thesis was written under the supervision of Kevin Pilgrim at Indiana University. I completed postdoctoral work at Jacobs University and the Institute for Mathematical Sciences and have been a visiting professor at the National Center for Theoretical Sciences in Taiwan.

Papers and preprints:

Thurston's pullback map, invariant covers, and the global dynamics on curves, with M. Bonk, M. Hlushchanka
Preprint (2024).

Iterated monodromy groups of rational functions and periodic points over finite fields, with A. Bridy, R. Jones, G. Kelsey
Math. Ann. doi:10.1007/s00208-023-02745-0, (2023).

On dynamical gaskets generated by rational maps, Kleinian groups, and Schwarz reflections, with M. Lyubich, S. Merenkov, S. Mukherjee
Conform. Geom. Dyn. 27 (2023), 1-54.

On deformation space analogies between Kleinian reflection groups and antiholomorphic rational maps, with Y. Luo, S. Mukherjee
Geom. Funct. Anal. 32 (2022), 1428-1485.

Circle packings, kissing reflection groups, and critically fixed anti-rational maps, with Y. Luo, S. Mukherjee
Forum of Mathematics, Sigma, 10, E3 (2022).

A classification of postcritically finite Newton maps, with Y. Mikulich and D. Schleicher
In the Tradition of Thurston, Vol. II, ed. K. Ohshika and A. Papadopoulos, Springer, 421-448 (2022).

Combinatorial properties of Newton maps, with Y. Mikulich and D. Schleicher,
Indiana Univ. Math. J. 70 (2021), 1833-1867.

Puzzles and the Fatou-Shishikura injection for rational Newton maps , with K. Drach, D. Schleicher, and M. Sowinski,
Trans. Amer. Math. Soc. 374:2753-2784 (2021).

Invisible tricorns in real slices of rational maps, with S. Mukherjee,
Discrete Contin. Dyn. Syst., 41(4):1755-1797 (2021).

Quadratic Thurston maps with few postcritical points, with G. Kelsey,
Geom Dedicata 201:33 (2019).

Origami, affine maps, and complex dynamics, with W. Floyd, G. Kelsey, S. Koch, W. Parry, K. Pilgrim, and E. Saenz,
Arnold Math J. 3(3):365-395 (2017). (NETmap software available here)

Boundary values of the Thurston pullback map
Conform. Geom. Dyn. 17, 77-118 (2013).

Thesis

Spring 2024 teaching:

MATH 313 Elementary Linear Algebra
MATH 410/510 Intro to Analysis

Slides:

Boundary values of Thurston's pullback map
Classification of postcritically finite Newton maps

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