** Russell Lodge **

Department of Mathematics and CS

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:

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