Brandon Seward Associate Professor of Mathematics University of California San Diego AP&M 5739 bseward@ucsd.edu Curriculum Vitae Pronouns: they/them Course Websites: Math 140B Research seminar: Group Actions Seminar Research Interests: Ergodic theory Topological dynamics Descriptive set theory Group theory I study geometric and combinatorial properties of groups, their actions, and their associated Schreier graphs and orbit equivalence relations under the frameworks of measure theory, topology, and descriptive set theory.

Publications and Preprints
26.	Borel combinatorics of abelian group actions (with S. Gao, S. Jackson, and Edward Krohne) Submitted. [PDF]
25.	Minimal subdynamics and minimal flows without characteristic measures (with J. Frisch and A. Zucker) Submitted. [PDF]
24.	Borel asymptotic dimension and hyperfinite equivalence relations (with C. Conley, S. Jackson, A. Marks, and R. Tucker-Drob) Duke Mathematical Journal 172 (2023), no. 16, 3175-3226. [PDF]
23.	Bernoulli shifts with bases of equal entropy are isomorphic Journal of Modern Dynamics 18 (2022), 345-362. [PDF]
22.	The Koopman representation and positive Rokhlin entropy International Mathematics Research Notices (2023), no. 1, 350-371. [PDF]
21.	Continuous combinatorics of abelian group actions (with S. Gao, S. Jackson, and E. Krohne) To appear in Memoirs of the American Mathematical Society. [PDF]
20.	Positive entropy actions of countable groups factor onto Bernoulli shifts Journal of the American Mathematical Society 33 (2020), no. 1, 57-101. [PDF]
19.	Krieger's finite generator theorem for actions of countable groups III (with A. Alpeev) Ergodic Theory and Dynamical Systems 41 (2021), no. 10, 2881-2917. [PDF]
18.	Folner tilings for actions of amenable groups (with C. Conley, S. Jackson, D. Kerr, A. Marks, and R. Tucker-Drob) Mathematische Annalen 371 (2018), no. 1-2, 663-683. [PDF]
17.	Hyperfiniteness and Borel combinatorics (with C. Conley, S. Jackson, A. Marks, and R. Tucker-Drob) Journal of the European Mathematical Society 22 (2020), no. 3, 877-892. [PDF]
16.	Weak containment and Rokhlin entropy Submitted. [PDF]
15.	Cost, l^2-Betti numbers, and the sofic entropy of some algebraic actions (with D. Gaboriau) Journal d'Analyse Mathematique 139 (2019), 1-65. [PDF]
14.	Forcing constructions and countable Borel equivalence relations (with S. Gao, S. Jackson, and Edward Krohne) Journal of Symbolic Logic 87 (2022), no. 3, 873-893. [PDF]
13.	Krieger's finite generator theorem for actions of countable groups II Journal of Modern Dynamics 15 (2019), 1-39. [PDF]
12.	Krieger's finite generator theorem for actions of countable groups I Inventiones Mathematicae 215 (2019), no. 1, 265-310. [PDF]
11.	Borel structurability on the 2-shift of a countable group (with R. Tucker-Drob) Annals of Pure and Applied Logic 167 (2016), no. 1, 1-21. [PDF]
10.	Every action of a non-amenable group is the factor of a small action Journal of Modern Dynamics 8 (2014), no. 2, 251-270. [PDF]
9.	Locally nilpotent groups and hyperfinite equivalence relations (with S. Schneider) To appear in Mathematical Research Letters. [PDF]
8.	Arbitrarily large residual finiteness growth (with K. Bou-Rabee) Journal fur die reine und angewandte Mathematik (Crelle's Journal) 710 (2016), 199-204. [PDF]
7.	Ergodic actions of countable groups and finite generating partitions Groups, Geometry, and Dynamics 9 (2015), no. 3, 793-810. [PDF]
6.	Finite entropy actions of free groups, rigidity of stabilizers, and a Howe--Moore type phenomenon Journal d'Analyse Mathematique 129 (2016), no. 1, 309-340. [PDF]
5.	A subgroup formula for f-invariant entropy Ergodic Theory and Dynamical Systems 34 (2014), no. 1, 263-298. [PDF]
4.	Group colorings and Bernoulli subflows (with S. Gao and S. Jackson) Memoirs of the American Mathematical Society 241 (2016), no. 1141, 1-241. [PDF]
3.	Generalizing Magnus' characterization of free groups to some free products (with K. Bou-Rabee) Communications in Algebra 42 (2014), no. 9, 3950-3962. [PDF]
2.	Burnside's problem, spanning trees, and tilings Geometry & Topology 18 (2014), no. 1, 179-210. [PDF]
1.	A coloring property for countable groups (with S. Gao and S. Jackson) Mathematical Proceedings of the Cambridge Philosophical Society 147 (2009), no. 3, 579-592. [PDF]