**Research Interests:**

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

**Papers:**

“Which subsets of an infinite random graph look random?” Preprint.

(with Piotr Oprocha) “Ultrafilters and Ramsey-type shadowing phenomena in topological dynamics,” Preprint.

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

(with Jonathan Meddaugh and Brian Raines) “Shadowing is generic on dendrites,” Preprint.

(with Nate Ackerman) “Indivisible sets and well-founded orientations of the Rado graph,” Preprint.

“Abstract omega-limit sets,” Preprint.

“Ideals and idempotents in the uniform ultrafilters,” Preprint.

(with James Kelly and Tim Tennant) “The specification property and infinite entropy for certain classes of linear operators,” to appear in *Journal of Mathematical Analysis and Applications*.

(with Jonathan Verner) ” G-delta and co-meager semifilters,” *Fundamenta Mathematicae ***235** (2016), pp. 153-166.

(with Mike Mislove) “Every infinite group can have a non-measurable subgroup,” *Topology and its Applications ***210** (2016), pp. 144-146.

“Ramsey shadowing and minimal points,” *Proceedings of the American Mathematical Society ***144** (2016), pp. 2697-2703.

“On neight,” *Topology Proceedings ***47** (2016), pp. 1-18.

(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.

“P-sets and minimal right ideals in **N***,” *Fundamenta Mathematicae* **229** (2015), pp. 277-293.

(with Arnie Miller) “Partitions of 2^ω and completely ultrametrizable spaces,” *Topology and its Applications* **184** (2015), pp. 61-71.

“Completely ultrametrizable spaces and continuous bijections,” *Topology Proceedings* **45** (2015), pp. 233-252.

“Preservation and destruction in simple refinements,” *Topology and its Applications* **178** (2014), pp. 236-247.

(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.

(with Chris Good, Robin Knight, and Dave McIntyre) “Finite intervals in the lattice of topologies,” *Order ***31**, iss. 3 (2014), pp. 325-335.

(with Jan van Mill, and Rolf Suabedissen) “Homogeneity and generalizations of 2-point sets,” *Houston Journal of Mathematics* **40**, 3 (2014), pp. 885-898.

“The Toronto problem,” *Topology and its Applications* **162** (2014), pp. 76-90.

“A cardinal invariant related to cleavability,” *Topology and its Applications*** 160** (2013), pp. 412-420.

“Non-well-founded extensions of **V**,” *Mathematical Logic Quarterly ***159**, 3 (2013), pp. 167-176.

**Slides from Talks:**

*Ramsey theory meets topological dynamics*, 2017 Spring Topology and Dynamics Conference, Jersey City, 2017 (slides)

*Quotients of the shift map (for birds)*, Summer Conference on Topology and its Applications, Leicester, 2016 (slides)

*Quotients of the shift map (for frogs)*, Toposym, Prague, 2016 (slides)

*Ramsey-type results in topological dynamics*, AIMS conference, Orlando, 2016 (slides)

*Dynamics in N**, Baylor mathematics colloquium, Waco, 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, 2014 (slides)

*Stone Duality, More Duality, and Dynamics in β N*, Oxford Analytic Topology Seminar, Oxford, 2014 (slides)

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