Author ORCID Identifier
https://orcid.org/0009-0009-0672-4492
Date Available
8-12-2025
Year of Publication
2025
Document Type
Doctoral Dissertation
Degree Name
Doctor of Philosophy (PhD)
College
Arts and Sciences
Department/School/Program
Mathematics
Faculty
Christopher Manon
Abstract
Conformal blocks are objects in quantum field theory that arise from conformal trans- formations, which are symmetries that preserve angles but not length. This aspect of conformal field theory has various interactions with algebraic geometry.
In this dissertation, we explore the underlying algebra and geometry of spaces and algebras of conformal blocks over SLn. We then use this information along with techniques from combinatorial commutative algebra, algebraic geometry, and representation theory to find a presentation of the algebra of SL4-conformal blocks. With this presentation, we then use computational methods to learn about some of the geometric properties of this algebra.
Digital Object Identifier (DOI)
https://doi.org/10.13023/etd.2025.347
Recommended Citation
Hill, Casey B., "The Computational Algebra of Conformal Blocks" (2025). Theses and Dissertations--Mathematics. 124.
https://uknowledge.uky.edu/math_etds/124
