Russell Lodge

Department of Mathematics and CS


Office: Root Hall A-128

About me:

I am an assistant 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.

Papers and preprints:

Iterated monodromy groups of rational functions and periodic points over finite fields, with A. Bridy, R. Jones, G. Kelsey

On dynamical gaskets generated by rational maps, Kleinian groups, and Schwarz reflections, with M. Lyubich, S. Merenkov, S. Mukherjee
Accepted: Conform. Geom. Dyn.

On deformation space analogies between Kleinian reflection groups and antiholomorphic rational maps, with Y. Luo, S. Mukherjee
In press: Geom. Funct. Anal. (2022).

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

Fall 2022 teaching:

MATH 132 Calculus II (2 sections)
MATH 625 Dynamical systems

Slides:

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