Search for people, departments, or email addresses.
Physical & Biological Sciences Division
Mathematics Department
Ph.D. Candidate
Mathematics
Graduate
Mathematics
McHenry Library
n/a
McHenry Library
My primary field of study is the modular representation theory of finite groups. In particular, I study questions regarding invertible objects in some suitable category of representation-theoretic objects. Many of these objects are connected to a natural class of representations known as permutation representations.
For my dissertation, I completely classified the invertible objects of a certain representation category, the bounded homotopy category of p-permutation kG-modules. These objects, which I call "endotrivial complexes," are governed by a class of functions known as "Borel-Smith functions" and which show up in unexpected places. This suggests a purely geometric description of these functions which is not yet understood. Endotrivial complexes are also connected to one of the biggest unsolved conjectures in my field, Broue's abelian defect group conjecture.
Galois descent of splendid Rickard equivalences between blocks of p-nilpotent groups, submitted May 2024
On endotrivial complexes and the generalized Dade group, submitted March 2024
Relatively endotrivial complexes, submitted February 2024
Brauer pairs for splendid Rickard complexes (with J. V. Breland), submitted December 2023
Endotrivial complexes, Journal of Algebra, 650, 173-218 (2024)
A proof of the optimal leapfrogging conjecture (with A. T. Benjamin), Involve (to appear)
Challenging Knight’s Tours (with A. T. Benjamin), Math Horizons 25:3, 18-21 (2018)
See my website for more up-to-date information.
This campus directory is the property of the University of California at Santa Cruz. To protect the privacy of individuals listed herein, in accordance with the State of California Information Practices Act, this directory may not be used, rented, distributed, or sold for commercial purposes. For more details, please see the university guidelines for assuring privacy of personal information in mailing lists and telephone directories. If you have any questions please contact the ITS Support Center.
