Gizem Karaali

Professor of Mathematics
  • Expertise

    Expertise

    Gizem Karaali has a long-standing interest in the intersection of mathematics with the humanities. She is a founding editor of Journal of Humanistic Mathematics, a peer-reviewed open-access journal that publishes articles, essays, fiction and poetry with an emphasis on the aesthetic, cultural, historical, literary, pedagogical, philosophical, psychological, and sociological aspects of mathematics.

    She also created a provocative first-year seminar—which at Pomona means a writing-intensive, discussion-oriented class designed to engage a small group of first-year students in analytic readings and out-of-the-box thinking—titled “Can Zombies Do Math?” that requires students to think both about the nature of math as a human endeavor and, on a fundamental level, what it means to be human.

    Research Interests

    Karaali’s mathematics research involves algebraic objects of Representation Theory (e.g. Lie algebras and superalgebras, Weyl groups, and Coxeter groups) and certain algebraic and combinatorial structures on them (e.g. r-matrices, Lie bialgebra structures, and Bruhat orderings), which have deep geometric significance. Her scholarly interests include humanistic mathematics, pedagogy, and quantitative literacy, as well as social justice implications of mathematics and mathematics education.

    Areas of Expertise

    MATHEMATICS

    • Algebra and Geometry
    • Representation Theory
    • Algebraic Combinatorics
    • Quantitative Literacy
    • Humanistic Mathematics
    • Mathematics and Social Justice
  • Work

    Work

    Books

    Barcelo, H., Karaali, G., Orellana, R., editors; Recent Trends in Algebraic Combinatorics, Association for Women in Mathematics Series Volume 16, Springer Nature, Cham, 2019. 

    Tunstall, L., Karaali, G., Piercey, V., editors; Shifting Contexts, Stable Core: Advancing Quantitative Literacy in Higher Education, MAA Notes #88, MAA Press – an imprint of the American Mathematical Society, Washington DC, 2019.

    Karaali, G., Khadjavi, L., editors; Mathematics for Social Justice: Resources for the Col- lege Classroom, Classroom Resource Materials Volume 60, MAA Press – an imprint of the American Mathematical Society, Washington DC, 2019.

    Featured Publications

    With S. Aksoy, A. Azzam, C. Coppersmith, J. Glass, X. Zhao and X. Zhu, "Coalitions and Cliques in the School Choice Problem," in Involve, A Journal of Mathematics, Volume 8 Issue 5 (October 2015), pages 801–823.

    With C.F. Fowler and S.R. Garcia, "Ramanujan sums as supercharacters," in Ramanujan Journal, Volume 35 Issue 2 (November 2014), pages 205–241. 

    With J.L. Brumbaugh, M. Bulkow, P.S. Fleming, L.A. Garcia, S.R. Garcia, M. Michal, and A.P. Turner, "Supercharacters, exponential sums, and the uncertainty principle," in Journal of Number Theory, Volume 44 (November 2014), pages 151-175.

    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, "Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras", in Advances in Mathematics, Volume 229 Issue 4 (1 March 2012), pages 2310-2337.

    "On the quantization of zero-weight super dynamical r-matrices", Proceedings of the American Mathematical Society, Volume 140 Issue 1 (January 2012), pages 7-20.

    With S.K. Hsiao, "Multigraded combinatorial Hopf algebras and refinements of odd and even subalgebras," in Journal of Algebraic Combinatorics, Volume 34 Number 3 (November 2011), pages 451-506.

    "On Hopf Algebras and Their Generalizations"; Communications in Algebra, 36 (2008), pp.4341-4367.

    Other Peer-Reviewed Articles (selections)

    With Edwin Villafane Hernandez and Jeremy A. Taylor, "What’s in a Name? A Critical Review of Quantitative Literacy, Numeracy, and Quantitative Reasoning," in Numeracy, Volume 9 Issue 1 (January 2016), Article 6.

    "Metacognition in the Classroom: Motivation and Self-Awareness of Mathematics Learners," in PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, Volume 25 Issue 5 (May 2015), pages 439–452. 

    "Can Zombies Write Mathematical Poetry? Mathematical poetry as a model for humanistic mathematics," in Journal of Mathematics and the Arts, Volume 8, Issue 1-2, pages 38-45.

    "The Genius as a Characterization of the Creative Spirit in Mathematics and the Arts," in the 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.

    "The Brave New World of Open Access & Creative Commons: a Humanistic Experiment in Mathematical Publishing," in the Proceedings of the 2013 AMS Special Session on Topics and Issues in Electronic Publishing, pages 11-31.

    "An Evaluative Calculus Project: Applying Bloom’s Taxonomy to the Calculus Classroom," in PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, Volume 21 Issue 8 (November 2011), pages 719–731.

    With P. Choi, S.O. Sood, and E. Grosfils, "Envisioning a Quantitative Studies Center: A Liberal Arts Perspective," Numeracy, Vol. 3, Iss. 1 (2010), Article 4. 

    Other Select Writing

    Math Education: A Messy Problem” in Inside Higher Education, Views, May 3, 2016.  

    “On Genius, Prizes, and the Mathematical Celebrity Culture” in The Mathematical Intelligencer, Volume 37 Issue 3 (2015), pages 61–65.

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

    With F. Alayont and L. Pehlivan, "What Does It Take to Teach Nonmajors Effectively?" in FOCUS (newsletter of the Mathematical Association of America) Volume 32 Number 6 (2012), pages 11-12.

    "Humanistic Mathematics: An Oxymoron?" Diversity & Democracy 15:2, p. 21, 2012

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

  • Education

    Education

    Ph.D. in Mathematics
    University of California, Berkeley

    Bachelor of Science in Electrical Engineering and Mathematics
    ​Boğaziçi University

    Recent Courses Taught

    • Mathematics, Philosophy and the Real World
    • Calculus I
    • Calculus III
    • Linear Algebra
    • Introduction to Analysis
    • Abstract Algebra I: Groups & Rings
    • Abstract Algebra II: Representation Theory
  • Awards & Honors

    Awards & Honors

    National Security Agency (NSA), Young Investigator Award for continuing research on Yang-Baxter equations, super quantum groups and Hopf algebras, 2011-2013.

    National Endowment for the Humanities (NEH), Enduring Questions, NEH Enduring Questions Course on the Aims and Value of Education, 2014-2016.

    American Mathematical Society (AMS) Project NExT fellow (sepia dot), 2006-2007.