# Darlayne Addabbo

Hano Rund Postdoctoral Fellow, The University of Arizona

### I am the Hano Rund Postdoctoral Fellow at The University of Arizona. I was previously a Visiting Assistant Professor at The University of Notre Dame. I received my PhD in 2017 from the University of Illinois at Urbana-Champaign.

### Email: addabbo@math.arizona.edu

### Recent & Upcoming Talks and Conferences

"Lie Theory and its Applications in Physics", Bulgaria (June 19-25, 2023), title: TBA

AMS Central Sectional, special session on "Representation Theory, Geometry, and Mathematical Physics" at the University of Cincinatti (April 15-16, 2023), title: TBA

Rutgers University Lie Group/Quantum Mathematics Seminar (November 11, 2022), online, title: "Vertex operators for Imaginary gl2- subalgebras in the Monster Lie Algebra"

"Quantum Symmetries: Tensor categories, topological quantum field theories, vertex algebras", Centre de Recherches Mathematiques (October 2022) title: Higher level Zhu algebras

AMS Spring Western sectional Meeting, special session on "Some modern developments in the theory of vertex algebras" (May 14-15, 2022) online, title: Higher level Zhu algebras for vertex operator algebras"

Women in Noncommutative Algebra and Representation Theory (WINART) workshop, Banff International Research Station

Institute for Advanced Study, Women and Mathematics, online (May 2021), title: Higher level Zhu algebras

Joint Mathematics Meeting Special Session on "Quantum Algebra and Geometry", online (January 2021), title: Higher level Zhu Algebras for Vertex Operator Algebras

### Publications

Addabbo, Darlayne; Carbone, Lisa; Jurisich, Elizabeth; Khaqan, Maryam; Murray, Scott H. "Vertex operators for Imaginary gl2- subalgebras in the Monster Lie Algebra", arXiv:2210.16178

Addabbo, Darlayne; Barron, Katrina "On generators and relations for higher level Zhu algebras and applications", arXiv:2110.07671 (submitted)

Addabbo, Darlayne; Barron, Katrina "The level two Zhu algebra for the Heisenberg vertex operator algebra", arXiv:2206.12982 (submitted)

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)

### Recent Teaching

Fall 2022: Math 415A/515A, "Introduction to Abstract Algebra"

Spring 2022: Math 315 "Introduction to Number Theory and Modern Algebra"

Fall 2021: Math 413 "Linear Algebra"

Spring 2021: Math 313 "Introduction to Linear Algebra"

Fall 2020: Math 125 "Calculus 1"

### Selected Service and Outreach

I am co-leading the Women in Noncommutative Algebra and Representation Theory (WINART) network. (http://women-in-ncalg-repthy.org/)

I am co-organizing the Mathematical Physics and Probability Seminar at The University of Arizona.

I am also a mentor for The University of Arizona's Undergraduate Teaching Assistant Program.