About Me
I’m a computer scientist who studies category theory and logic. I am currently working with Elena Botoeva at the University of Kent on a monad calculus embedding of a query language for schemaless databases while I finish writing up my PhD on the foundations of graded monads under the supervision of Dominic Orchard.
My CV is here.
Publications
Victoria Vollmer, Danielle Marshall, Harley Eades III, & Dominic Orchard. A Mixed Linear and Graded Logic: Proofs, Terms, and Models. 33rd EACSL Annual Conference on Computer Science Logic. (CSL 2025). arxiv
Victoria Vollmer, Marco Paviotti, & Dominic Orchard. On the 2-category of Graded Monads. Under review
Ongoing Projects
(Thesis) “The Structure of Structure: Selected Stories on Graded Monads.” This work gathers three very different stories of extending theories or results based or about monads to graded monads. These stories show how graded monads share the same properties that monads possess that makes them so applicable but bring their own fine-grained flavor.
Foundations of Graded Monads: Foundations of graded monads: Joint work with Dominic and Marco on the 2-category of graded monads, distributive laws for graded monads, and free constructions. The initial draft on the theoretical core has been submitted and we are continuing with another paper applying the free graded monad to effect systems.
Generalized Multicategories for Graded Monads: Joint work with Dominic Orchard which extends the generalized multicategories of Hermida and Leinster. We take a cartesian graded monad and define the category of multicategories whose structure is defined by that graded monad.
A Monadic Calculus for Schemaless Databases: Joint work with Elena Botoeva on a monadic calculus encoding for MQuery-a query language for mongo db. We use the tree structure of JSON documents formulated as a monad to define the stages of MQuery. We are concurrently developing a Haskell library as a proof of concept.
Talks
(Upcoming) CT. On the Category of Graded Monads. Baltimore, MD USA. July 2026 (abstract)
PLAS seminar. Grothendieck Construction for Graded Monads Parts 1 & 2. Kent, UK. Jan 2026
PSSL 111. Graded Monads, Graded Multicategories, and Graded Adjoint Logic. Bologna, Italy. Sep 2025
SANDWICH seminar. The 2-Category of Graded Monads. Cambridge, UK. Feb 2025
CSL 2025. A Mixed Linear and Graded Logic: Proofs, Terms, and Models. Amsterdam, Netherlands. Feb 2025 (slides)
S-REPLS 15. A Mixed Linear and Graded Logic: Proofs, Terms, and Models. Kent, UK. July 2024
SYCO. A Mixed Linear and Graded Logic. Paris, France (remote). April 2023 (slides)
Women in Logic. A Mixed Linear and Graded Logic: Proofs, Terms, and Models. August 2022. (slides)