Research
I am a mathematician and I am quite proud of it! Below is a rather disrespectful cartoon about why I might feel so proud:
Ok, this is not quite how I feel, but I thought it would pique your
interest... You can find this and many more at this link. And if you want a different
perspective, check this
out.
But more seriously, let me give you some specifics:
I completed my PhD in Mathematics at UC Berkeley in May
2004, under the supervision of
Nicolai Reshetikhin
and Vera Serganova. The title of my thesis
was rmatrices on Lie Superalgebras.
(Ask me what a Lie superalgebra is if you want me to talk breathlessly for
half an hour... If on the other hand you are up for a longer chat, ask me
about rmatrices...)
I spent the next two years at the University of California, Santa Barbara,
where my mentor was Milen
Yakimov. Due to union issues my title at UCSB was visiting scholar,
but the position in fact was what many will call a postdoc.
I then started working at Pomona College (in July 2006) as an assistant professor of mathematics. Currently, (as of July 2012), I am an associate professor with tenure.
On this page you will find a rather cursory list of my research related
activities. Eventually I will put a link here to a more or less comprehensible
account of my research (in regular English if I can pull it). But if you are
impatient, and you are interested in what I do when I close my office
door, or if you like algebra (linear or abstract) and wish to discuss
possibilities for a senior thesis, please drop me a line. I try to respond to
emails within 24 hours of receiving them (especially during the academic year; over the summer months it may take me a bit longer...).
For students who might be interested, here is where you can read about senior theses written by my earlier students.
This page is (perpetually) under construction. But a rather uptodate summary of everything I have done that in one way or another relates to my professional life can be found here (this is my CV, dated as marked).
Research Interests
 Quantum Groups, Hopf Algebras
 Super Representation Theory, Lie Superalgebras
 Combinatorial Representation Theory, Algebraic Combinatorics
 TwoSided Matching and Game Theory
Other Areas of Expertise
 Quantitative Literacy
 Humanistic Mathematics
 Mathematics and Social Justice
External Grants
 National Endowment for the Humanities (NEH)
Enduring Questions 20142016
Project title: Education and Its Discontents: A Course on the Purpose and Values of Education
 National Security Agency (NSA)
Young Investigator Award 20112013
Project title: YangBaxter equations, super quantum groups and generalized Hopf algebras
Publications and Preprints
Mathematical Research (Preliminary versions / preprints are available on the arxiv):
 School Choice as a OneSided Matching Problem: Cardinal Utilities and Optimization
with S. Aksoy, A. Azzam, C. Coppersmith, J. Glass, X. Zhao, and X. Zhu
Submitted for publication, current version
available on the electronic archives as arXiv:1304.7413
 Coalitions and Cliques in the School Choice Problem
with S. Aksoy, A. Azzam, C. Coppersmith, J. Glass, X. Zhao, and X. Zhu
Involve: A Journal of Mathematics Volume 131 Issue 5 (October 2015),
pages 801823.
Available at http://msp.org/involve/2015/85/p09.xhtml
 Supercharacters, exponential sums, and the uncertainty principle
with J. L. Brumbaugh, M. Bulkow, P. S. Fleming, L. A. Garcia, S. R. Garcia, M. Michal, and A. P. Turner
J. Number Theory 144 (2014),
pages 151175.
 Ramanujan sums as supercharacters
with C. F. Fowler and S. R. Garcia
Ramanujan J., Volume 35 Issue 2 (November 2014),
pages 205241.
Available at http://link.springer.com/article/10.1007%2Fs111390139478y.
 A CostMinimizing Algorithm for School Choice
with S. Aksoy, A. Azzam, C. Coppersmith, J. Glass, X. Zhao, and X. Zhu
ISAIM 2012 (International Symposium on Artificial Intelligence and Mathematics, Fort Lauderdale, Florida, USA, January 911, 2012) Proceedings (2012).
Available at http://www.cs.uic.edu/pub/Isaim2012/WebPreferences/ISAIM2012_ComSoc_Aksoy_etal.pdf.
 Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras
with M. Aguiar, C. Andre, C. Benedetti, N. Bergeron, Z. Chen, P. Diaconis, A. Hendrickson, S. K. Hsiao, I. M. Isaacs, A. Jedwab, K. Johnson, A. Lauve, T. Le, S. Lewis, H. Li, K. Magaard, E. Marberg, JC. Novelli, A. Pang, F. Saliola, L. Tevlin, JY. Thibon, N. Thiem, V. Venkateswaran, C. R. Vinroot, N. Yan, and M. Zabrocki
Advances in Mathematics, Volume 229 Issue 4 (1 March 2012), pages 23102337.
MR2880223
 Supercharacters, symmetric functions in noncommuting variables (extended abstract)
with M. Aguiar, C. Andre, C. Benedetti, N. Bergeron, Z. Chen, P. Diaconis, A. Hendrickson, S. K. Hsiao, I. M. Isaacs, A. Jedwab, K. Johnson, A. Lauve, T. Le, S. Lewis, H. Li, K. Magaard, E. Marberg, JC. Novelli, A. Pang, F. Saliola, L. Tevlin, JY. Thibon, N. Thiem, V. Venkateswaran, C. R. Vinroot, N. Yan, and M. Zabrocki
FPSAC 2011 (Reykjavik, Iceland) DMTCS Proceedings, AO, 2011, pages 314.
Available at http://www.fpsac.org/FPSAC11/SITE2011/proceedings/dmAO0102.pdf

Classical Kloosterman sums: representation theory, magic squares, and Ramanujan multigraphs;
with P. S. Fleming and S. R. Garcia
J. Number Theory 131 (2011),
pages 661680.
MR2753270

On the quantization of zeroweight super dynamical rmatrices;
Proc. Amer. Soc. Math. 140 (2012), pages 720.
MR2833513
 Multigraded combinatorial Hopf algebras and refinements of odd and even subalgebras; with S. K. Hsiao
J. Algebr. Comb. 34 (2011), pages 451506.
MR2836370
 Spanning sets for Moebius vertex algebras satisfying arbitrary
difference conditions; with G. Buhl
J. Algebra 320 (2008),
pages 33453364.
MR2450731
 On Hopf Algebras and Their Generalizations;
Comm. Algebra 36 (2008),
pages 43414367.
MR2473333
 Dynamical Quantum Groups  The Super Story;
Contemp. Math. 441 (2007), pages 1952.
MR2381534
 Super Solutions of the Dynamical YangBaxter Equation;
Proc. Amer. Math. Soc. 134
(2006), pages 25212531.
MR2213729
 A New Lie Bialgebra Structure on sl(2,1);
Contemp. Math. 413 (2006), pages 101122.
MR2262367
 Constructing rmatrices on Simple Lie Superalgebras;
J. Algebra 282 (2004), pages 83102.
MR2095573
Other PeerReviewed Articles:
 A Humanistic Reading Component for an IntroductiontoProofs Course
Beyond Lecture: Techniques to Improve Student ProofWriting Across the Curriculum, edited by Rachel Schwell, Aliza Steurer, and Jennifer Franko Vasquez, Mathematical Association of America, Washington DC, 2016, pages 123133.
 What's in a Name? A Critical Review of Quantitative Literacy, Numeracy, and Quantitative Reasoning; with Edwin H. Villafane Hernandez and Jeremy Alexander Taylor
Numeracy (journal of the National Numeracy
Network), Vol.9, Iss. 1 (2016), Article 2.
Available at http://scholarcommons.usf.edu/numeracy/vol9/iss1/art2/
 Metacognition in the Classroom: Motivation and SelfAwareness of Mathematics Learners
PRIMUS, Vol. 25, Iss. 5 (May 2015), pages 439452.
Available at http://www.tandfonline.com/doi/abs/10.1080/10511970.2015.1027837.
 Can Zombies Write Mathematical Poetry? Mathematical poetry as a model for humanistic mathematics
Journal of Mathematics and the Arts, Volume 8 Issue 12 (2014), pages 3845.
Available at http://www.tandfonline.com/doi/abs/10.1080/17513472.2014.926685.
 The Genius as a Characterization of the Creative Spirit in Mathematics and the Arts
Proceedings of Bridges 2014: Mathematics, Music, Art, Architecture, Culture, edited by Gary Greenfield, George Hart, and Reza Sarhangi, Tessellations Publishing, Phoenix, 2014, pages 413416.
Available at http://archive.bridgesmathart.org/2014/bridges2014413.html.
 The Brave New World of Open Access & Creative Commons: a Humanistic Experiment in Mathematical Publishing
Proceedings of the 2013 AMS Special Session on Topics and Issues in Electronic Publishing, edited by Klaus Kaiser, Steven G. Krantz, and Bernd Wegner, pages 11Ð31.
Available at http://www.emis.de/proceedings/TIEP2013/02karaali.pdf.
 An Evaluative Calculus Project: Applying Bloom's Taxonomy to the
Calculus Classroom
PRIMUS, Vol. 21, Iss. 8 (November 2011), pages 719731.
Available at http://www.tandfonline.com/doi/full/10.1080/10511971003663971#.VL5YU1pHGMU.
 Envisioning a Quantitative Studies Center: A Liberal Arts
Perspective; with P. I. Choi, S. Owsley
Sood and E. B. Grosfils
Numeracy (journal of the National Numeracy
Network), Vol.3, Iss. 1 (2010), Article 4.
Available at http://services.bepress.com/numeracy/vol3/iss1/art4
 Life After WolframAlpha: What You (and Your Students) Need to
Know; with B. Yoshiwara
Loci (January 2010).
DOI: 10.4169/loci003365.
Available at http://dx.doi.org/10.4169/loci003365
 Word Problems: Reflections on Embedding Quantitative Literacy in
a Calculus Course;
Numeracy
(journal of the National Numeracy Network), Vol.1, Iss. 2 (2008),
Article 6.
Available at http://services.bepress.com/numeracy/vol1/iss2/art6
Extended Book Reviews:
 Mathematics and art: a cultural history by Lynn Gamwell,
Journal of Mathematics and the Arts, Volume 10 Issue 14 (2016), pages 8792.
Available at http://www.tandfonline.com/doi/full/10.1080/17513472.2016.1242186.
 The Problems of Contemporariness and Voice: Review of Literacy & Math ematics: A Contemporary Approach to Quantitative Literacy by Jay P. Abramson and Matthew A. Isom,
Numeracy (journal of the National Numeracy Network), Volume 9 Number 2 (July 2016), Article 11.
Available at http://scholarcommons.usf.edu/numeracy/vol9/iss2/art11
 Really Big Numbers, by Richard Evan Schwartz;
The Boy Who Loved Math: The Improbable Life of Paul Erdő
s, by Deborah Heiligman;
The Short Seller, by Elissa Brent Weissman,
Association for Women in Mathematics Newsletter, Volume 45 Number 4 (JulyAugust 2015), pages 1719.
 Mathematics in Popular Culture: Essays on Appearances in Film, Fiction, Games, Television and Other Media, edited by Jessica K. Sklar and Elizabeth S. Sklar;
Loving+Hating Mathematics: Challenging the Myths of Mathematical Life, by Reuben Hersh and Vera JohnSteiner;
Mathematicians: An Outer View of The Inner World, by Mariana Cook,
Association for Women in Mathematics Newsletter, Volume 43 Number 6 (NovemberDecember 2013), pages 2225.
 Encyclopedia of Mathematics and Society by Sarah J. Greenwald and Jill E. Thomley,
College Mathematics Journal, Volume 44 Number 4 (September 2013), pages 332335.
 Philosophy of Science after Feminism by Janet Kourany;
Association for Women in Mathematics Newsletter, Volume 42 Number 1 (JanuaryFebruary 2012), pages 810.
Brief Book Reviews:
 The Best Writing on Mathematics: 2010 edited by Mircea Pitici;
Mathematics Teacher,
Volume 105 Number 9 (May 2012), page 717.
Editorials:
 Connections (Editorial); with M. Huber
Journal of Humanistic Mathematics, Vol.6, Iss. 2 (2016), pages 12.
Available at http://scholarship.claremont.edu/jhm/vol6/iss2/2/
 Not Just In the Eye of the Beholder (Editorial); with M. Huber
Journal of Humanistic Mathematics, Vol.6, Iss. 1 (2016), pages 12.
Available at http://scholarship.claremont.edu/jhm/vol6/iss1/2/
 Inspiring Mathematical Experiences (Editorial); with M. Huber
Journal of Humanistic Mathematics, Vol.5, Iss. 2 (2015), pages 12.
Available at http://scholarship.claremont.edu/jhm/vol5/iss2/2/
 A Mathematician's Choice (Editorial); with M. Huber
Journal of Humanistic Mathematics, Vol.5, Iss. 1 (2015), pages 12.
Available at http://scholarship.claremont.edu/jhm/vol5/iss1/2/
 Mathematical Perspectives (Editorial); with M. Huber
Journal of Humanistic Mathematics, Vol.4, Iss. 2 (2014), pages 12.
Available at http://scholarship.claremont.edu/jhm/vol4/iss2/2/
 Turn! Turn! Turn! (Editorial); with M. Huber
Journal of Humanistic Mathematics, Vol.4, Iss. 1 (2014), page 1.
Available at http://scholarship.claremont.edu/jhm/vol4/iss1/1/
 Mathematics Rocks! (Editorial); with M. Huber
Journal of Humanistic Mathematics, Vol.3, Iss. 2 (2013), page 1.
Available at http://scholarship.claremont.edu/jhm/vol3/iss2/2/
 Math: That Thing You Do (Editorial); with M. Huber
Journal of Humanistic Mathematics, Vol.3, Iss. 1 (2013), pages 12.
Available at http://scholarship.claremont.edu/jhm/vol3/iss1/2/
 Games Mathematicians Play (Editorial); with M. Huber
Journal of Humanistic Mathematics, Vol.2, Iss. 2 (2012), page 1.
Available at http://scholarship.claremont.edu/jhm/vol2/iss2/2/
 Mathematical creation (Editorial); with M. Huber
Journal of Humanistic Mathematics, Vol.2, Iss. 1 (2012), page 1.
Available at http://scholarship.claremont.edu/jhm/vol2/iss1/2/
 Vampire Statistics and Other Mathematical Odditites (Editorial); with M. Huber
Journal of Humanistic Mathematics, Vol.1, Iss. 2 (2011), page 1.
Available at http://scholarship.claremont.edu/jhm/vol1/iss2/2/
 Welcome to the Journal of Humanistic Mathematics (Editorial); with M. Huber
Journal of Humanistic Mathematics, Vol.1, Iss. 1 (2011), page 1.
Available at http://scholarship.claremont.edu/jhm/vol1/iss1/2/
Guest Blog Posts and Other Contributions to Online Projects:
 The Power of Two: Two Tips for Mathematicians,
Guest blog entry for American Mathematical Society eMentoring Network, posted on March 14, 2016.
Available at http://blogs.ams.org/mathmentoringnetwork/2016/03/14/thepoweroftwotwotipsformathematicians/.
 Summer Cleaning: (Digital) Organization Basics for Mathematicians,
Guest blog entry for American Mathematical Society eMentoring Network, posted on May 21, 2015.
Available at http://blogs.ams.org/mathmentoringnetwork/2015/05/21/summercleaningdigitalorganizationbasicsformathematicians/.
 Women in Maths: Gizem Karaali,
Contribution to the Women in Maths Project, posted on May 20, 2015.
Available at https://www.facebook.com/womeninmaths/.
 Math Talk: Preparing Your Conference Presentation,
Guest blog entry for American Mathematical Society eMentoring Network, posted on August 4, 2014.
Available at http://blogs.ams.org/mathmentoringnetwork/2014/08/04/mathtalkpreparingyourconferencepresentation/.
 Why You Need a Summer Plan,
Guest blog entry for American Mathematical Society eMentoring Network, posted on May 23, 2014.
Available at http://blogs.ams.org/mathmentoringnetwork/2014/05/23/whyyouneedasummerplan/.
 Vocalized: What do you wish you could tell your women students? with eight other Pomona faculty,
Contribution to the Vocalized Project of the Pomona College Women's Union, posted on April 28, 2014.
Available at http://www.facebook.com/PomonaWomensUnion/albums/10152506914949180/.
 The Fundamental Principle of Productivity: What they DON'T teach you in graduate school,
Guest blog entry for American Mathematical Society eMentoring Network, posted on April 7, 2014.
Available at http://blogs.ams.org/mathmentoringnetwork/2014/04/07/thefundamentalprincipleofproductivitywhattheydontteachyouingraduateschool/.
 Grandma Got STEM! Selma Karaali and Artemis Karaali,
Guest blog entry for Grandma Got STEM (a Web 2.0 project on raising public awareness about stereotypes about gender, age and maternity embodied in comments about grandmothers), posted on April 11, 2013.
Available at http://ggstem.wordpress.com/2013/04/11/selmakaraaliandartemiskaraali/.
Mathematical Poetry:
 Math and Metaphor OR A TwoLetter Curse Word, (poem)
Bridges 2016 Poetry Anthology, edited by Sarah Glaz, 2016; page 60.
 The Mathematician's Villanelle, (poem)
Math Horizons, Volume 22 Issue 1 (February 2015), page 23.
 The Colors of Math, (poem)
The Mathematical Intelligencer, Volume 35 Issue 1 (March 2013), page 4.
Other Writing About Mathematics & The Mathematical Community:
 Math Education: A Messy Problem;
Inside Higher Education, Views, May 2, 2016.
Available at https://www.insidehighered.com/views/2016/05/02/matheducationdeservessupportandattentionessay
Reprinted in Vermont Council of Teachers of Mathematics Newsletter, May 2016
Available at http://mathinvermont.blogspot.com/2016_05_01_archive.html
 Collaboration and Creativity in Southern California: An Offering; with A. Radunskaya
Association for Women in Mathematics Newsletter, Volume 46 Number 2 (MarchApril 2016), pages 3032.
 WANTED: Journalists of Humanistic Mathematics; with M. Huber
Journal of Humanistic Mathematics, Vol.6, Iss. 1 (2016), page 307.
Available at http://scholarship.claremont.edu/jhm/vol6/iss1/27/
 What if ... math were not required in K12 education?,
Pomona College Magazine, Fall 2015 (Volume 52 Number 1), pages 23.
Available at http://magazine.pomona.edu/2015/fall/whatif/.
 On Genius, Prizes, and the Mathematical Celebrity Culture,
The Mathematical Intelligencer, Volume 37 Issue 3 (2015), pages 6165.
 Can Zombies Do Math?,
In Mind in Mathematics: Essays on Mathematical Cognition and Mathematical Method, edited by Mariana Bockarova, Marcel Danesi, Dragana Martinovic and Rafael Nunez, 2015; pages 140153.
 Nesin Math Village: Mathematics as a Revolutionary Act,
The Mathematical Intelligencer, Volume 36 Issue 2 (2014), pages 4549.
 What Does It Take to Teach Nonmajors Effectively?; with F. Alayont and L. Pehlivan,
FOCUS (newsletter of the Mathematical Association of America), Volume 32 Number 6 (2012), pages 1112.
 A Tale of Two Workshops: Two Workshops, Three Papers, New Ideas,
AIMatters (Newsletter of the American Institute of Mathematics), Autumn 2012, page 11.
 Humanistic Mathematics: An Oxymoron?
Diversity & Democracy, a publication of the Association of American Colleges and Universities, Volume 15 Number 2 (Spring 2012), page 21.
Available at http://www.diversityweb.org/DiversityDemocracy/vol15no2/karaali.cfm
 In Defense of Frivolous Questions;
Inside Higher Education, Views, April 10, 2012.
Available at http://www.insidehighered.com/views/2012/04/10/essaydefensecoursesaskseeminglyfrivolousquestions

Can Zombies Do Math? In Defense of Frivolous Questions;
Pomona College Magazine, Fall 2012 (Volume 49 Number 1), pages 2829.
Available at http://magazine.pomona.edu/2012/fall/canzombiesdomath/
 Have You Seen This? Journal of Humanistic Mathematics;
MSOR Connections, Vol.11, Iss. 2 (Summer 2011), page 43.
Available at http://mathstore.ac.uk/headocs/Karaali.pdf
 A Different Pencil Too Good to be Ignored? A First Look at WolframAlpha;
with B. Yoshiwara
FOCUS (newsletter of the Mathematical Association
of America), Vol.29, no:5 (2009), page 15
 Mathematicians Playing a Role in Math Education: What We Learned at the IME/MIME Workshop; with A. Bargagliotti and R.
Chidambaram
FOCUS (newsletter of the Mathematical Association of America), Vol.28, no:8 (2008), pages 2627
 What I learned from the MAA Digital Library workshop;
FOCUS (newsletter of the Mathematical Association of America), Vol.26, no:9 (2006), pages 1819
Short Survey Articles (These were
written at various times for various reasons and put here for whoever
may find them interesting or useful):
 Deformation Quantization  A Brief Survey (PDF)
 (Kaehler)Ricci Flow on (Kaehler) Manifolds (PDF)
 Basic Facts about Weakly Symmetric Spaces (PDF)
 Quantum Moment(um) Map(ping)s  A Hopf Algebra Approach (PDF)
 Flag Manifolds and Toric Geometry (PDF)
For Gizem Karaali's presentations and other professional activities, see her CV, dated as marked.
To go back to Gizem Karaali's main webpage, click here.