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 r-matrices 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 r-matrices...)

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 up-to-date 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

Other Areas of Expertise

External Grants

Publications and Preprints

Mathematical Research (Preliminary versions / preprints are available on the arxiv):

  1. School Choice as a One-Sided 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

  2. 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 801--823.
    Available at http://msp.org/involve/2015/8-5/p09.xhtml

  3. 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 151--175.

  4. Ramanujan sums as supercharacters with C. F. Fowler and S. R. Garcia
    Ramanujan J., Volume 35 Issue 2 (November 2014), pages 205--241.
    Available at http://link.springer.com/article/10.1007%2Fs11139-013-9478-y.

  5. A Cost-Minimizing 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 9-11, 2012) Proceedings (2012).
    Available at http://www.cs.uic.edu/pub/Isaim2012/WebPreferences/ISAIM2012_ComSoc_Aksoy_etal.pdf.

  6. 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, J-C. Novelli, A. Pang, F. Saliola, L. Tevlin, J-Y. Thibon, N. Thiem, V. Venkateswaran, C. R. Vinroot, N. Yan, and M. Zabrocki
    Advances in Mathematics, Volume 229 Issue 4 (1 March 2012), pages 2310--2337.
    MR2880223

  7. 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, J-C. Novelli, A. Pang, F. Saliola, L. Tevlin, J-Y. Thibon, N. Thiem, V. Venkateswaran, C. R. Vinroot, N. Yan, and M. Zabrocki
    FPSAC 2011 (Reykjavik, Iceland) DMTCS Proceedings, AO, 2011, pages 3-14.
    Available at http://www.fpsac.org/FPSAC11/SITE2011/proceedings/dmAO0102.pdf

  8. Classical Kloosterman sums: representation theory, magic squares, and Ramanujan multigraphs; with P. S. Fleming and S. R. Garcia
    J. Number Theory 131 (2011), pages 661--680.
    MR2753270

  9. On the quantization of zero-weight super dynamical r-matrices;
    Proc. Amer. Soc. Math. 140 (2012), pages 7-20.
    MR2833513

  10. Multigraded combinatorial Hopf algebras and refinements of odd and even subalgebras; with S. K. Hsiao
    J. Algebr. Comb. 34 (2011), pages 451-506.
    MR2836370

  11. Spanning sets for Moebius vertex algebras satisfying arbitrary difference conditions; with G. Buhl
    J. Algebra 320 (2008), pages 3345--3364.
    MR2450731

  12. On Hopf Algebras and Their Generalizations;
    Comm. Algebra 36 (2008), pages 4341-4367.
    MR2473333

  13. Dynamical Quantum Groups - The Super Story;
    Contemp. Math. 441 (2007), pages 19-52.
    MR2381534

  14. Super Solutions of the Dynamical Yang-Baxter Equation;
    Proc. Amer. Math. Soc. 134 (2006), pages 2521-2531.
    MR2213729

  15. A New Lie Bialgebra Structure on sl(2,1);
    Contemp. Math. 413 (2006), pages 101-122.
    MR2262367

  16. Constructing r-matrices on Simple Lie Superalgebras;
    J. Algebra 282 (2004), pages 83-102.
    MR2095573

Other Peer-Reviewed Articles:

  1. A Humanistic Reading Component for an Introduction-to-Proofs Course
    Beyond Lecture: Techniques to Improve Student Proof-Writing Across the Curriculum, edited by Rachel Schwell, Aliza Steurer, and Jennifer Franko Vasquez, Mathematical Association of America, Washington DC, 2016, pages 123-133.

  2. 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/

  3. Metacognition in the Classroom: Motivation and Self-Awareness of Mathematics Learners
    PRIMUS, Vol. 25, Iss. 5 (May 2015), pages 439-452.
    Available at http://www.tandfonline.com/doi/abs/10.1080/10511970.2015.1027837.

  4. Can Zombies Write Mathematical Poetry? Mathematical poetry as a model for humanistic mathematics
    Journal of Mathematics and the Arts, Volume 8 Issue 1-2 (2014), pages 38-45.
    Available at http://www.tandfonline.com/doi/abs/10.1080/17513472.2014.926685.

  5. 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 413-416.
    Available at http://archive.bridgesmathart.org/2014/bridges2014-413.html.

  6. 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 1131.
    Available at http://www.emis.de/proceedings/TIEP2013/02karaali.pdf.

  7. An Evaluative Calculus Project: Applying Bloom's Taxonomy to the Calculus Classroom
    PRIMUS, Vol. 21, Iss. 8 (November 2011), pages 719-731.
    Available at http://www.tandfonline.com/doi/full/10.1080/10511971003663971#.VL5YU1pHGMU.

  8. 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

  9. Life After Wolfram|Alpha: 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

  10. 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:

  1. Mathematics and art: a cultural history by Lynn Gamwell,
    Journal of Mathematics and the Arts, Volume 10 Issue 1-4 (2016), pages 87-92.
    Available at http://www.tandfonline.com/doi/full/10.1080/17513472.2016.1242186.

  2. 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

  3. 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 (July-August 2015), pages 17--19.

  4. 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 John-Steiner; Mathematicians: An Outer View of The Inner World, by Mariana Cook,
    Association for Women in Mathematics Newsletter, Volume 43 Number 6 (November-December 2013), pages 22--25.

  5. Encyclopedia of Mathematics and Society by Sarah J. Greenwald and Jill E. Thomley,
    College Mathematics Journal, Volume 44 Number 4 (September 2013), pages 332--335.

  6. Philosophy of Science after Feminism by Janet Kourany;
    Association for Women in Mathematics Newsletter, Volume 42 Number 1 (January-February 2012), pages 8-10.

Brief Book Reviews:

  1. The Best Writing on Mathematics: 2010 edited by Mircea Pitici;
    Mathematics Teacher, Volume 105 Number 9 (May 2012), page 717.

Editorials:

  1. Connections (Editorial); with M. Huber
    Journal of Humanistic Mathematics, Vol.6, Iss. 2 (2016), pages 1-2. Available at http://scholarship.claremont.edu/jhm/vol6/iss2/2/

  2. Not Just In the Eye of the Beholder (Editorial); with M. Huber
    Journal of Humanistic Mathematics, Vol.6, Iss. 1 (2016), pages 1-2. Available at http://scholarship.claremont.edu/jhm/vol6/iss1/2/

  3. Inspiring Mathematical Experiences (Editorial); with M. Huber
    Journal of Humanistic Mathematics, Vol.5, Iss. 2 (2015), pages 1-2. Available at http://scholarship.claremont.edu/jhm/vol5/iss2/2/

  4. A Mathematician's Choice (Editorial); with M. Huber
    Journal of Humanistic Mathematics, Vol.5, Iss. 1 (2015), pages 1-2. Available at http://scholarship.claremont.edu/jhm/vol5/iss1/2/

  5. Mathematical Perspectives (Editorial); with M. Huber
    Journal of Humanistic Mathematics, Vol.4, Iss. 2 (2014), pages 1-2. Available at http://scholarship.claremont.edu/jhm/vol4/iss2/2/

  6. 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/

  7. 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/

  8. Math: That Thing You Do (Editorial); with M. Huber
    Journal of Humanistic Mathematics, Vol.3, Iss. 1 (2013), pages 1-2. Available at http://scholarship.claremont.edu/jhm/vol3/iss1/2/

  9. 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/

  10. 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/

  11. 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/

  12. 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:

  1. The Power of Two: Two Tips for Mathematicians,
    Guest blog entry for American Mathematical Society e-Mentoring Network, posted on March 14, 2016.
    Available at http://blogs.ams.org/mathmentoringnetwork/2016/03/14/the-power-of-two-two-tips-for-mathematicians/.

  2. Summer Cleaning: (Digital) Organization Basics for Mathematicians,
    Guest blog entry for American Mathematical Society e-Mentoring Network, posted on May 21, 2015.
    Available at http://blogs.ams.org/mathmentoringnetwork/2015/05/21/summer-cleaning-digital-organization-basics-for-mathematicians/.

  3. Women in Maths: Gizem Karaali,
    Contribution to the Women in Maths Project, posted on May 20, 2015.
    Available at https://www.facebook.com/womeninmaths/.

  4. Math Talk: Preparing Your Conference Presentation,
    Guest blog entry for American Mathematical Society e-Mentoring Network, posted on August 4, 2014.
    Available at http://blogs.ams.org/mathmentoringnetwork/2014/08/04/math-talk-preparing-your-conference-presentation/.

  5. Why You Need a Summer Plan,
    Guest blog entry for American Mathematical Society e-Mentoring Network, posted on May 23, 2014.
    Available at http://blogs.ams.org/mathmentoringnetwork/2014/05/23/why-you-need-a-summer-plan/.

  6. 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/.

  7. The Fundamental Principle of Productivity: What they DON'T teach you in graduate school,
    Guest blog entry for American Mathematical Society e-Mentoring Network, posted on April 7, 2014.
    Available at http://blogs.ams.org/mathmentoringnetwork/2014/04/07/the-fundamental-principle-of-productivity-what-they-dont-teach-you-in-graduate-school/.

  8. 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/selma-karaali-and-artemis-karaali/.

Mathematical Poetry:

  1. Math and Metaphor OR A Two-Letter Curse Word, (poem)
    Bridges 2016 Poetry Anthology, edited by Sarah Glaz, 2016; page 60.

  2. The Mathematician's Villanelle, (poem)
    Math Horizons, Volume 22 Issue 1 (February 2015), page 23.

  3. The Colors of Math, (poem)
    The Mathematical Intelligencer, Volume 35 Issue 1 (March 2013), page 4.

Other Writing About Mathematics & The Mathematical Community:

  1. Math Education: A Messy Problem;
    Inside Higher Education, Views, May 2, 2016.
    Available at https://www.insidehighered.com/views/2016/05/02/math-education-deserves-support-and-attention-essay
    Reprinted in Vermont Council of Teachers of Mathematics Newsletter, May 2016
    Available at http://mathinvermont.blogspot.com/2016_05_01_archive.html

  2. Collaboration and Creativity in Southern California: An Offering; with A. Radunskaya
    Association for Women in Mathematics Newsletter, Volume 46 Number 2 (March-April 2016), pages 30--32.

  3. 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/

  4. What if ... math were not required in K-12 education?,
    Pomona College Magazine, Fall 2015 (Volume 52 Number 1), pages 2-3.
    Available at http://magazine.pomona.edu/2015/fall/what-if/.

  5. On Genius, Prizes, and the Mathematical Celebrity Culture,
    The Mathematical Intelligencer, Volume 37 Issue 3 (2015), pages 61-65.

  6. 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 140-153.

  7. Nesin Math Village: Mathematics as a Revolutionary Act,
    The Mathematical Intelligencer, Volume 36 Issue 2 (2014), pages 45--49.

  8. 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 11--12.

  9. A Tale of Two Workshops: Two Workshops, Three Papers, New Ideas,
    AIMatters (Newsletter of the American Institute of Mathematics), Autumn 2012, page 11.

  10. 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

  11. In Defense of Frivolous Questions;
    Inside Higher Education, Views, April 10, 2012.
    Available at http://www.insidehighered.com/views/2012/04/10/essay-defense-courses-ask-seemingly-frivolous-questions

  12. Can Zombies Do Math? In Defense of Frivolous Questions;
    Pomona College Magazine, Fall 2012 (Volume 49 Number 1), pages 28-29.
    Available at http://magazine.pomona.edu/2012/fall/can-zombies-do-math/

  13. 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

  14. A Different Pencil Too Good to be Ignored? A First Look at Wolfram|Alpha; with B. Yoshiwara
    FOCUS (newsletter of the Mathematical Association of America), Vol.29, no:5 (2009), page 15

  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 26-27

  16. What I learned from the MAA Digital Library workshop;
    FOCUS (newsletter of the Mathematical Association of America), Vol.26, no:9 (2006), pages 18-19

Short Survey Articles (These were written at various times for various reasons and put here for whoever may find them interesting or useful):


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.