aBa's Webpage

aBa doing research with his advisor Tymoczko's cat

Rm. 526 in Hibbard Hall

Email: mbirika@uwec.edu

Fall '23 Schedule

Older Schedules (art?)

aBa (אבא) Mbirika
University of Wisconsin-Eau Claire
Department of Mathematics - HHH508
105 Garfield Avenue
Eau Claire, WI 54701

Current Position

(2022 to Present) -- Professor at University of Wisconsin-Eau Claire
(2017 to 2022) -- Associate Professor at University of Wisconsin-Eau Claire
(2013 to 2017) -- Assistant Professor at University of Wisconsin-Eau Claire

Previous Positions

(2010 to 2013) -- Postdoctoral Fellow and Instructor at Bowdoin College (in Brunswick, Maine)
(2004 to 2010) -- Graduate Teaching Assistant at University of Iowa (in Iowa City, Iowa)
Univ of Iowa logo
Bowdoin Polar Bear


Ph.D. in Mathematics (2010) -- University of Iowa
M.S. in Mathematics (2006) -- University of Iowa
B.A. (2004) -- Sonoma State University

Professional Documents

CLICK HERE to see links to my Associate Professor Promotion and Tenure Binders, CV, Research and Teaching Statements, Class Evaluations, etc

Do you want to ask me to write a Letter of Recommendation for you?

Then first CLICK HERE and read this advice in its entirety before requesting.

Teaching (at University of Wisconsin-Eau Claire)

Fall 2023 - Math 104 (Section 001 and 002) - Finite Mathematics - syllabus and constantly updated Notes Available Here
Fall 2023 - Math 425 - Abstract Algebra I - syllabus and constantly updated Notes Available Here
Fall 2023 - Research on Narayana and various other sequences with Morgan Fiebig 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.

Previous Teaching 2010 to 2013 (at Bowdoin College)

CLICK HERE to see an exhaustive list of all the classes I taught from 2010 to 2013 before teaching at UWEC.

Teaching Awards at UWEC

2022 - UWEC Certificate of Recognition for Contributions to Students (32 total awarded campus-wide) - click here to see award
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

Research Publications

  1. 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) -- Published by Journal of Integer Sequences, 26 No.6, Article 23.6.4 (2023), 24pp. (Available by clicking here).
  2. 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).
  3. 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.)
  4. 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).
  5. 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).
  6. 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)
  7. 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).
  8. 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).
  9. 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).
  10. 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).
  11. 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).
Accepted (and awaiting publication details) Submitted
Preprints (Ready to submit):
In Preparation: Contributions to the On-Line Encyclopedia of Integer Sequences (OEIS):

Interdisciplinary Research Publications

Expository Math Writings

Textbooks and Course Packets (self-published and public domain)

This textbook was written by myself and co-author Rita Post over the Summer 2018 and Fall 2019 semester. It was first used in my Spring 2019 number theory course Math 341 at UWEC. The book has two forms as follows:
The following course packet was written by me for my students in Math 104. The first version was used in my Fall 2020 class.

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

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

Variety of Useful Resources written by my students

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.

Current Research (this section needs updating)

Broadly speaking, I am interested in combinatorics as related to areas such as combinatorial representation theory and algebraic geometry/topology.  My collaborator Julianna Tymoczko (recently from University of Iowa and now at Smith College) and I worked on a joint project on truncated symmetric functions towards a combinatorial description of the cohomology ring of Hessenberg varieties, which are a generalization of Springer varieties. We recently completed work on a project on co-FI-modules and representation stability of the cohomology of Springer varieties. My collaborators Thomas Pietraho, Bill Silver, and I worked on a joint paper on the sign representations of imprimitive complex reflection groups, G(r,p,n).  During my Spring '08 semester residence at MSRI, I begun a project (currently on hold  - but would love to start again perhaps with a research student here at UWEC) on the Schur-Weyl duality of the alternating group begun with Tom Halverson of Macalester College and continued with co-advisor Fred Goodman of University of Iowa.

Here are brief introductions to some of the objects or ideas listed above that I think about:
  1. 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.
  2. 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.

Research Projects with Undergraduates at UWEC:

Research Workshops Attended

Recent/Future Invited Talks/Conferences/Colloquiums

Previous Invited Conference/Colloquium/Seminar Talks Given (from 2006--Present)

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

What is "Math in the Woods"?

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.

Service (at University of Wisconsin-Eau Claire)

CLICK HERE to see an exhaustive list of my previous service from 2013--Present.

Previous Service (at Bowdoin College and University of Iowa)

CLICK HERE to see an exhaustive list of my previous service from 2004--2013.

Professional Affiliations

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

Personal Stuff

UWEC Class Photos

Bowdoin Class Photos and Calculus Gatherings

Photos of Friends and Family

My PhD Family

B, the letter after A

UWEC Leadership Fellows 2014--2015

An interview in a local Maine paper Coastal Journal

Article in Bowdoin's Academic Spotlight feature on Postdocs

Interview of aBa by Megan Monday of Love Wisconsin

Fun Stuff

Wacky Flyers I Made for Math Club (at Univ of Iowa)

Some older Wacky Math Newsletters that I co-created (at Univ of Iowa)

Video Interviews of aBa (filmed at UWEC)

Blugold Spotlight on Faculty video (filmed by Jesse Yang in the UWEC IMC Dept.)

My Power-of-AND video (filmed by Glen Mabie in UWEC News Bureau Dept.)

UWEC TV-10 Video in Fa'14 (filmed by UWEC student Abby Reimer for BNN Blugold News Now Behind the Desk Series)

Interview by Paige Wilde in Sp'17 (filmed by UWEC student Paige Wilde for a Public Relations course)

Videos of Certain Research Talks

A co-FI-module Structure on the Cohomology of Springer Varieties (Fields Institute in Toronto, Canada in July 2015)

MAA Invited Address on Two Research Projects Birthed from Curiosity, Recreation, and Joy (Joint Mathematics Meeting in Denver, Colorado in January 2020)

Videos of me explaining mathematical concepts to my students via song/rap

Calculus II -- Solids of Revolution Rap (Undergraduate Level)

I wrote this for my Spring 2012 Bowdoin students in Calculus II.  Lyrics sheet available here.

Graph Theory and Enumerative Combinatorics Rap (Undergraduate Level)

This is my first ever combinatorial "poem".  I wrote it for my Bowdoin students in Spring 2011 to give them a wee break and a fun overview of the two major topics covered in our Math 258 course.  Lyrics sheets with blackboard shots available by clicking here.

Patriotic Real/Complex Analysis Rap (Masters/PhD Level)

When I found out my office mate Jonas Meyer was holding analysis class on a school holiday, I felt bummed out for the students.  So I decided to write them a math treat.  The holiday was July 4th (the next day), so there's a mix of patriotism in this poem about analysis.  Lyric sheet available here.

Bijective Function Rap (Undergraduate Level)

This poem was delivered to my Abstract Algebra class at the Univ of Iowa in Spring 2009.  I actually wrote it while I was an undergrad at Sonoma State University in Northern California.  Lyric sheet available here.

An Algebra Rap (First-year College Level)

The above is a poem I wrote for the class I taught in Fall 2008 at the Univ of Iowa.  My friend Max filmed me in a Chinese restaurant in NYC with some sorta Blackberry gizmo or something.  I wasn't convinced that the machine had the capabilities to record a video, but it did it seems.  Click above to watch/listen.  Lyrics sheet available here.

Bridges of Konigsberg Rap (UWEC - Discrete Math Class)

I delivered this poem to Dr. Carolyn Otto's Discrete Math course (Math 314) at UW-Eau Claire in the Spring of 2016.  I was the substitute teacher for Carolyn this particular day and on her lesson plan was an introduction to graph theory via the well-known Bridges of Konigsberg problem.  Hence I was inspired to deliver to these students this poem that I wrote on exactly this particular graph theory problem.  Lyrics sheet available here.

Miscellaneous videos I made where I am not singing mathematics to students

A complete proof of the Snake Lemma

In this video, myself and my former students Katie Henschell (Quotes) and Taylor Kriesel (Knit Mama) give a complete detailed proof of the celebrated Snake Lemma. What is unique about this video is that students Quotes and Knit Mama did this with me a few days after their graduation from UWEC in May 2021. So instead of partying after graduation, they took a deep dive into exploring the finer intricacies of this awesome result and delivering a clear concise proof. YAY!!!

Why is the UWEC Math Club t-shirt so cool?

UWEC Math Club President Sara DeBrabander (2015-2016) and I made this video to explain the mathematics behind the math club t-shirt which our math club designed this year.  It's a very cool t-shirt, but a little understanding of the complex numbers and Euler's famous identity (melding e, i , and pi) helps to better appreciate the t-shirt.

Roomba Robot Vacuum video that turns into a "Tour of aBa's House" video

Yes, I got hooked by those videos of cats riding on top of robot Roomba vacuums.  So though I don't have a cat, I decided to buy this vacuum.  I must admit the unused vacuum of mine is now collecting more dust on top of it then it does inside of it.  Ha.  This video shows the vacuum in action for about 3 minutes, then I get bored of that and decide to give an impromptu tour of my home and bicycle.

Teaching-Assistant for a course on Math for Elementary Education Majors while I was a grad student at the University of Iowa
7aBa teaching outdoors Spring 2006
... 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 Oct. 31, 2023 (Jewish Calendar: 16th of Cheshvan, 5784), 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:

Back to my UWEC 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.