**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 β N*, 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 β N*, Oxford Analytic Topology Seminar, Oxford UK, 2014 (slides)

*Completely Ultrametrizable Spaces and Continuous Bijections*, 2014 Spring Topology and Dynamics Conference, Richmond VA (slides)