aBa's
Webpage
Office:
Rm.
102 in Searles Hall
Office
Phone: 207 725 3131
Email:
ambirika@bowdoin.edu
- Paper
Mail
- Aba Mbirika
Department of Mathematics
- Bowdoin College
8600 College Station
Brunswick, ME 04011
USA
Current Position
(2010 to present) -- Postdoctoral Fellow and Instructor at Bowdoin
College
Tenure-Track Position
(Beginning Fall 2013) -- Assistant Professor at Univ of Wisconsin
at Eau Claire
Education
Ph.D. in Mathematics (2010) -- University of Iowa
M.S. in Mathematics (2006) -- University of Iowa
B.A. (2003) -- Sonoma State University
Professional Documents
1) Curriculum
Vitae
2) Research
Statement and
a list of publications with abstracts available by clicking here.
3) Two-page
Summary of
my Research Statement
4) Teaching
Statement
5) Teaching
Evaluation Summaries (from Univ of Iowa) (2005--2010)
6) Teaching
Evaluation Summaries (from Bowdoin College) (2010--2012)
7) All written student comments from my most
recent class
(40pgs)
Research Publications
- Generalizing Tanisaki's
ideal
via ideals of truncated symmetric
functions. (Joint
work with Julianna Tymoczko) -- Published by the Journal
of Algebraic
Combinatorics (2012). (Available arXiv-version by clicking here).
- A Hessenberg
generalization
of the Garsia-Procesi basis for the
cohomology ring of Springer varieties.
Published by
Electronic
Journal of Combinatorics (2010). (Available by clicking here).
- Analysis of symmetric
function
ideals: towards a combinatorial
description of the cohomology ring of Hessenberg varieties. Theses
and Dissertations. Paper 708 (2010). (Available by clicking
here).
Preprints:
- On the sign representations for
the
complex reflection groups G(r,p,n). (Joint work with Thom
Pietraho and Bill Silver). Preprint on arXiv available here.
In Preparation:
- Towards a Schur-Weyl
duality
for the alternating group.
(In
progress -- draft available here).
Expository Math and Interdisciplinary
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unpublished results, and also includes exercises and project ideas that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).
Preprints:
- The Three Giri of Paradiso
XXXIII. (Joint work with
Arielle Saiber). Submitted to Dante Studies, January 2013.
Teaching (at Bowdoin College)
Spring 2013 - Differential Calculus - syllabus and a more
personal syllabus
companion
Fall 2012 - Combinatorics: Graph Theory and Enumeration Principles - syllabus and a first day of class quiz!
Summer 2012 - Bowdoin Science Experience (Topic: Lattice point
geometry and graph theory) - photos
Spring 2012 - Integral Calculus - syllabus
Fall 2011 - Integral Calculus - syllabus
Summer 2011 - Bowdoin Science Experience (Topic: Mathematical induction
and number theory) - photos and my
students' presentations
Spring 2011 - Combinatorics: Graph Theory and Enumeration Principles -
syllabus
Fall 2010 - Differential Calculus - syllabus
and a more personal syllabus
companion
Summer 2010 - Bowdoin Science Experience - (Topic: Linear algebra &
multivariable calculus. Co-taught with Thom Pietraho)
Teaching
(at
University of Iowa)
Spring 2009 - Abstract Algebra - (Teaching Assistant) - syllabus
Fall 2008 - Basic Algebra II - A precalculus course - (Instructor) - syllabus
Fall 2007 - Calculus I - (Teaching Assistant)
Summer 2007 - Vigre REU Teaching Assistant in Graph Theory (and
Undergraduate Research Advisor)
Summer 2006 - Alliance REU Teaching Assistant in Linear
Algebra
(Summer REU for underrepresented students in Mathematics)
Spring 2006 - Logic of Arithmetic - A course for students in elementary
education - (Teaching Assistant)
Fall 2005 - Calculus and Matrix Algebra for Business - (Teaching
Assistant)
Teaching Awards
2005 - Catherine Wegner Outstanding Mathematics Teaching
Assistant Award
2006 - The University of Iowa Outstanding Teaching Assistant Award (25
total awarded campus-wide)
2009 - University Housing Academic Excellence Award (34 total awarded
campus-wide)
Current Research
I am in my third year of a three-year Postdoctoral Fellowship at
Bowdoin College. Broadly speaking, I am interested in
combinatorics as related to areas such as combinatorial representation
theory and algebraic/topological combinatorics. My
collaborator
Julianna
Tymoczko
(recently from University of Iowa and now at Smith College) and I
recently wrote up our results 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. I am
also doing some collaborative work on the hyperoctahedral group with Thomas Pietraho of Bowdoin
College. 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
Bowdoin College!?) 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 selected objects and ideas that I think about:
- On my Schur-Weyl
duality project. This 2 page write-up describes the problem 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.
MSRI Resident Spring 2008 at
Berkeley, CA
In the Spring semester of 2008, I was a Program Associate at the
Combinatorial
Representation Theory Program.
During this semester,
I begun research with four different residents: Georgia Benkart, Steve
Doty, Sasha Kleschev, and Tom Halverson. Of the four
projects, I
am continuing the work started with Tom Halverson on the alternating
group. Thus far I have completely determined the branching
rules
for this group. Towards a Schur-Weyl duality of this group, I
am
investigating the centralizer of its action on an n-fold tensor product
of its permutation representation. Vaughn Jones (also in
residence this semester) talked with me about his findings on the
symmetric group's centralizer, i.e. the so-called partition algebra.
This
work was done by him in 1992. So far no one has done the
alternating group analogue. I am attempting to accomplish
this.
Recent conferences/colloquiums I've been invited to speak at
April 19-22, 2013 - NSF USTARS
Conference (Underrepresented Students in
Topology and Algebra Research Symposium) - Title: Robinson-Schensted correspondence between
complex reflection groups G(r,p,n) and pairs of multitableaux -
(Purdue
University)
Invited
Conference/Colloquium/Seminar Talks Given
1. Various talks in the Representation Theory Seminar on
GL(2)-representations over a finite field - 2006 to 2007 (University of
Iowa)
2. Various talks in the Representation Theory Seminar on Nondegenerate
Smooth Representations - 2006 to 2007 (University of
Iowa)
3. Two talks in the Algebraic Geometry Seminar on Flag Varieties and
Grassmanians of different Lie Type - Fall 2007 (University of Iowa)
4. VIGRE REU Seminar talk on Partition Theory - Summer 2008 (University
of Iowa)
5. GAUSS talk to Prospective Graduate Students - Title: All of Math
Grad School in a Nutshell -
March 2009 (University of Iowa)
6. AMS Sectional Meeting [Special Session on Algebra, Geometry and
Combinatorics] - Title: Cohomology
of Hessenberg Varieties -
March 2009
(University of Illinois at Urbana-Champaign)
7. History talk to undergrads - Title: Euler, Da Man!
- April 2009
(Winona State University at Minnesota)
8. Heartland Math Talk - Title: Interesting
Aspects of Number
Partitions - April 2009
(University of Wisconsin at LaCrosse)
9. Combinatorial Algebraic Geometry on Flag Varieties Conference -
Title:
Intro to Schubert Calculus
- June 2009 (University of Iowa)
10. Algebraic Geometry Seminar - Title: A combinatorial
description of
H^*(Peterson) - September
2009 (University of Iowa)
11. MAA Iowa Sectional Meeting - Title: Cool combinatorics
arising in a
cohomology hunt! - October
2009 (University of Northern Iowa)
12. Title:
What sort of mathematics
does aBa do? - February 2010
(University of Wisconsin at Eau Claire)
13. Title: Are
algebraic geometers
trying to take over the world?
-
February 2010 (Bowdoin College in Maine)
14. Title: Are algebraic
geometers trying to take over the
world?
- March 2010 (Wake Forest University in North Carolina)
15. AMS Central Section Meeting [Special Session on Combinatorial
Representation Theory] - Title: Exploring
the cohomology ring of
generalized Springer varieties
- April 2010 (Macalester College
in
Minnesota)
16. MAA Math Fest [Special Session on Combinatorial Games and
Schubert Calculus] - Title: Ideals of
symmetric functions and their
application to cohomology rings of Hessenberg varieties
- August
2010
(Pittsburgh, PA) - Abstract
17. M.I.T. Combinatorics Seminar - Title: Ideals of partial
symmetric
functions and a generalization of the Tanisaki ideal
- October
2010
(Massachusetts Institute of Technology) - Abstract
18. Math Colloquium - Title: From
Lewis Carroll to an Interesting
Conjecture -- The Rabbit Hole Exposed!?
- October 2010 (Colby
College
in Maine) - Abstract
19. MAA Northeastern Section Meeting - Title: What's
cool about combinatorics?
- November 2010 (Providence College in Rhode Island) - Abstract
20. AMS Central Section Meeting [Special Session on
Geometric Representation Theory] - Title: Commutative algebra meets
geometric
representation theory -
(University of Iowa at Iowa City, IA),
also attended pre-conference workshop on "Applications to Schubert
Calculus" - March 18-20, 2011 (University of Iowa) - Abstract
21. AMS Eastern Section Meeting [Special Session on
Combinatorial Representation Theory] - Title: Combinatorial commutative
algebra meets an
object from geometric representation theory
- April 9-10, 2011
(College of the
Holy Cross at Worcester, MA) - Abstract
22. Faculty Research Seminar - Title: Commutative algebraic
techniques to
investigate the cohomology ring of certain family of varieties
-
April 2011 (Bowdoin College)
23. AMS Southeastern Section Meeting [Special
Session on Symmetric functions] - Title: Truncated symmetric functions with an
application to generalized Springer theory - September 24-25,
2011 (Wake Forest University in
Winston Salem, NC) - Abstract -
Slides
24. M*A*T*H Colloquium - Title: Do
you value the value of Pi? - March 14, 2012 (Sonoma State
University) - Abstract
- Video
Recording (click on high speed version)
25. NSF USTARS Conference
(Underrepresented Students in Topology and
Algebra Research Symposium) - Title: Two
families united as one - A symmetric functions tale - April
2012 (University of Iowa) - Group Photo
26. SACNAS [Scientific
Symposia Session in Number Theory] - Title: A number theoretic connection to a problem
in graph theory - October 11-14, 2012 - (Seattle, WA)
27. The February 2013 on-campus job interview talks:
- February 1, 2013: Smith College (two talks) -- (1) Math
lunch talk for students, and (2) Research talk for faculty
- February 4, 2013: Bucknell University -- Research talk for
faculty
- February 11, 2013: Harvey Mudd College -- Research talk for
faculty and students
- February 14, 2013: Reed College -- Research talk for
faculty and students
- February 18, 2013: University of Wisconsin at Eau Claire --
Research/Colloquium talk for faculty and students
Service (at Bowdoin College
and Maine Community)
September 2010 - Bowdoin Common Good Day volunteer at People Plus, a
teen and older adult center in Brunswick, ME
Fall
2010 to
Spring 2011 - Building atmosphere coordinator for Searles Hall (revitalization of the Math
Common Room -
Searles 214 with Emma Chiappetta '11)
April 2011 - Judge for Bowdoin Entertainment Board's Battle of the Bands
April 2011 - Assisted with the 2nd night Passover seder at The Cedars,
a Jewish senior center in Portland, ME
Summer 2010, 2011, and 2012 - Bowdoin
Science Experience instructor
October 2011 - Runway model for Bowdoin Career Planning's Do's and Dont's Fashion Show
January 2011 & 2012
- Sat on faculty panel for Lincoln
Middle School's ELL program's visit with students.
February 2012 - Judge for Class of 2014's Mr. Polar Bear Contest
September 2012 - Bowdoin Common Good Day volunteer at ArtVan, a mobile arts therapy
program in Bath, ME
November 2012 - Explore Bowdoin - met with prospective students from
various diverse backgrounds
November 2012 - Discussing Difference - A Bowdoin ResLife-sponsored
event to involve students in open and honest conversations regarding
diversity, privilege and difference.
Service (at Univ of Iowa)
2005 to Present - Undergraduate Math Club
Advisor
Fall 2005 - Tutor for displaced victims of Hurricane Katrina
2005, 2007, Present - Undergraduate Math Lab Tutor
2008 to Present - English Buddy Program (tutored English to help
foreign math graduate students pass the SPEAK exam)
Professional Affiliations
Member, American Mathematical Society -- AMS
Member, Mathematical Association of America -- MAA
Member, Northeastern
Section NExT Fellow
Member, Project NExT
Fellow (Blue 10 Dot)
Personal Stuff
Fun Stuff
Videos of me explaining mathematical concepts to my students via
song/rap
I wrote this for my Spring 2012 Bowdoin students in Calculus II.
Lyrics sheet available here.
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.
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.
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.
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.
| Teaching a Course on Math for
Elementary Education Majors at Univ of Iowa in 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 (Pi Day + 1) March 15, 2013, by
extra-planetary
beings from a galaxy near you. Go U Bears!!
Click
on the bear below to go to my official Bowdoin faculty webpage:
PROCLAIMER:
Most people do some disclaiming at the bottom of their webpages.
I've decided to PROCLAIM, instead. Click
on "Proclaimer", and Tibetan
Buddhist scholar Chögyam Trungpa Rinpoche will introduce
this
film up to the 4min marker. The meat of the film's discussion
begins at
the 9min marker. Also when asked how/why/when I got interested in
math, I usually answer with words like "outdoor raves / free technivals /
full moon gatherings". I
found mathematics on many sunrises and moonsets in deserts, farms,
fields, and Pacific coast beaches--somewhere between minimal detroit
house, deep house, tribal house, and hard acid techno
house (see map on House) at this link.
