{"id":35,"date":"2012-01-30T18:02:02","date_gmt":"2012-01-30T18:02:02","guid":{"rendered":"http:\/\/wrbrian.wordpress.com\/?page_id=5"},"modified":"2026-01-28T15:44:56","modified_gmt":"2026-01-28T20:44:56","slug":"research","status":"publish","type":"page","link":"https:\/\/pages.charlotte.edu\/willbrian\/research\/","title":{"rendered":"Research"},"content":{"rendered":"

Papers:<\/strong><\/p>\n

with Alan Dow, “A parametrized \u2662 for the Laver property and automorphisms of P(\u03c9)\/Fin,” preprint. (pdf<\/a>)<\/p>\n

\u201cDoes\u00a0P<\/em>(\u03c9)\/fin know its right hand from its left?\u201d preprint. (pdf<\/a>)<\/p>\n

with Rene Gril Rogina, “Endpoint-homogeneous fans,” to appear in Fundamenta Mathematicae<\/em>. (pdf<\/a>)<\/p>\n

with Chris Stuart, “Small-dimensional normed barrelled spaces,” to appear in Israel Journal of Mathematics<\/em>. (pdf<\/a>)<\/p>\n

with Ilijas Farah, “Conjugating trivial automorphisms of P<\/em>(N<\/strong>)\/Fin,” to appear in Transactions of the American Mathematical Society<\/em>. (pdf<\/a>)<\/p>\n

with Hector Barriga-Acosta and Alan Dow, \u201cOn Roitman\u2019s principles MH and \u0394,\u201d to appear in\u00a0Israel Journal of Mathematics<\/em>. (pdf<\/a>)<\/p>\n

“Cardinal invariants of a meager ideal,” Topology and its Applications <\/em>379<\/strong> (2026), article no. 109516. (pdf<\/a>)<\/p>\n

with Alan Dow and KP Hart, “M<\/strong>*, N<\/strong>*, and H<\/strong>*,” Topology and Its Applications <\/em>373<\/strong> (2025), article no. 109539. (pdf<\/a>)<\/p>\n

with Rene Gril Rogina, “The classification of two lines Mahavier products,” Journal of Dynamical and Control Systems<\/em>\u00a031<\/strong> (2025), article no. 2. (pdf<\/a>)<\/p>\n

\u201cPartitioning the real line into Borel sets,\u201d\u00a0Journal of Symbolic Logic\u00a0<\/em>89<\/strong>\u00a0(2024), pp. 549-568. (pdf<\/a>)<\/p>\n

\u201cThe Borel partition spectrum at successors of singular cardinals,\u201d\u00a0Proceedings of the American Mathematical Society<\/em>\u00a0152<\/strong>\u00a0(2024), pp. 855-867. (pdf<\/a>)<\/p>\n

with Steven Clontz, \u201cElementary submodels, coding strategies, and an infinite real\u00a0<\/span>number game<\/span>,\u201d\u00a0Topology Proceedings\u00a0<\/em>62<\/strong>\u00a0(2023), pp. 151-161. (pdf<\/a>)<\/p>\n

\u201cCovering versus partitioning with the Cantor space,\u201d\u00a0Topology and its Applications\u00a0<\/em>323<\/strong>\u00a0(2023), article no. 108280. (pdf<\/a>)<\/p>\n

\u201cCovering versus partitioning with Polish spaces,\u201d\u00a0Fundamenta Mathematicae\u00a0<\/em>260<\/strong>\u00a0(2023), pp. 21-39. (pdf<\/a>)<\/p>\n

with Taras Banakh and Alejandro R\u00edos Herrej\u00f3<\/span>n, \u201cFirst-countable Lindel\u00f6f scattered spaces,\u201d\u00a0Topology and Its Applications\u00a0<\/em>322<\/strong>\u00a0(2022), article no. 108318. (pdf<\/a>)<\/p>\n

with Alan Dow and Saharon Shelah: \u201cThe independence of GCH and a combinatorial principle related to Banach-Mazur games,\u201d\u00a0Archive for Mathematical Logic\u00a0<\/em>61<\/strong>\u00a0(2022), pp. 1-17. (pdf<\/a>)<\/p>\n

with Alan Dow: “Small cardinals and small Efimov spaces,” <\/span>Annals of Pure and Applied Logic <\/em>173<\/strong> (2022), article no. 103043 (<\/span>pdf<\/a>)<\/span><\/p>\n

with Alan Dow, Dave Milovich, and Lynne Yengulalp: “Telg\u00e1rsky’s conjecture may fail,” Israel Journal of Mathematics<\/em> 242<\/strong> (2021), pp. 325-358. (pdf<\/a>)<\/p>\n

with Paul Larson: “Choosing between incompatible ideals,” European Journal of Combinatorics<\/em>\u00a026<\/strong> (2021), article no. 103349. (pdf<\/a>)<\/p>\n

with Neil Hindman: “Factoring a minimal ultrafilter into a thick part and a syndetic part,” Fundamenta Mathematicae <\/em>252<\/strong> (2021), pp. 121-145. (pdf<\/a>)<\/p>\n

“The isomorphism class of the shift map,” Topology and its Applications <\/em>283<\/strong> (2020), article no. 107343. (pdf<\/a>)<\/p>\n

with James Kelly: “Linear operators with infinite entropy,” <\/span>Journal of Mathematical Analysis and Applications <\/em>487<\/strong>, vol. 2 (2020), article no. 123981 (<\/span>pdf<\/a>)<\/span><\/p>\n

with Andreas Blass, J\u00f6rg Brendle, Joel David Hamkins, Michael Hardy, and Paul Larson: “The rearrangement number,” Transactions of the American Mathematical Society <\/em>373<\/strong> (2020), pp. 41-69. (link<\/a>)<\/p>\n

with J\u00f6rg Brendle and Joel David Hamkins: “The subseries number,”\u00a0Fundamenta Mathematicae<\/em>\u00a0247<\/strong> (2019), pp. 49-85. (link<\/a>)<\/p>\n

“Three conditionally convergent series, but not four,”\u00a0Bulletin of the London Mathematical Society <\/em>51 <\/strong>(2019), pp. 207-222. (link<\/a>)<\/p>\n

“Universal flows and automorphisms of P<\/em>(\u03c9)\/fin,”\u00a0Israel Journal of Mathematics\u00a0<\/em>233\u00a0<\/strong>(2019), pp. 453-500. (pdf<\/a>)<\/p>\n

with Jonathan Meddaugh and Brian Raines: “Shadowing is generic on dendrites,”\u00a0Discrete and Continuous Dynamical Systems – Series<\/em> S<\/em> 12<\/strong>, no. 8 (2019), pp. 2211-2220. (link<\/a>)<\/p>\n

with Nate Ackerman: “Indivisible sets and well-founded orientations of the Rado graph,”\u00a0Mathematical Logic Quarterly<\/em>\u00a065<\/strong>, iss. 1 (2019), pp. 46-56. (link<\/a>)<\/p>\n

“Which subsets of an infinite\u00a0random graph look random?”\u00a0Mathematical Logic Quarterly<\/em>\u00a064<\/strong>, iss. 6 (2018), pp. 478-486. (link<\/a>)<\/p>\n

“Abstract omega-limit sets,”\u00a0Journal of Symbolic Logic\u00a0<\/em>83<\/strong> (2018), pp. 477-495. (link<\/a>)<\/p>\n

with Piotr Oprocha: “Ultrafilters and Ramsey-type shadowing phenomena in topological dynamics,”\u00a0Israel Journal of Mathematics <\/em>227<\/strong> (2018), pp. 423-454. (link<\/a>)<\/p>\n

“Ideals and idempotents in the uniform ultrafilters,”\u00a0\u00a0Topology and its Applications <\/em>237<\/strong> (2018), pp. 53-66.\u00a0(link<\/a>)<\/p>\n

with James Kelly and Tim Tennant: “The specification property and infinite entropy for certain classes of linear operators,”\u00a0Journal of Mathematical Analysis and Applications <\/em>453<\/strong> (2017), pp. 917-927. (link<\/a>)<\/p>\n

with Jonathan Verner: “G-delta and co-meager semifilters,”\u00a0Fundamenta Mathematicae\u00a0<\/em>235<\/strong> (2016), pp. 153-166. (link<\/a>)<\/p>\n

with Mike Mislove: “Every infinite group can have a non-measurable subgroup,”\u00a0Topology and its Applications <\/em>210<\/strong> (2016), pp. 144-146.\u00a0(link<\/a>)<\/p>\n

“Ramsey shadowing and minimal points,” Proceedings of the American Mathematical Society\u00a0<\/em>144<\/strong> (2016), pp. 2697-2703.\u00a0(link<\/a>)<\/p>\n

“On neight,”\u00a0Topology Proceedings\u00a0<\/em>47<\/strong> (2016), pp. 1-18.\u00a0(link<\/a>)<\/p>\n

with Jonathan Meddaugh and Brian Raines: “Chain transitivity and variations of the shadowing property,” Ergodic Theory and Dynamical Systems\u00a0<\/em>35<\/strong>, no. 7 (2015), pp. 2044-2052.\u00a0(link<\/a>)<\/p>\n

“P-sets and minimal right ideals in N<\/strong>*,”\u00a0Fundamenta Mathematicae<\/em> 229<\/strong> (2015), pp. 277-293.\u00a0(link<\/a>)<\/p>\n

with Arnie Miller:\u00a0“Partitions of 2^\u03c9 and completely ultrametrizable spaces,”\u00a0Topology and its Applications<\/em> 184<\/strong> (2015), pp. 61-71.\u00a0(link<\/a>)<\/p>\n

“Completely ultrametrizable spaces and continuous bijections,”\u00a0Topology Proceedings<\/em> 45<\/strong> (2015), pp. 233-252.\u00a0(link<\/a>)<\/p>\n

“Preservation and destruction in simple refinements,”\u00a0Topology and its Applications<\/em> 178<\/strong> (2014), pp. 236-247.\u00a0(link<\/a>)<\/p>\n

with Mike Mislove: “From Haar to Lebesgue via domain theory,” in\u00a0Horizons of the Mind: a tribute to Prakash Panangaden<\/em>, eds. F. van Breugel et. al., Lecture Notes in Computer Science, Springer, 2014.\u00a0(link<\/a>)<\/p>\n

with Chris Good, Robin Knight, and Dave McIntyre: “Finite intervals in the lattice of topologies,”\u00a0Order\u00a0<\/em>31<\/strong>, iss. 3 (2014), pp. 325-335.\u00a0(link<\/a>)<\/p>\n

with Jan van Mill and Rolf Suabedissen: “Homogeneity and generalizations of 2-point sets,”\u00a0Houston Journal of Mathematics<\/em> 40<\/strong>, 3 (2014), pp. 885-898.\u00a0(link<\/a>)<\/p>\n

“The Toronto problem,”\u00a0Topology and its Applications<\/em> 162<\/strong> (2014), pp. 76-90.\u00a0(link<\/a>)<\/p>\n

“A cardinal invariant related to cleavability,”\u00a0<\/span>Topology and its Applications<\/em> 160<\/strong> (2013), pp. 412-420.\u00a0(link<\/a>)<\/span><\/p>\n

“Non-well-founded extensions of V<\/strong>,”\u00a0<\/span>Mathematical Logic Quarterly\u00a0<\/em>159<\/strong>, iss. 3 (2013), pp. 167-176.\u00a0(link<\/a>)<\/span><\/p>\n

Slides from Talks:<\/strong><\/p>\n

An uncountable analogue of Fra\u00efss\u00e9’s theorem<\/em>, Set-theoretic topology meeting in Messina, Sicily (slides<\/a>)<\/p>\n

Order-reversing maps on<\/em> N<\/strong>* and<\/em> H<\/strong>*, 58th Spring Topology and Dynamics Conference, Newport News, VA, 2025 (slides<\/a>)<\/p>\n

Endpoint-homogeneous fans<\/em>, 2nd Maribor workshop on topological dynamics and continuum theory, Maribor, 2025 (slides<\/a>)<\/p>\n

Does P(\u03c9)\/Fin know its right hand from its left?\u00a0<\/em>3-part tutorial at the Winter School, Hejnice, Czech Republic, 2025 (part1<\/a>, part2<\/a>, part3<\/a>)<\/p>\n

Does P(\u03c9)\/Fin know its right hand from its left?<\/em> MAMLS, Rutgers, 2024 (slides<\/a>)<\/p>\n

Trivial self-homeomorphisms of \u03c9*<\/em>, Summer Topology Conference, Coimbra, 2024 (slides<\/a>)<\/p>\n

Does \u03c9* know its right hand from its left?<\/em>\u00a0PALS online seminar, 2024 (slides<\/a>)<\/p>\n

Partitions of the real line<\/em>, Set-theoretic topology meeting, Oaxaca, 2023 (slides<\/a>)<\/p>\n

The uniformity number of a meager ideal<\/em>, Spring Topology and Dynamics Conference, 2023 (slides<\/a>)<\/p>\n

Partitioning the real line into Borel sets<\/em>, PALS online seminar, 2023 (slides<\/a>)<\/p>\n

Partitioning the real line into Borel sets<\/em>, TOPOSYM, Prague, 2022 (slides<\/a>)<\/p>\n

Partitions of the real line<\/em>, Spring Topology and Dynamical Systems Conference, Waco TX, 2022 (slides<\/a>)<\/p>\n

Partitioning versus covering with topological spaces<\/em>, Southeastern section meeting of the AMS, 2021 (slides<\/a>)<\/p>\n

Covering versus partitioning with Polish spaces<\/em>, BLAST, 2021 (slides<\/a>)<\/p>\n

Covering versus partitioning with Polish spaces<\/em>, Spring Topology and Dynamics Conference, 2021 (slides<\/a>)<\/p>\n

Limited-information strategies in Banach-Mazur games<\/em>, Toronto Set Theory Seminar, 2020 (slides<\/a>)<\/p>\n

Limited-information strategies in Banach-Mazur games<\/em>, Online Logic Seminar, 2020 (slides<\/a>)<\/p>\n

Small Efimov spaces and the splitting number of the reals<\/em>, AMS Joint Meetings, Gainesville FL, 2019 (slides<\/a>)<\/p>\n

Seven questions about<\/em> \u03c9*<\/em>, BLAST, Boulder CO, 2019 (slides<\/a>)<\/p>\n

Seven questions about \u03c9*<\/em>, Spring Topology and Dynamics Conference, Birmingham AL, 2019 (slides<\/a>)<\/p>\n

Universal automorphisms of\u00a0P<\/em>(\u03c9)\/fin, BLAST, Denver CO, 2018 (slides<\/a>)<\/p>\n

Factoring a minimal ultrafilter into a thick part and a syndetic part<\/em>, 2018 Summer Conference on Topology and its Applications, Bowling Green KY (slides<\/a>)<\/p>\n

Self-homeomorphisms of\u00a0N<\/strong><\/em>* and their quotients<\/em>, 2018 Spring Topology and Dynamics Conference, Auburn AL (slides<\/a>)<\/p>\n

Autohomeomorphisms of N<\/strong>*<\/em>, Conference in honor of Gary Gruenhage’s 70th birthday, Auburn AL, 2017 (slides<\/a>)<\/p>\n

About \u03b2N<\/strong><\/em>, job interview talk, UNC Charlotte, 2017 (slides<\/a>)<\/p>\n

Ramsey theory meets topological dynamics<\/em>, 2017 Spring Topology and Dynamics Conference, Jersey City NJ, 2017 (slides<\/a>)<\/p>\n

Quotients of the shift map (for birds)<\/em>, Summer Conference on Topology and its Applications, Leicester UK, 2016 (slides<\/a>)<\/p>\n

Quotients of the shift map (for frogs)<\/em>, Toposym, Prague, 2016 (slides<\/a>)<\/p>\n

Ramsey-type results in topological dynamics<\/em>, AIMS conference, Orlando FL, 2016 (slides<\/a>)<\/p>\n

Dynamics in\u00a0N<\/strong>*<\/em>, Baylor mathematics colloquium, Waco TX, 2015 (slides<\/a>)<\/p>\n

Ultrafilters on semifilters<\/em>, Winter School in Abstract Analysis, Hejnice (Czech Rep.), 2015 (slides<\/a>)<\/p>\n

Preservation under refinement<\/em>, International Conference for Topology and its Applications, Nafpaktos (Greece), 2014 (slides<\/a>)<\/p>\n

Ramsey shadowing and recurrence<\/em>, Galway Topology Colloquium, Birmingham UK, 2014 (slides<\/a>)<\/p>\n

Stone Duality, More Duality, and Dynamics in \u03b2N<\/strong><\/em>, Oxford Analytic Topology Seminar, Oxford UK, 2014 (slides<\/a>)<\/p>\n

Completely Ultrametrizable Spaces and Continuous Bijections<\/em>, 2014 Spring Topology and Dynamics Conference, Richmond VA (slides<\/a>)<\/p>\n","protected":false},"excerpt":{"rendered":"

Papers: with Alan Dow, “A parametrized \u2662 for the Laver property and automorphisms of P(\u03c9)\/Fin,” preprint. (pdf) \u201cDoes\u00a0P(\u03c9)\/fin know its right hand from its left?\u201d preprint. (pdf) with Rene Gril Rogina, “Endpoint-homogeneous fans,” to appear in Fundamenta Mathematicae. (pdf) with Chris Stuart, “Small-dimensional normed barrelled spaces,” to appear in Israel Journal of Mathematics. (pdf) with […]<\/p>\n","protected":false},"author":2373,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-35","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pages.charlotte.edu\/willbrian\/wp-json\/wp\/v2\/pages\/35","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pages.charlotte.edu\/willbrian\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/pages.charlotte.edu\/willbrian\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/pages.charlotte.edu\/willbrian\/wp-json\/wp\/v2\/users\/2373"}],"replies":[{"embeddable":true,"href":"https:\/\/pages.charlotte.edu\/willbrian\/wp-json\/wp\/v2\/comments?post=35"}],"version-history":[{"count":12,"href":"https:\/\/pages.charlotte.edu\/willbrian\/wp-json\/wp\/v2\/pages\/35\/revisions"}],"predecessor-version":[{"id":85,"href":"https:\/\/pages.charlotte.edu\/willbrian\/wp-json\/wp\/v2\/pages\/35\/revisions\/85"}],"wp:attachment":[{"href":"https:\/\/pages.charlotte.edu\/willbrian\/wp-json\/wp\/v2\/media?parent=35"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}