# Darlayne Addabbo

Hano Rund Postdoctoral Fellow, University of Arizona

## I am the Hano Rund Postdoctoral Fellow at the University of Arizona. My postdoctoral mentors are Profs. Anton Izosimov and Christoph Keller. I received my PhD in 2017 from the University of Illinois at Urbana-Champaign under the direction of Prof. Maarten Bergvelt. I was previously a Visiting Assistant Professor at the University of Notre Dame, where my mentor was Prof. Katrina Barron. My research is in vertex operator algebras and integrable systems.

Email: addabbo@math.arizona.edu

### Recent & Upcoming Talks and Conferences

Joint Mathematics Meetings, Special Session on "Quantum Algebra and Geometry", online January 6-9, 2021

Rocky Mountain Rep Theory Seminar, October 22, 2020

University of Arizona, Mathematical Physics and Probability Theory Seminar, September 23, 2020

September 20-25, 2020, "Women in Mathematical Physics" workshop at the Banff International Research Station. (Now online September 21-22, 2020.)

University of Arizona, Algebraic Geometry Seminar, September 17, 2020

February 6, 2020, Iowa State University Algebra and Geometry Seminar

Joint Mathematics Meeting Special Session on Mathematical Aspects of Conformal Field Theory, January 2020, Denver, Colorado

November 8, 2019, QuaSy-Con 2019: An informal Quantum Symmetries Conference in the U.S. Midwest, University of Illinois at Urbana-Champaign

November 1, 2019, Applied Mathematics Colloquium at New Jersey Institute of Technology

October 24, 2019, Undergraduate Mathematics Colloquium at Illinois State University

October 12-13, 2019, American Mathematical Society Special Session on Representations of Lie Algebras, Vertex Operators, and Related Topics, Binghamton, NY

### Publications & Preprints

Addabbo, Darlayne; Barron, Katrina "On Generators and Relations for Higher Level Zhu Algebras for Certain Vertex Operator Algebras and Applications" (in preparation)

Addabbo, Darlayne; Barron, Katrina "Higher Level Zhu Algebras for n>1 for the Heisenberg Vertex Operator Algebra" (in preparation)

Addabbo, Darlayne; Bergvelt, Maarten "Difference hierarchies for nT τ-functions." *Internat. J. Math.* 29 (2018), no. 13, 1850090, 29 pp.

Addabbo, Darlayne; Bergvelt, Maarten "τ-functions, Birkhoff factorizations and difference equations." *SIGMA Symmetry Integrability Geom. Methods Appl.* 15 (2019), Paper No. 023, 42 pp. 17B80

Addabbo, Darlayne; Bervelt, Maarten "Generalizations of Q-systems and orthogonal polynomials from representation theory." *Lie algebras, vertex operator algebras, and related topics, *1–13, Contemp. Math., 695, *Amer. Math. Soc., Providence, RI,* 2017.

### Recent Grants & Awards

Mathematical Sciences Research Institute (MSRI), Summer for Women in Mathematics (SWiM) Research Program Award (2020), Rescheduled for Summer 2021

American Mathematical Society-Simons Travel Grant (2018-2020)

Association for Women in Mathematics-National Science Foundation Travel Grant (2018)

### Teaching

This Fall 2020 semester, I am teaching Math 125 (Calculus I) at the University of Arizona.

This past Spring 2020, I taught teaching Abstract Algebra: Group Theory and Ring Theory.

During the summer before last, I developed and ran a special summer course on the representation theory of finite groups. The students read and presented on all of Benjamin Steinberg's "Representation Theory of Finite Groups: An Introductory Approach". At the end of the summer, I helped teach the students to use LaTeX to make posters on what they learned. I hope the students enjoyed the program as much as I did!

More information on my teaching can be found in my CV .