My research interests lie in the intersection of dynamics, geometry, and number theory. My primary area of study is in homogeneous dynamics, especially effective and sparse equidistribution problems for horospherical flows, but I am also broadly interested in dynamical systems and ergodic theory, discrete subgroups of Lie groups, hyperbolic geometry, number theory, functional analysis, and the fascinating ways in which these fields are intertwined.
Publications
M. Luethi and T. McAdam, Density of almost-primes along horospherical orbits in SL(3,Z)\SL(3,R), In Preparation.
T. McAdam and Xiaoxing Yu, Origami slope gaps and the Hall distribution, arXiv Preprint arXiv:2508.16186, Submitted (2025).
F. Al Assal, N. Ali, U. Arengo, T. McAdam, C. Newman, N. Scully, and S. Zhou, Slope gap distribution of the double heptagon and an algorithm for determining winning vectors, arXiv Preprint arXiv:2508.19252, Submitted (2025).
J. Berman, T. McAdam, A. Miller-Murthy, C. Uyanik, and H. Wan, Slope gap distributions of saddle connections on the 2n-gon, Discrete and Continuous Dynamical Systems, Series A, 43 (2023), 1-56.
T. McAdam, Almost-prime times in horospherical flows on the space of lattices, Journal of Modern Dynamics, 15 (2019), 277-327.
Effective equidistribution in homogeneous dynamics with applications in number theory, Ph.D. Thesis, University of California San Diego, (2019).
J. Jacobsen and T. McAdam, A boundary value problem for integrodifference population models with cyclic kernels, Discrete and Continuous Dynamical Systems, Series B, 19 (2014), no. 10, 3191-3207.