**Research Interests:**

My main research interests are in topological dynamics, set theory, and topology. A current CV can be found here.

**Papers:**

“Three conditionally convergent series,” Preprint.

(with Neil Hindman) “Factoring a minimal ultrafilter into a thick part and a syndetic part,” Preprint.

“Universal flows and automorphisms of *P*(ω)/fin,” Preprint.

(with Jörg Brendle and Joel David Hamkins) “The subseries number,” Preprint.

(with Andreas Blass, Jörg Brendle, Joel David Hamkins, Michael Hardy, and Paul Larson) “The rearrangement number,” Preprint.

“Which subsets of an infinite random graph look random?” Preprint, to appear in *Mathematical Logic Quarterly*.

(with Jonathan Meddaugh and Brian Raines) “Shadowing is generic on dendrites,” Preprint, to appear in *Discrete and Continuous Dynamical Systems – Series S*

(with Nate Ackerman) “Indivisible sets and well-founded orientations of the Rado graph,” Preprint, to appear in *Mathematical Logic Quarterly*.

“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**, 3 (2013), pp. 167-176. (link)

**Slides from Talks:**

*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)