# 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 and Upcoming Talks and Conferences

"Unveiling Infinite Symmetries: Mini Course on Algebraic Structures of Generalized Kac-Moody Type" at the Canadian Mathematical Society Summer Meeting (July 2024), lecture title: TBA

14th Southeastern Lie Theory Workshop, University of Virigina (March 1-3, 2024), title: "Vertex operators for imaginary gl2-subalgebras in the Monster Lie algebra"

Rutgers University Lie Group/Quantum Mathematics Seminar (November 10, 2023), online, title: Vertex Operators for Imaginary gl_2-subalgebras in the Monster Lie Algebra

"Lie Theory and its Applications in Physics", Bulgaria (June 19-25, 2023), title: "Vertex operators for imaginary gl2-subalgebras in the Monster Lie algebra''

13th Southeastern Lie Theory Workshop, North Carolina State University (May 12-14, 2023), title: "Vertex operators for Imaginary gl2- subalgebras in the Monster Lie Algebra"

AMS Central Sectional, special session on "Representation Theory, Geometry, and Mathematical Physics" at the University of Cincinnati (April 15-16, 2023), title: "Vertex operators for Imaginary gl2- subalgebras in the Monster Lie Algebra"

Southwest Strings Meeting, The University of Arizona (March 24-25, 2023), title: "Vertex operators for Imaginary gl2- subalgebras in the Monster Lie Algebra"

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

### Papers

Addabbo, Darlayne "On Huang's Associative Algebras for Vertex Operator Algebras", (In preparation) 2023

Addabbo, Darlayne; Keller, Christoph "Generalized Theta Functions on Vertex Operator Algebras", (In preparation) 2023

Addabbo, Darlayne; Carbone, Lisa; Jurisich, Elizabeth; Khaqan, Maryam; Murray, Scott H. "A Monstrous Lie Group", (In preparation) 2023

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, ACCEPTED to Journal of Pure and Applied Algebra.

Addabbo, Darlayne; Barron, Katrina "On generators and relations for higher level Zhu algebras and applications", J. Algebra 623 (2023), 496-540, https://doi.org/10.1016/j.jalgebra.2023.02.023

Addabbo, Darlayne; Barron, Katrina "The level two Zhu algebra for the Heisenberg vertex operator algebra", Communications in Algebra (2023), https://doi.org/10.1080/00927872.2023.2184638

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.

### Upcoming Conference/Workshop Organization

Special Session on "New Developments in Infinite Dimensional Lie algebras, Vertex Operator Algebras and the Monster" at the Joint Meeting American Mathematical Society-Unione Matematica Italiana July 2024

Women in Noncommutative Algebra and Representation Theory Workshop (WINART4) 2025 at the Banff International Research Station

### Recent Grants & Awards

Awarded Honorable Mention - The University of Arizona 2024 Outstanding Postdoctoral Scholar Award

Proposal for the Women in Noncommutative Algebra and Representation Theory (WINART4) workshop has been ACCEPTED by the Banff International Research Station. The workshop will take place in 2025.

2023 Teaching and Service Award for Post Docs

Association for Women in Mathematics-National Science Foundation Travel Grant (2023)

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 2023: "Introduction to Linear Algebra"

Spring 2023: Math 415B "Second Course in Abstract Algebra"

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.