Office: Rm. 526 in Hibbard Hall

Email: mbirika@uwec.edu

**Address:**- aBa (אבא) Mbirika
- University of Wisconsin-Eau Claire
- Department of Mathematics - HHH508

105 Garfield Avenue

Eau Claire, WI 54701

USA

(2017 to 2022) -- Associate Professor at University of Wisconsin-Eau Claire

(2013 to 2017) -- Assistant Professor at University of Wisconsin-Eau Claire

(2004 to 2010) -- Graduate Teaching Assistant at University of Iowa (in Iowa City, Iowa)

M.S. in Mathematics (2006) -- University of Iowa

B.A. (2004) -- Sonoma State University

- Curriculum Vitae (last
updated on October 8, 2022)

Spring 2023 - Math 426 - Abstract Algebra II - syllabus and constantly updated Notes Available Here

Spring 2023 - Continuing research on linear recurrence sequences with Janeč Shrader and Dr. Jürgen Spilker (emeritus faculty of University of Freiburg, Germany)

CLICK HERE to see an exhaustive list of all the classes I taught from 2013 to the present at UWEC. This may be useful to prospective students as these contain links to former course syllabi.

2016 - UWEC Certificate of Recognition for Contributions to Students (39 total awarded campus-wide) - click here to see award

2014 - UWEC Certificate of Recognition for Contributions to Students (22 total awarded campus-wide) - click here to see award

*GCD of sums of k consecutive squares of generalized Fibonacci numbers*. (Joint work with Jurgen Spilker) -- Published by Fibonacci Quarterly,**60**No.5 (2022), 255--269. (Available by clicking here).

*GCD of sums of k consecutive Fibonacci, Lucas, and generalized Fibonacci numbers*. (Joint work with Dan Guyer) -- Published by Journal of Integer Sequences,**24**No.9, Article 21.9.8 (2021), 25pp. (Available by clicking here). (This arXiv version is easier to navigate with better numbering system.)

- New methods to find patches of
invisible integer lattice points. (Joint work with Austin
Goodrich and Jasmine Nielsen) -- Published by Involve: A Journal of
Mathematics,
**14**No.2 (2021), 283--310. (Available by clicking here).

- Representation stability of Springer
varieties and some combinatorial consequences. (Joint work with
Julianna Tymoczko) -- Published by Journal of Algebraic Combinatorics,
**53**No.3 (2021), 897--920. (Available by clicking here).

- An Euler phi function for the Eisenstein integers and some applications. (Joint work with Emily Gullerud) -- Published by Integers: Electronic Journal of Combinatorial Number Theory, 20, Paper No. A20 (2020), 28pp. (Available by clicking here)
- 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).

- Tantalizing properties of subsequences of the Fibonacci sequence modulo 10. To appear in Rocky Mountain Journal of Mathematics. (Joint work with Dan Guyer and Miko Scott) (arXiv version available by clicking here)

- None at the moment

*Tridiagonal real symmetric matrices with a connection to Pascal’s triangle and the Fibonacci sequence*. (Joint work with Emily Gullerud and Rita Post) (arXiv version available by clicking here)*Pell and associated Pell braid sequences as GCDs of sums of k consecutive Pell and balancing-related numbers*. (Joint work with Janeč Schrader and Jürgen Spilker) (arXiv version available by clicking here)

- Towards a Schur-Weyl duality for the alternating group. (In progress) (Available by clicking here).
- Involutions in the hyperoctahedral group. (Joint work with Rita Post and Ryan Stodola)

- A213273 (sequence): The smallest m such that the complete bipartite graph K_{n,n} has a coprime labeling using labels from {1,...,m}. Available by clicking here.
- A210219 (paper and formula links):
*GCD of all sums of n consecutive Fibonacci numbers*. Available by clicking here. - A229339 (paper and formula links):
*GCD of all sums of n consecutive Lucas numbers*. Available by clicking here.

- 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).

- 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).

**The Power of Proofs [AND] Number Theory**. (Joint work with Rita Post). Self-published with Creative Commons License (CC BY-NC-SA), 2019.

- Number_Theory_Book_student_version
(last revision in January 2020)

- Number_Theory_Book_teacher_version (last revision in June 2019)

**Finite Mathematics - The Power of [Math 104]**. Self-published with Creative Commons License (CC BY-NC-SA), 2022.- Math 104 Course Packet (last revision in January 2023)

The following course packet was written by me for my students in Math
314. The first version was used in my Fall 2022 class.

**Discrete Mathematics - The Power of [Math 314]**. Self-published with Creative Commons License (CC BY-NC-SA), 2022.- Math_314_Course_Packet (last revision in August 2022)

The following course packet was written by me for my students in Math
425. The first version was used in my Fall 2021 class.

**Abstract Algebra I - The Power of [Math 425]**. Self-published with Creative Commons License (CC BY-NC-SA), 2021.- Math 425 Course Packet (last revision in August 2021)

**NOTE/WARNING**: Some of the documents below are solutions
to exercises in some textbooks. These may not be error-free, so if you are
a STUDENT "borrowing" solutions from these documents, **you
should NOT be doing that**. You should work on your own solutions
first and then maybe glance at what you find here.

**A Handy Guide to the Basics of LaTeX**. Author: Dan Guyer. Self-published with Creative Commons License (CC BY), 2021.- LaTeX Guide by Dan Guyer (last revision in August 2021)
- The following was written by students and myself in my Spring 2020 course on primitive roots and quadratic reciprocity. Authors: Jonah Amundsen, Dan Guyer, Bob Langer, aBa Mbirika, and Maggie Reardon (Spring 2020)
- The following is preliminary results on the Fibonacci and Lucas sequences identities. Author: Janeč Schrader (Summer 2022)
- The following is preliminary results in elementary number theory
identities, and Pell, Pell-Lucas, balancing, cobalancing,
Lucas-balancing, and Lucas-cobalancing identites. Author: Janeč Shrader
(Summer 2022).
**WARNING**: Some exercises are not complete due to Janeč and I conducting research in Fall 2022.

Here are brief introductions to some of the objects or ideas listed above that I think about:

- On my Schur-Weyl duality project. This 2 page write-up describes the problem that I am working on. It is also a good introduction for an undergraduate interested in doing research with me on this project.
- Complex reflection groups. This 5 page write-up briefly describes the family of imprimitive complex reflection groups (giving various combinatorial ways of viewing their elements), irreducible representations of these groups, a description (and an example) of a generalized Robinson-Schensted correspondence between these groups and pairs of same-shape multitableaux, and some combinatorial implications of the latter map.

- Lattice point visibility: In 2013-2014, my two students Jasmine Nielsen and Austin Goodrich research n-by-n square patches of invisible lattice points in the integer lattice - see our ORSP Grant Proposal for more info. This project was continued in an SREU project - see our ORSP Grant Proposal for more info.
- Generalized lattice point visibility: In 2015-2016, my two students Sara DeBrabander and Michele Gebert research lattice point visibility along generalized lines of sights (e.g., parabolic lines of sights) - see our ORSP Grant Proposal for more info.
- Longest increasing subsequences in G(r,p,n): In Summer 2016, my three students Rita Post, Ryan Stodola, and Stan/Jingtai Liu research various combinatorial statistics on elements in the complex reflection groups G(r,p,n) - see our ORSP Grant Proposal for more info.
- Permutation statistics on complex reflection groups: In 2016-2017, my three students from Summer 2016 continue their work. This time we focus on involutory conjugacy classes in the hyperoctahedral group G(2,1,n). - see our ORSP Grant Proposal for more info.
- Characteristic polynomials and
eigenvalues for a family of tridiagonal real symmetric matrices:
From Summer 2017-Spring 2018, my students Emily Gullerud and Rita Post
investigated the spectrum of a certain class of tridiagonal matrices. We
found a tantalizing connection between this spectrum and certain
diagonals in Pascal's triangle. There is no ORSP grant proposal for this
project as we did this purely for research joy!

- Combinatorial applications of Gaussian and Eisenstein integers: In Summer 2017, my student Emily Gullerud and I investigate combinatorial applications of Gaussian and Eisenstein integers - see our ORSP Grant Proposal for more info.
- Involutory and orientation-preserving symmetries in the hyperoctahedral group G(2,1,n): In 2017-2018, my three students Emily Gullerud, Rita Post, and McKenzie Scanlan are continuing work on the involutory conjugacy classes started in the 2016-2017 year with Liu-Post-Stodola. Furthermore, we investigate the splitting criterion for the alternating group A(2,1,n) conjugacy classes. - see our ORSP Grant Proposal for more info.
- GCD of sums of k consecutive Fibonacci, Lucas, and generalized Fibonacci numbers: In Spring 2019, my student Dan Guyer and I began investigating the GCD of sums of k consecutive Gibonacci numbers. This unfunded research project led to a preprint that was finalized by January 2021 and ready for submission to a journal. There is no ORSP grant proposal for this project as we did this purely for research joy!
- Properties of the Fibonacci sequence modulo 10: In Summer 2019, my two students Dan Guyer and Miko Scott investigate patterns in the subsequences of the Fibonacci sequence modulo 10. - see our ORSP Grant Proposal for more info.
- (1) Properties of the Fibonacci sequence modulo 10 (continued) and (2) The Catalan sequence application to Pascal's triangle: In 2019-2020, there were two distinct projects. The first was a continuation of the Summer 2019 project with Dan Guyer and Miko Scott. The second is a project on a Catalan-weighted binomial sum formula that is conjectured by Dr. aBa to give the Betti numbers of the cohomology ring of the Springer variety. This research is conducted with students Dan Guyer, Miko Scott, and Maggie Reardon. - see our ORSP Grant Proposal for more info.
- An analysis of primitive roots and Menon’s Identity in the Eisenstein integer ring: In 2020-2021, my students Dan Guyer and Lily began investigating the primitive roots in the Eisenstein integer ring by examining the units groups of certain quotients modulo ideals generated by powers of an Eisenstein prime. - see our ORSP Grant Proposal for more info.
**Generalizing the Fibonacci sequence modulo 10 research project to arbitrary moduli**: In 2021-2022, my students Alyssa Franks and Javier Sanchez generalized the modulo 10 Fibonacci research project (from Summer and Fall 2019) to arbitrary moduli settings. - see our ORSP Grant Proposal for more info (: This proposal was for a different project, that was completed by Dr. aBa and Dr. Jurgen Spilker of Freiburg University in Germany before the research with Franks and Sanchez would begin. Hence, Franks, Sanchez, and Dr. aBa deviated from this proposal and attempted a different research question).**NOTE**

- [Fields Institute] - July
22-24, 2015 - Workshop on Recent
Developments on the Geometry and Combinatorics of Hessenberg Varieties
- Fields Institute in Toronto, Canada

- [AIM, ICERM, and NSF] - Summer 2012 - Workshop on Research Experience for Undergraduate Faculty - ICERM in Providence, RI.
- [University of Iowa] - March
2011 - Workshop on Applications of Schubert Calculus - Iowa City, IA

- [MSRI] - Spring 2008 - Program
Associate at the Combinatorial
Representation
Theory Program - Berkeley, CA

- [Fields Institute] - January
2007 - Workshop on the Representation
Theory of Reductive Algebraic Groups - University of Ottawa in
Canada

- [MSRI and VIGRE]
- Summer 2006 - Two-week Mini-course
on SL(2,R) - University of Utah

- The Twentieth International Conference on Fibonacci Numbers and Their Applications - Title: GCD of sums of $k$ consecutive Fibonacci, Lucas, and generalized Fibonacci numbers - July 25-29, 2022 - (University of Sarajevo in Sarajevo, Bosnia and Herzegovina) - Abstract
- High Point University Math Colloquium - Title:
*Mind-blowingly awesome subsequences in the Fibonacci sequence modulo 10*- Sept 17, 2021 - (High Point, NC) - Abstract - Providence College Math Colloquium - Title:
*Tantalizing explorations in the Fibonacci and Gibonacci Sequences*- Apr 29, 2021 - (Providence, RI) - Abstract - STEM Summer Bridge Math Presentation - Title: My
Path to Becoming a Math Major and The Beauty of Math - July 20,
2020 - (Sam Houston State University in Huntsville, TX)

- Sonoma State University Math Festival (Main Invited Speaker) - Title:
Mathematics Research Inspired by
Astrology: The Fibonacci Sequence Modulo 10 - Apr. 22, 2020 -
(Rohnert Park, CA) - Abstract

- Winona State Math Colloquium - Title: Two Research Projects Birthed from Curiosity, Recreation, and Joy - Feb 28, 2020 - (Winona, MN) - Abstract
- AMS-MAA Joint Mathematics Meeting [MAA Invited Address] - Title: Two Research Projects Birthed from Curiosity, Recreation, and Joy - January 14-18, 2020 - (Denver, CO) - Video of Talk
- aBa, update this and add your talks between
Jan 2018 and Jan 2020 !!!!!

- AMS-MAA Joint Mathematics Meeting [AMS Contributed Paper Session on
Matrices and Matroids] - Title: Characteristic
polynomials
and eigenvalues for a family of tridiagonal real symmetric matrices
and a tantalizing connection to Pascal's triangle - January
10-13, 2018 - (San Diego, CA) - Abstract

- Mathematics Seminar - Title: An
Euler phi function for the Eisenstein integers and some tantalizing
applications - Nov. 17, 2017 (Florida Gulf Coast University at
Fort Myers, FL) - Abstract

- AMS Central Sectional Meeting [Special Session on Algebraic Combinatorics of Flag Varieties] - Title: Combinatorial consequences of the representation stability of the cohomology of Springer varieties - Sept 9-10, 2017 (University of North Texas at Denton, TX) - Abstract
- AMS Central Sectional Meeting [Special Session on Combinatorics and Representation Theory of Reflection Groups: Real and Complex] - Title: Involutory and orientation-preserving symmetries in the hyperoctahedral group - Sept 9-10, 2017 (University of North Texas at Denton, TX) - Abstract

CLICK HERE to see an exhaustive
list of my talks and presentations given since 2006.

*Math in the Woods* is an event that is hosted by the UWEC Math
Dept at the beginning of each Fall semester. A main goal of the event is
to have fun and build community. We host the event here in a park in Eau
Claire. All are welcome: students and their families, faculty/staff and
their families, and even our dogs too! At *Math in the Woods*,
you'll find a community of new friends and great company.

Here is a link to a photo journal of our most recent event: Math_in_the_Woods_Fall_2021_photo_journal.

Member, Mathematical Association of America -- MAA

Member, Project NExT Fellow (Blue 10 Dot)

Teaching-Assistant for a course on Math for Elementary Education Majors
while I was a grad student at the University of Iowa |

7 |

... sometimes teaching indoors on a nice day is such a drag - that's when you need a blackboard on wheels!! |

This page was last modified on Jan. 29, 2023 (Jewish Calendar: 7th of Shevat, 5783), by extra-planetary beings from a galaxy near you. Go U Blugolds!!

Click
on
the bear below to go to the UWEC math faculty webpage:

PROCLAIMER: Click on "Proclaimer", and Tibetan Buddhist scholar Chogyam Trungpa Rinpoche introduces this film up to the 4min marker. The meat of the film's discussion begins at the 9min marker. Also when asked how/why I got interested in and high as a mountain on math, I usually answer with words like "outdoor raves / technivals / full moon gatherings / vacant warehouse breakins / etc". I found mathematics on many sunrises & moonsets in deserts, farms, fields, and Pacific coast beaches--somewhere between minimal Detroit house, deep house, tribal house, acid, and hard acid techno house (see map on House) at this link. If you were one of the many beautiful souls who evolved with me through our trancedelic bliss & harmony on those mornings dancing to the sunrise in Northern California, then you might recall the bass bins oozing Psychotropic Hypnosis or perhaps Frankie Knuckles' Whistle Song or perhaps this ANTHEM OF HOUSE MUSIC: Can You Feel It? And of course the nights too under the stars, we shared love and light while being transmutated and uplifted by housey beatz like this, that, and the other trancier thing in our blessed Trance Frandisco, California, resonating this future sound of SF. Peace, Love, Unity, and Respect.

RESPECTS: Love&LIGHT to Wicked, Come-Unity, the Gathering, The End-Up's Housing Project, Your Sister's House, Rave Called Sharon, the Sunset Crew, Friends and Family, Floppy's, Zippy Pronoia, Megatripolis, Autonomous Mutant Fest, Semi-Permanent Autonomous Zone (SPAZ), Consortium of Collective Consciousness (CCC), and all the sound system collectives! Lastly, respects to my Pleiadian mates and their message.

PRONOIA: the sneaking suspicion that others are conspiring to help you (and you them!). Symptoms of Pronoia include sudden attacks of optimism and outbreaks of goodwill.