Special Session Honoring Mariel Vázquez

Monday, October 26 · 5:00–6:30 p.m.
Ballroom A

This special session honors the memory and scientific legacy of Professor Mariel Vázquez, who passed away on July 5, 2026. Mariel was an internationally recognized applied mathematician and a professor in the Departments of Mathematics and Microbiology and Molecular Genetics at UC Davis. Her truly interdisciplinary research brought together mathematics, molecular biology, and polymer physics, with pioneering applications of topology and knot theory to the study of the structure of DNA.

Mariel was a beloved colleague, dedicated teacher, mentor, and advocate for a more inclusive mathematical and scientific community. Her impact extended well beyond her research to the many students, trainees, colleagues, and collaborators whose lives and careers she influenced. This session brings together colleagues and collaborators to celebrate her work and her enduring scientific and personal legacy. 

Three of Mariel’s longtime collaborators will speak about research that reflects the breadth and continuing influence of her work: 

Lattice Models of Polymers with applications to DNA Topology

Chris Soteros · University of Saskatchewan

I will review the many significant contributions that Mariel Vázquez made to the study of entanglements in polymers and biopolymers using lattice models. Mariel’s contributions include: groundbreaking numerical studies of the effects of enzyme action (such as strand-passage and strand-exchange) on the topology simplification of DNA in solution; characterizing polymer entanglements in terms of minimal step numbers and writhe; establishing that knots and links are `"localized" for polymers in nano-channels; and modelling the effects of salt concentration on DNA knotting. The last topic was a collaboration with myself and Matthew Schmirler that is still in progress; I will provide an update on the latest results.

Mathematical models to study RNA-DNA hybrids

Nataša Jonoska · University of South Florida

R-loops are co-transcriptional transient three-stranded nucleic acid formations that occur during transcription. They are RNA-DNA hybrids that form when the nascent RNA hybridizes to the template DNA, freeing the DNA coding strand. These events may affect double strand DNA break repairs as well as gene expression levels. With this presentation we describe a mathematical model for R-loops using a formal grammar approach. The model is trained on experimental single molecule R-loop foot-printing data. Although the model has no explicit topological information, the R-loop grammar model is able to predict R-loop formation on plasmids with varying starting topologies. These results are part of joint project with Mariel Vázquez.

Site-specific recombination modeled as a band surgery

Koya Shimokawa · Ochanomizu University

Band surgery provides a useful topological model for local reconnection phenomena involving knots and links. In site-specific recombination, a coherent band surgery describes the local action of a recombinase on circular DNA. I will first discuss our results on the stepwise unlinking of DNA catenanes, including the uniqueness of the pathway under a crossing-reducing condition and the classification of shortest pathways when the crossing number is allowed to remain unchanged. I will then explain how the same framework extends beyond DNA recombination to anti-parallel reconnection of vortex knots and links. Motivated by this application, we remove the restriction on the number of components appearing in intermediate states and obtain a substantially richer family of shortest unlinking pathways. This is a joint work with Mariel Vázquez and Kai Ishihara.