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 and J. T. Neugebauer. Solutions of Boundary Value Problems at Resonance with Periodic and Antiperiodic Boundary Conditions Involve, 12(2019), no. 1, 171--180.
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. Schreier's Formula for some Free Probability Invariants. To appear in International Mathematics Research Notices. doi:10.1093/imrn/rnaf263, arxiv:2307.13867
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.