Zajj Daugherty

Assistant Professor

Main Affiliation

Mathematics

Areas of Expertise/Research

  • Representation Theory
  • Combinatorics

Building

North Academic Center

Office

6/301

Phone

212-650-6957

Zajj Daugherty

Research

I work mainly in combinatorial representation theory. Specifically, I study how combinatorial objects (like partitions, tableaux, lattices, etc.) encode structure of algebras similar to the group algebra of the symmetric group, Brauer algebras, graded and affine Temperley-Lieb, Hecke, and Birman-Murakami-Wenzl algebras, etc. My thesis work, completed in 2010 at the University of Wisconsin--Madison, began the study of two-boundary Hecke algebras.

Education

Postdoctoral positions:
Research Fellow in Representation Theory, University of Melbourne, Fall 2014
John Wesley Young Research Instructor, Dartmouth College, Summer 2011–Summer 2014
Postdoctoral Fellow, Institute for Computational and Experimental Research in Mathematics, Spring 2013
Visiting Assistant Professor of Mathematics, St. Olaf College, Fall 2010–Spring 2011

Degrees:
Ph.D. Mathematics, University of Wisconsin–Madison, August 2010

Dissertation title: Degenerate two-boundary centralizer algebras
Advisor: Arun Ram
Minor: Mathematics education

M.A. Mathematics, University of Wisconsin–Madison, December 2006

B.S. Mathematics (with distinction), Harvey Mudd College, May 2005

Courses Taught

Math 201: Calculus 1
Math 202: Calculus 2
Math 308: Bridge to Advanced Mathematics
Math 345: Theory of Numbers
Math 365: Elements of Combinatorics
Math A49: Modern Algebra I
Math B49: Modern Algebra II
Math A68: Combinatorial Analysis

Publications

The affine VW supercategory, with Martina Balagovic, Zajj Daugherty, Inna Entova-Aizenbud, Iva Halacheva, Johanna Hennig, Mee Seong Im, Gail Letzter, Emily Norton, Vera Serganova, and Catharina Stroppel, preprint (to appear in Selecta).

Quasisymmetric Power Sums, with Cristina Ballantine, Angela Hicks, Sarah Mason, and Elizabeth Niese, preprint; extended abstract published DMTCS Proceedings for FPSAC 2018. Full version accepted pending revisions.

Translation functors and Kazhdan-Lusztig multiplicities for the Lie superalgebra p(n), with Martina Balagovic, Inna Entova Aizenbud, Iva Halacheva, Johanna Hennig, Mee Seong Im, Gail Letzter, Emily Norton, Vera Serganova, Catharina Stroppel, Mathematical Research Letters Vol.26, no.3.

Two boundary Hecke algebras and combinatorics of type C, with Arun Ram, preprint.

Centralizers of the infinite symmetric group, with Peter Herbrich, DMTCS Proceedings for FPSAC 2014.

Quasi-partition algebra, with Rosa Orellana, J. Algebra, Vol 404 (2014), 124--151

Affine and degenerate affine BMW algebras: actions on tensor space, with Arun Ram and Rahbar Virk, Selecta Math., 19-2 (2013) 611--653.

Affine and degenerate affine BMW algebras: The center, with Arun Ram and Rahbar Virk, Osaka J. Math., Volume 51, Number 1 (2014), 257--285.

Degenerate two-boundary centralizer algebras, Pacific J. Math., 258-1 (2012) 91--142.

Degenerate two-boundary centralizer algebras, Dissertation.

Voting, the symmetric group, and representation theory, with A. K. Eustis, G. Minton, M. E. Orrison, American Mathematical Monthly 116 (2009), no. 8, 667--687.

Integrality of Quotients of Wronskians of the Andrews-Gordon Series, Integers, 6 (2006).

An Algebraic Approach to Voting Theory, Senior thesis, Harvey Mudd College (2005).

Selected Awards

Simons Foundation Collaboration Grants for Mathematicians #586728 “Combinatorics and representation theory of centralizer algebras” $42,000 (2018–2023)

National Science Foundation Recruitment and Mentoring in Mathematics Program Grant (Senior Personnel) #1820731 $477,136 (2018–2021)

Membership to two sessions of MSRI Summer Research for Women in Mathematics, $6,996 (2018)

PSC-CUNY Research Award, #61204-00 49, $3,500 (2018–2019)

PSC-CUNY Research Award, #69636-00 47, $6,000 (2016–2017)

National Science Foundation Individual Grant DMS-1162010 “Combinatorics and representation theory of centralizer algebras” $82,543 (2012–2017)

Australian Research Council Discovery Grant DP130100674 “Tantalizer algebras and generalized lattice models,” with A. Ram, $350,000 (2013–2016)

AMS-Simons Travel Grant (2012–2014)

Recent Service Activities

Mentor for Math Alliance (2019–Present)

Departmental Social Amenities Treasurer (2019–Present)

Research leader for WINART2: Women in Noncommutative Algebra and Representation Theory workshop (2019).

Faculty advisor for CCNY AWM chapter (2018–Present)

Coauthor and administrator for the website for Women in Algebraic Combinatorics and associated mailing list, http://www.womeninac.org/. (2017–Present)

Member of the Program Committee for the international conference on Formal Power Series and Algebraic Combinatorics (FPSAC) (2017)

Organizer of mathematics colloquium at CCNY (2016–2018)

Presenter at College & Career Week, Girls Prep Bronx (2016, 2017)

Mentor for WinS Mentoring Program at CCNY (2016)