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Alan Roche Department of Mathematics University of Oklahoma Norman, OK 73019-3103 Office: PHSC 1112 Email: aroche (at) ou (dot) edu |
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Welcome! The picture is not me: it's Aoibhe, pronounced A V as in the letters. Mine was merely the mortal hand and eye that dared to frame her consummate symmetry.
My research area is algebra, mainly representation theory. And in representation theory, I've mainly studied representations of p‒adic groups, a subject with close ties to number theory. Recently, however, I've found myself writing semi-expository pieces on more elementary topics. Some are listed below. Aoibhe studies CATegory theory and purr‒obability.
Some Recent Papers
- A Note on Dual Modules and the Transpose (with T. Madsen and C. R. Vinroot) Arch. Math. (Basel) 114 (2020), no. 3, 247-257.
- Four Group-theoretic Proofs of Wedderburn's Little Theorem Irish Math. Soc. Bulletin 88 (2021), 57-68.
- A Tale of Two Cyclicities: Counting in Finite Cyclic Groups and Finite Fields (with J. Cohen) Amer. Math. Monthly 129 (2022), no. 7, 660-676.
- A Characterization of Cyclic Groups via Indices of Maximal Subgroups Irish Math. Soc. Bulletin 89 (2022), 65-72.
- Which Finite Rings Have the Most or Fewest Units? (with J. Cohen) Amer. Math. Monthly 129 (2022), no. 8, 717-733.
In Progress
- A Short Proof of the Riemann Hypothesis
Teaching
In fall 2022, I'm teaching calculus (MATH 2924) and probability (MATH 4733).
Grab Bag
To do.