Brandon Seward

Assistant Professor of Mathematics
University of California San Diego
AP&M 5739
Curriculum Vitae
Pronouns: He/him/his

Course website: Math 140C (Spring 2021)
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
24. Borel asymptotic dimension and hyperfinite equivalence relations
(with C. Conley, S. Jackson, A. Marks, and R. Tucker-Drob)
Submitted. [PDF]
23. Bernoulli shifts with bases of equal entropy are isomorphic
Submitted. [PDF]
22. The Koopman representation and positive Rokhlin entropy
Submitted. [PDF]
21. Continuous combinatorics of abelian group actions
(with S. Gao, S. Jackson, and E. Krohne)
Submitted. [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)
To appear in Ergodic Theory and Dynamical Systems. [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)
Submitted. [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)
Submitted. [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]