PhD in Mathematics, 2016
University of Cincinnati
BA with honors in Mathematics, 2010
University of Cincinnati
numerical range doi: 10.1080/03081087.2021.1895702 arXiv: 2009.01300 [math.FA]
essential codimension doi: 10.1007/s00020-019-2560-0 arXiv: 1902.09367 [math.OA]
essential codimension diagonals of operators doi: 10.7900/jot.2017dec01.2221 arXiv: 1712.06554 [math.OA] html
diagonals of operators doi: 10.1512/iumj.2018.67.6291 arXiv: 1602.08435 [math.FA]
essential codimension diagonals of operators doi: 10.1007/s00020-017-2365-y arXiv: 1609.06754 [math.OA] html
diagonals of operators doi: 10.7900/jot.2014nov05.2054 arXiv: 1410.7441 [math.FA]
diagonals of operators doi: 10.1016/j.jfa.2014.10.020 arXiv: 1403.4917 [math.FA]
a project to characterize diagonals of operators, especially selfadjoint operators, in terms of spectral data.
a project to generalize the notion of essential codimension due to Brown–Douglas–Fillmore, as well as to understand its ramifications.
This project investigates generalizations of the standard numerical range and their associated properties.