My research has been on derivations on von Neumann algebra and their crossed product by a finite group with connections to free probability theory and representations of von Neumann algebras in the non-tracial setting.
Articles:
Published:
A. Garcia Guinto. Schreier's Formula for some Free Probability Invariants. Int. Math. Res. Not. IMRN(2025), no. 17 rnaf263 doi:10.1093/imrn/rnaf263, arxiv:2307.13867
A. Garcia Guinto, M. Lorentz, and B. Nelson. Murray-von Neumann dimension for strictly semifinite weights, J. Funct. Anal. 289 (2025), no. 5.
A. Garcia Guinto and J. T. Neugebauer. Solutions of Boundary Value Problems at Resonance with Periodic and Antiperiodic Boundary Conditions Involve, 12(2019), no. 1, 171--180.
Preprint:
A. Garcia Guinto, and Y. Miyamoto. On modular invariants of twisted group von Neumann algebras of almost unimodular groups. (preprint 2025)
A. Garcia Guinto. Projective representations of almost unimodular groups. (preprint 2025)
A. Garcia Guinto, and B. Nelson. Almost unimodular groups. (preprint 2025)
Presentations:
Schreier's Formula for some Free Probability Invariants A presentation that I gave at Groundwork in Operator Algebras Lecture Series Reseach Showcase of my paper listed above.