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aBa Mbirika, Ph.D.

aBa Mbirika
Titles
  • Associate Professor
Departments
  • Mathematics
  • Blugold Supercomputing Cluster
Contact
Office Locations



Research and Creative Activities
  • Combinatorics 
  • Commutative algebra 
  • Combinatorial representation theory 
  • Algebraic combinatorics
  • Number theory
  • Lattice point geometry 
  • Graph labelings 
  • Complex reflection groups
Education
  • Ph,D., University of Iowa (Mathematics)
  • M.A., University of Iowa (Mathematics)
  • B.A., Sonoma State University (Mathematics)
Published Research

Research Publications

  • Lattice point visibility on generalized lines of sights. (Joint work with Edray Goins, Pamela Harris, and Bethany Kubik) -- Published by the American Mathematical Monthly, 125 No.7 (2018), 593--601. (Available by clicking here).
  • Coprime and prime labelings of graphs. (Joint work with Adam Berliner, Nate Dean, Jonelle Hook, Alison Marr, and Cayla McBee) -- Published by Journal of Integer Sequences, 19 No.5, Article 16.5.8 (2016), 14 pp. (Available by clicking here).
  • On the sign representations for the complex reflection groups G(r,p,n). (Joint work with Thom Pietraho and Bill Silver) -- Published by Beitrage zur Algebra und Geometrie, 57, Issue 4 (2016), 851--858, DOI 10.1007/s13366-016-0289-3, (Online published version available by clicking here).
  • Generalizing Tanisaki's ideal via ideals of truncated symmetric functions. (Joint work with Julianna Tymoczko) -- Published by Journal of Algebraic Combinatorics, 37 (2012), 167--199. (Available by clicking here).
  • A Hessenberg generalization of the Garsia-Procesi basis for the cohomology ring of Springer varieties. Published by Electronic Journal of Combinatorics, 17 No.1, Research Paper 153 (2010). (Available by clicking here).

Submitted

  • Representation stability of Springer varieties and some combinatorial consequences. (Joint work with Julianna Tymoczko) -- (arXiv version of paper available by clicking here).
  • An Euler phi function for the Eisenstein integers and some applications. (Joint work with Emily Gullerud) (Available by clicking here)

Preprints (Almost ready to submit):[NOTE: Check my webpage for most updated versions!!!!]

  • New methods to find patches of invisible integer lattice points. (Joint work with Austin Goodrich and Jasmine Nielsen) (Available by clicking here).
  • Characteristic polynomials and eigenvalues for a family of tridiagonal real symmetric matrices. (Joint work with Emily Gullerud and Rita Post) (DRAFT available by clicking here)

Interdisciplinary Research Publications

  • The Three Giri of Paradiso XXXIII. (Joint work with Arielle Saiber). Published by the journal, Dante Studies, 131 (2013): 237--272. (Available by clicking here).

Expository Math Writings

  • Hidden trees in the forest: On lattice points and prime labelings of graphs. This paper was inspired by my one-week residency at an AIM-NSF workshop called "Research Experiences for Undergraduate Faculty" at ICERM in Providence, RI, in June 2012. It contains some of our unpublished results, and also includes exercises and project ideas that faculty can use to involve undergraduates in research in the areas of Combinatorics, Graph Theory, and Number Theory (2012). (Available by clicking here).
  • On a coin-flip problem and its connection to pi. I wrote this with the intention of using it as a teaching (learning) tool for other faculty (students). Hence many exercises are included (2011). (Available by clicking here).
Professional Memberships

Member, American Mathematical Society -- AMS
Member, Mathematical Association of America -- MAA
Member, Project NExT Fellow (Blue 10 Dot)