Brandon Seward Assistant Professor of Mathematics University of California San Diego AP&M 5739 bseward@ucsd.edu Curriculum Vitae Pronouns: He/him or they/them Course website: Math 240B (Winter 2022) Research seminar: Group Actions Seminar Research Interests:

Publications and Preprints  
24.  Borel asymptotic dimension and hyperfinite equivalence
relations (with C. Conley, S. Jackson, A. Marks, and R. TuckerDrob) Submitted. [PDF] 
23.  Bernoulli shifts with bases of
equal entropy are isomorphic Submitted. [PDF] 
22.  The Koopman representation and
positive Rokhlin entropy To appear in International Mathematics Research Notices. [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, 57101. [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, 28812917. [PDF] 
18.  Folner tilings for actions of
amenable groups (with C. Conley, S. Jackson, D. Kerr, A. Marks, and R. TuckerDrob) Mathematische Annalen 371 (2018), no. 12, 663683. [PDF] 
17.  Hyperfiniteness and Borel
combinatorics (with C. Conley, S. Jackson, A. Marks, and R. TuckerDrob) Journal of the European Mathematical Society 22 (2020), no. 3, 877892. [PDF] 
16.  Weak containment and Rokhlin
entropy Submitted. [PDF] 
15.  Cost, l^2Betti numbers, and the sofic
entropy of some algebraic actions (with D. Gaboriau) Journal d'Analyse Mathematique 139 (2019), 165. [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), 139. [PDF] 
12.  Krieger's
finite generator theorem for actions of countable groups I Inventiones Mathematicae 215 (2019), no. 1, 265310. [PDF] 
11.  Borel
structurability on the 2shift of a countable group (with R. TuckerDrob) Annals of Pure and Applied Logic 167 (2016), no. 1, 121. [PDF] 
10.  Every
action of a nonamenable group is the factor of a small action Journal of Modern Dynamics 8 (2014), no. 2, 251270. [PDF] 
9.  Locally
nilpotent groups and hyperfinite equivalence relations (with S. Schneider) Submitted. [PDF] 
8.  Arbitrarily
large residual finiteness growth (with K. BouRabee) Journal fur die reine und angewandte Mathematik (Crelle's Journal) 710 (2016), 199204. [PDF] 
7.  Ergodic
actions of countable groups and finite generating partitions Groups, Geometry, and Dynamics 9 (2015), no. 3, 793810. [PDF] 
6.  Finite
entropy actions of free groups, rigidity of stabilizers, and a
HoweMoore type phenomenon Journal d'Analyse Mathematique 129 (2016), no. 1, 309340. [PDF] 
5.  A
subgroup formula for finvariant entropy Ergodic Theory and Dynamical Systems 34 (2014), no. 1, 263298. [PDF] 
4.  Group
colorings and Bernoulli subflows (with S. Gao and S. Jackson) Memoirs of the American Mathematical Society 241 (2016), no. 1141, 1241. [PDF] 
3.  Generalizing
Magnus' characterization of free groups to some free products (with K. BouRabee) Communications in Algebra 42 (2014), no. 9, 39503962. [PDF] 
2.  Burnside's
problem, spanning trees, and tilings Geometry & Topology 18 (2014), no. 1, 179210. [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, 579592. [PDF] 