Frobenius and Verschiebung for K-theory of Endomorphisms, joint with Sanjana Agarwal, Jonathan Campbell, Kate Ponto, Zhonghui Sun. Submitted.
Coherence for Pseudo Commutative Monads. Available from the arxiv. Will submit soon!
Coherence for Pseudo Symmetric Multifunctors. In Theory and Applications of Categories. Vol. 41, No. 47, 2024.
Theses:
PhD Thesis: Pseudo symmetric multifunctors: Coherence and Examples. (2024) We prove a coherence theorem for pseudo symmetric multifunctors enriched in Cat as defined by Donald Yau, and provide new examples in the form of a coherence theorem for symmetric pseudo commutative monads. As a consequence we prove that inverse K-theory preserves certain En algebras. In particular, any En-algebra in spectra (parameterized by a free En-operad) can be realized as the K-theory of some permutative category.
Master Thesis: Sheaves of First Order Structures on a Locale. We prove that the category of first order structures on a locale is isomorphic to a certain category of first order structures taking truth values in the locale. This allows us to write down a sheafification functor based on previous work by Fourman and Scott. We also generalize the results obtained by Caicedo for sheaves of structures on a topological space to the locale context.
Undergrad Thesis (in spanish): Chaitin's Ω-Numbers and Incompleteness. We correct the proof of the main theorem in an article by C.S. Calude which generalizes work by Solovay.