Research
Research Publications and Preprints
On rank filtrations of algebraic K-theory and Steinberg modules,
with J Miller and P Patzt.
ArXiv preprint ArXiv:2303.00245. Submitted.
On the codimension-two cohomology of SL_n(Z),
with B Brück, J Miller, P Patzt, and R Sroka.
ArXiv preprint ArXiv:2204.11967. Submitted.
Stability properties of moduli spaces,
with R Jiménez Rolland.
Notices of the American Mathematical Society 69.4 (2022).
Expository. The ArXiv version (ArXiv:2201.04096) contains an extended bibliography.
Mapping class group actions on configuration spaces and the Johnson filtration,
with A Bianchi and J Miller.
Transactions of the American Mathematical Society 375, no. 08 (2022): 5461-5489.
On the generalized Bykovskii presentation of Steinberg modules,
with A Kupers, J Miller, and P Patzt.
International Mathematics Research Notices 2022, no. 13 (2022): 10347-10401.
FI-hyperhomology and ordered configuration spaces,
with J Miller.
Proceedings of the American Mathematical Society 148 (2020): 993-1002.
Non-integrality of some Steinberg modules,
with J Miller, P Patzt, and D Yasaki.
Journal of Topology 13.2 (2020): 441-459.
Quantitative representation stability over linear groups,
with J Miller.
International Mathematics Research Notices 2020, no. 22 (2020): 8624-8672.
Central stability for the homology of congruence subgroups and the second homology of Torelli groups,
with J Miller and P Patzt.
Advances in Mathematics 354 (2019): 106740.
Stability for hyperplane complements of type B/C and statistics on squarefree polynomials over finite fields,
with R Jiménez Rolland.
The Quarterly Journal of Mathematics 70.2 (2019): 565-602.
Higher order representation stability and ordered configuration spaces of manifolds,
with J Miller.
Geometry & Topology 23.5 (2019): 2519-2591.
Generating functions and statistics on spaces of maximal tori in classical Lie groups,
with J Fulman and R Jiménez Rolland.
New York Journal of Mathematics 23 (2017), 165–191.
Convergence criteria for FIW–algebras and polynomial statistics on maximal tori in type B/C,
with R Jiménez Rolland.
Advances in Mathematics 310 (2017), 121–158.
FIW–modules and constraints on classical Weyl group characters.
Mathematische Zeitschrift 281 (2015), no. 1-2, 1–42.
FIW–modules and stability criteria for representations of classical Weyl groups.
Journal of Algebra 420 (2014), 269–332.
Representation stability for the cohomology of the pure string motion groups.
Algebraic & Geometric Topology 12 (2012), no. 2, 909–931.
Decomposing inversion sets of permutations and applications to faces of the Littlewood-Richardson cone,
with R Dewji, I Dimitrov, A McCabe, M Roth, and D Wehlau.
Journal of Algebraic Combinatorics, 45 (2017), no. 4, 11739–1216.
The non-commutative cycle lemma,
with C Armstrong, J A Mingo, and R Speicher.
Journal of Combinatorial Theory Series A 117 (2010), no. 8, 1158–1166.
Non-research publications
Solved and unsolved problems, Problem 257.
European Mathematical Society Magazine 123 (2022), pp. 57–66.
Solved and unsolved problems, Solution to Problem 257.
European Mathematical Society Magazine 125 (2022), pp. 53–62.
Advice from our advisor: Benson Farb
Notices of the American Mathematical Society 68.10 (2021): 1752–1755.
Notes
These are some brief notes and graphics to illustrate the correspondence between string motions and automorphisms of the free group.
Topic Exam
I took my topic exam at the University of Chicago in February 2011. My topic proposal is available here: The Cohomology of Configuration Space and Representation Stability.
Undergraduate Projects
I received my B.Sc.H. from Queen's University in Kingston, Canada.
In the summer of 2009, I took part in a project on Littlewood Richardson Coefficients and Coxeter Groups with Mike Roth and Ivan Dimitrov, with the support of an NSERC USRA. My colleagues completed our project the following year: Decomposing Inversion Sets of Permutations and Applications to Faces of the Littlewood-Richardson Cone (with R Dewji, I Dimitrov, A McCabe, M Roth, and D Wehlau).
In the summer of 2008, I took part in a project on Free Probability and Random Matrices with Roland Speicher and James A. Mingo, supported by an NSERC USRA.
Some of our work is available here: The non-commutative cycle lemma. (with C Armstrong, J A Mingo, and R Speicher.)