Research Interests:
My main research interests are in set theory, topology, and topological dynamics. A current CV can be found here.
Papers:
“Does P(ω)/fin know its right hand from its left?” preprint. (pdf)
with Rene Gril Rogina, “Endpoint-homogeneous fans,” preprint. (pdf)
with Rene Gril Rogina, “The classification of two lines Mahavier products,” preprint. (pdf)
with Hector Barriga-Acosta and Alan Dow, “On Roitman’s principles MH and Δ,” to appear in Israel Journal of Mathematics. (pdf)
“Cardinal invariants of a meager ideal,” to appear in Topology and its Applications. (pdf)
“Partitioning the real line into Borel sets,” Journal of Symbolic Logic 89 (2024), pp. 549-568. (pdf)
“The Borel partition spectrum at successors of singular cardinals,” Proceedings of the American Mathematical Society 152 (2024), pp. 855-867. (pdf)
with Steven Clontz, “Elementary submodels, coding strategies, and an infinite real number game,” Topology Proceedings 62 (2023), pp. 151-161. (pdf)
“Covering versus partitioning with the Cantor space,” Topology and its Applications 323 (2023), article no. 108280. (pdf)
“Covering versus partitioning with Polish spaces,” Fundamenta Mathematicae 260 (2023), pp. 21-39. (pdf)
with Taras Banakh and Alejandro Ríos Herrejón, “First-countable Lindelöf scattered spaces,” Topology and Its Applications 322 (2022), article no. 108318. (pdf)
with Alan Dow and Saharon Shelah: “The independence of GCH and a combinatorial principle related to Banach-Mazur games,” Archive for Mathematical Logic 61 (2022), pp. 1-17. (pdf)
with Alan Dow: “Small cardinals and small Efimov spaces,” Annals of Pure and Applied Logic 173 (2022), article no. 103043 (pdf)
with Alan Dow, Dave Milovich, and Lynne Yengulalp: “Telgársky’s conjecture may fail,” Israel Journal of Mathematics 242 (2021), pp. 325-358. (pdf)
with Paul Larson: “Choosing between incompatible ideals,” European Journal of Combinatorics 26 (2021), article no. 103349. (pdf)
with Neil Hindman: “Factoring a minimal ultrafilter into a thick part and a syndetic part,” Fundamenta Mathematicae 252 (2021), pp. 121-145. (pdf)
“The isomorphism class of the shift map,” Topology and its Applications 283 (2020), article no. 107343. (pdf)
with James Kelly: “Linear operators with infinite entropy,” Journal of Mathematical Analysis and Applications 487, vol. 2 (2020), article no. 123981 (pdf)
with Andreas Blass, Jörg Brendle, Joel David Hamkins, Michael Hardy, and Paul Larson: “The rearrangement number,” Transactions of the American Mathematical Society 373 (2020), pp. 41-69. (link)
with Jörg Brendle and Joel David Hamkins: “The subseries number,” Fundamenta Mathematicae 247 (2019), pp. 49-85. (link)
“Three conditionally convergent series, but not four,” Bulletin of the London Mathematical Society 51 (2019), pp. 207-222. (link)
“Universal flows and automorphisms of P(ω)/fin,” Israel Journal of Mathematics 233 (2019), pp. 453-500. (pdf)
with Jonathan Meddaugh and Brian Raines: “Shadowing is generic on dendrites,” Discrete and Continuous Dynamical Systems – Series S 12, no. 8 (2019), pp. 2211-2220. (link)
with Nate Ackerman: “Indivisible sets and well-founded orientations of the Rado graph,” Mathematical Logic Quarterly 65, iss. 1 (2019), pp. 46-56. (link)
“Which subsets of an infinite random graph look random?” Mathematical Logic Quarterly 64, iss. 6 (2018), pp. 478-486. (link)
“Abstract omega-limit sets,” Journal of Symbolic Logic 83 (2018), pp. 477-495. (link)
with Piotr Oprocha: “Ultrafilters and Ramsey-type shadowing phenomena in topological dynamics,” Israel Journal of Mathematics 227 (2018), pp. 423-454. (link)
“Ideals and idempotents in the uniform ultrafilters,” Topology and its Applications 237 (2018), pp. 53-66. (link)
with James Kelly and Tim Tennant: “The specification property and infinite entropy for certain classes of linear operators,” Journal of Mathematical Analysis and Applications 453 (2017), pp. 917-927. (link)
with Jonathan Verner: “G-delta and co-meager semifilters,” Fundamenta Mathematicae 235 (2016), pp. 153-166. (link)
with Mike Mislove: “Every infinite group can have a non-measurable subgroup,” Topology and its Applications 210 (2016), pp. 144-146. (link)
“Ramsey shadowing and minimal points,” Proceedings of the American Mathematical Society 144 (2016), pp. 2697-2703. (link)
“On neight,” Topology Proceedings 47 (2016), pp. 1-18. (link)
with Jonathan Meddaugh and Brian Raines: “Chain transitivity and variations of the shadowing property,” Ergodic Theory and Dynamical Systems 35, no. 7 (2015), pp. 2044-2052. (link)
“P-sets and minimal right ideals in N*,” Fundamenta Mathematicae 229 (2015), pp. 277-293. (link)
with Arnie Miller: “Partitions of 2^ω and completely ultrametrizable spaces,” Topology and its Applications 184 (2015), pp. 61-71. (link)
“Completely ultrametrizable spaces and continuous bijections,” Topology Proceedings 45 (2015), pp. 233-252. (link)
“Preservation and destruction in simple refinements,” Topology and its Applications 178 (2014), pp. 236-247. (link)
with Mike Mislove: “From Haar to Lebesgue via domain theory,” in Horizons of the Mind: a tribute to Prakash Panangaden, eds. F. van Breugel et. al., Lecture Notes in Computer Science, Springer, 2014. (link)
with Chris Good, Robin Knight, and Dave McIntyre: “Finite intervals in the lattice of topologies,” Order 31, iss. 3 (2014), pp. 325-335. (link)
with Jan van Mill and Rolf Suabedissen: “Homogeneity and generalizations of 2-point sets,” Houston Journal of Mathematics 40, 3 (2014), pp. 885-898. (link)
“The Toronto problem,” Topology and its Applications 162 (2014), pp. 76-90. (link)
“A cardinal invariant related to cleavability,” Topology and its Applications 160 (2013), pp. 412-420. (link)
“Non-well-founded extensions of V,” Mathematical Logic Quarterly 159, iss. 3 (2013), pp. 167-176. (link)
Slides from Talks:
Trivial self-homeomorphisms of ω*, Summer Topology Conference, Coimbra, 2024 (slides)
Does ω* know its right hand from its left? PALS online seminar, 2024 (slides)
Partitions of the real line, Set-theoretic topology meeting, Oaxaca, 2023 (slides)
The uniformity number of a meager ideal, Spring Topology and Dynamics Conference, 2023 (slides)
Partitioning the real line into Borel sets, PALS online seminar, 2023 (slides)
Partitioning the real line into Borel sets, TOPOSYM, Prague, 2022 (slides)
Partitions of the real line, Spring Topology and Dynamical Systems Conference, Waco TX, 2022 (slides)
Partitioning versus covering with topological spaces, Southeastern section meeting of the AMS, 2021 (slides)
Covering versus partitioning with Polish spaces, BLAST, 2021 (slides)
Covering versus partitioning with Polish spaces, Spring Topology and Dynamics Conference, 2021 (slides)
Limited-information strategies in Banach-Mazur games, Toronto Set Theory Seminar, 2020 (slides)
Limited-information strategies in Banach-Mazur games, Online Logic Seminar, 2020 (slides)
Small Efimov spaces and the splitting number of the reals, AMS Joint Meetings, Gainesville FL, 2019 (slides)
Seven questions about ω*, BLAST, Boulder CO, 2019 (slides)
Seven questions about ω*, Spring Topology and Dynamics Conference, Birmingham AL, 2019 (slides)
Universal automorphisms of P(ω)/fin, BLAST, Denver CO, 2018 (slides)
Factoring a minimal ultrafilter into a thick part and a syndetic part, 2018 Summer Conference on Topology and its Applications, Bowling Green KY (slides)
Self-homeomorphisms of N* and their quotients, 2018 Spring Topology and Dynamics Conference, Auburn AL (slides)
Autohomeomorphisms of N*, Conference in honor of Gary Gruenhage’s 70th birthday, Auburn AL, 2017 (slides)
About βN, job interview talk, UNC Charlotte, 2017 (slides)
Ramsey theory meets topological dynamics, 2017 Spring Topology and Dynamics Conference, Jersey City NJ, 2017 (slides)
Quotients of the shift map (for birds), Summer Conference on Topology and its Applications, Leicester UK, 2016 (slides)
Quotients of the shift map (for frogs), Toposym, Prague, 2016 (slides)
Ramsey-type results in topological dynamics, AIMS conference, Orlando FL, 2016 (slides)
Dynamics in N*, Baylor mathematics colloquium, Waco TX, 2015 (slides)
Ultrafilters on semifilters, Winter School in Abstract Analysis, Hejnice (Czech Rep.), 2015 (slides)
Preservation under refinement, International Conference for Topology and its Applications, Nafpaktos (Greece), 2014 (slides)
Ramsey shadowing and recurrence, Galway Topology Colloquium, Birmingham UK, 2014 (slides)
Stone Duality, More Duality, and Dynamics in βN, Oxford Analytic Topology Seminar, Oxford UK, 2014 (slides)
Completely Ultrametrizable Spaces and Continuous Bijections, 2014 Spring Topology and Dynamics Conference, Richmond VA (slides)
