Explore a mathematical seminar presentation where Dr. Chiara Damiolini from the University of Texas at Austin delves into the fascinating world of conformal blocks and their relationship with vertex operator algebras. Learn how conformal blocks are constructed using both geometric data (projective curves with marked points) and representation theoretic elements (vertex algebra V and V-modules). Discover how these blocks form sheaves on the moduli space of curves, exhibiting unique combinatorial and functorial properties. Gain insights into current open problems in the field and understand the collaborative research conducted with A. Gibney, D. Krashen, and N. Tarasca. Part of the "New equivariant methods in algebraic and differential geometry" event series at the Isaac Newton Institute, this hour-long talk bridges fundamental concepts in algebraic geometry and representation theory.