My research interests center in Mathematical Education and Algebraic Topology .
Mathematical Education
- Examining the Role and Impact of Artificial Intelligence in Teaching and Learning in Mathematics.
- Maximizing technology for effective and individualized feedback
- Designing active learning activities for upper-level math courses
- Examining the Efficacy of Flipped and Blended Classroom Models
- Implementing exploratory projects for undergraduate math courses of any level
Algebraic Topology
I am mainly interested in studying the equivariant cohomology of finite group actions on several spaces, including polyhedral products. My methods integrate and link knowledge from algebraic topology, group cohomology, transformation groups, and toric topology among other areas in mathematics.
Future and Current Projects
- Combinatorial topology of generalized moment angle complexes (J. w/ Doug Ravenel)
- Free and Flat extension pairs in equivariant cohomology.
- Equivariant cohomology for dihedral group actions.
- Combinatorial and topological relations of the canonical action on $n$-gon polyhedral products
- Topology of Polyhedral products arising from distinguishable simplicial complexes
Past Projects
- Equivariant formality of Polyhedral products arising from the \(n\)-gon. 2021. (J. w/ Fred Cohen)
- Equivariant cohomology for semi-direct product actions. 2020
- Quotient criterion for syzygies for 2-torus actions. 2020
Relevant Experience
- University of Rochester Topology group (2021-2023). Seminar organizer (2021-2022).
- Long Term Visitor fellow at the Fields Institute. Toronto. Thematic Program on Toric Topology
- Graduate Student Seminar Organizer. University of Western Ontario. 2019
Data Science
- Micromaster in Statistics and Data Science (General track). MITx Online. 2020.
- Certificate Correlation-one DataScience4All Program. (2020)
- Participant Brainhack Western 2019 relating mathematics and neuroscience, winning an innovative award for our proposed project on How does the brain sound.
Preprints and written documents worth sharing
- The equivariant cohomology for semidirect product actions. arXiv Preprint, 2021. - Submitted-
- The quotient criterion in equivariant cohomology for elementary 2-abelian group actions. arXiv Preprint, 2020. - Submitted-
- Equivariant cohomology for 2-torus actions and torus actions with compatible involutions. Doctoral dissertation, 2020.
- Duistermaat's Theorem on cohomologically symplectic spaces.
- Equivariant cohomology: A topological and an algebraic approach. Beamer of a talk given in Syracuse University
- On the automorphism group of Riemann surfaces.
- Equivariant cohomology for torus action and a compatible involution. Beamer of a talk given in Temple University, Phildaelphia.
- About The Lyndon-Hochschild-Serre Spectral Sequence.
- Computations on Equivariant Cohomology.
- Clifford Algebras and Milnor's Conjecture for n=2.
- Conjugation spaces.
- Cobordism and Group of Homotopy spheres. Master Thesis
- Categorical representation of Banach spaces. (In Spanish)
- Glivenko's Theorem for the Model-intuitionistic Logic. (In Spanish)