Clinton

Past Courses

Spring 2024 Math Studies Algebra II

Spring 2024 Topics in Algebra: Mathematical Paradoxes (lecture notes)

Fall 2023 Math Studies Algebra I

Fall 2022 Matrix Theory

Fall 2022 Descriptive Set Theory

Spring 2022 Math Studies Algebra II

Spring 2022 Set Theory

Fall 2021 Math Studies Algebra I

Spring 2021 Set Theory

Fall 2020 Matrix Theory

Fall 2020 Descriptive Set Theory

Spring 2020 Math Studies Algebra II

Spring 2020 Topics in Algebra: Mathematical Paradoxes

Fall 2019 Math Studies Algebra I

Spring 2019 Combinatorics

Fall 2018 Matrix Theory

Fall 2018 Descriptive Set Theory

Spring 2018 Set Theory

Fall 2017 Basic Logic

Fall 2017 Algebra I

Spring 2017 Math Studies Algebra II

Fall 2016 Basic Logic

Fall 2016 Descriptive Ergodic Theory

Spring 2016 Algebraic Structures

Fall 2015 Descriptive Set Theory

Spring 2015 Set Theory

Fall 2014 Algebraic Structures

Papers, preprints, and notes

• Measurable regular subgraphs, with M. Bowen and F. Weilacher
• Quasi-invariant measures concentrating on countable structures, with C. Jahel and A. Panagiotopoulos
• Local version of Vizing's theorem for multi-graphs, with J. Grebík and O. Pikhurko
• One-ended spanning subforests and treeability of groups, with D. Gaboriau, A.S. Marks, and R.D. Tucker-Drob
• Divisibility of spheres with measurable pieces, with J. Grebík and O. Pikhurko
• Borel asymptotic dimension and hyperfinite equivalence relations, with S.C. Jackson, A.S. Marks, B. Seward, and R.D. Tucker-Drob
• Equitable colorings of Borel graphs, with A. Bernshteyn
• Measurable realizations of abstract systems of congruences, with A.S. Marks and S.T. Unger
• Unfriendly colorings of graphs with finite average degree, with O. Tamuz
• Folner tilings for actions of amenable groups, with S.C. Jackson, D. Kerr, A.S. Marks, B. Seward, and R.D. Tucker-Drob
• Hyperfiniteness and Borel combinatorics, with S.C. Jackson, A.S. Marks, B. Seward, and R.D. Tucker-Drob
• Incomparable actions of free groups, with B.D. Miller
• Measurable perfect matchings for acyclic locally countable Borel graphs, with B.D. Miller
• The smooth ideal, with J.D. Clemens and B.D. Miller
• Measure reducibility of countable Borel equivalence relations , with B.D. Miller
• Orthogonal measures and ergodicity, with B.D. Miller
• A bound on measurable chromatic numbers of locally finite Borel graphs, with B.D. Miller
• Brooks's theorem for measurable colorings, with A.S. Marks and R.D. Tucker-Drob
• Distance from marker sequences in locally finite Borel graphs, with A.S. Marks
• Measure-theoretic unfriendly colorings
• Stationary probability measures and topological realizations, with A.S. Kechris and B.D. Miller
• Measurable chromatic and independence numbers for ergodic graphs and group actions, with A.S. Kechris
• Ultraproducts of measure preserving actions and graph combinatorics, with A.S. Kechris and R.D. Tucker-Drob
• Canonizing relations on nonsmooth sets
• An antibasis result for graphs of infinite Borel chromatic number, with B.D. Miller
• Brooks' theorem for Bernoulli shifts
• Descriptive set-theoretic dichotomy theorems and limits superior, with D. Lecomte and B.D. Miller
• Definability of small puncture sets, with A.E. Caicedo, J.D. Clemens, and B.D. Miller
• Partition relations via ideal products
• Defining non-empty small sets from families of finite sets, with A.E. Caicedo, J.D. Clemens, and B.D. Miller
• Finite monoid-valued measure algebras