Yuly Billig

Yuly Billig is a Professor in the School of Mathematics and Statistics at Carleton University. He specializes in representation theory of infinite-dimensional Lie algebras, vertex algebras, and soliton theory. His research bridges algebraic structures with applications in mathematical physics, including studies of Kac-Moody algebras and their representations. He co-developed a Maple package for computations in Lie algebras and vertex algebras, available on GitHub. Billig founded the Carleton Math Enrichment Centre, offering courses in mathematics, physics, and computer science for students from grades 3 to 12. His work also extends to wavelet analysis and digital signal processing, reflected in his course MATH 4822/5822 on Wavelets and Signal Processing. His research has been published in leading journals such as Advances in Mathematics, Journal of Algebra, and Communications in Contemporary Mathematics.

Key research interests include:

• Representation theory of infinite-dimensional Lie algebras
• Vertex algebras and their applications
• Soliton theory and nonlinear PDEs
• Geometric and algebraic structures in mathematical physics

Recent publications focus on dense clusters in hypergraphs, sheaf modules on algebraic varieties, and gauge modules for vector field algebras. His contributions to computational tools and educational outreach highlight his dual role as a researcher and educator.