Previous Work in Algebraic Topology

Before transitioning to Topological Data Analysis (TDA), my Ph.D. research focused on knot theory through the lens of Goodwillie-Weiss Calculus. By sampling a knot with an increasing number of points, one obtains an approximation of the space of all knots through a discrete sequence of finite configurations. This process gives rise to the Goodwillie-Sinha Spectral Sequence, that provides precious information on the cohomology of the space of all knots.

My contribution, in collaboration with Prof. Salvatore, involved studying this spectral sequence modulo 2, resolving a conjecture by Vassiliev. As zero-dimensional cohomology of the space of all knots describes knot invariants, these calculations have the potential to shed light on classical problems from knot theory.

In parallel, I am working with Dr. Casarin on infinity-categorical approaches to multicomplexes—a homotopic deformation of bicomplexes that enables significant simplifications in spectral calculations. We plan to extend the multicomplex-based methods from my Ph.D. thesis, developed for the Goodwillie-Sinha Spectral Sequence, to a broader class of Bousfeld-Kan spectral sequences.

Collaboration & Contact

I welcome collaborations, particularly in applying TDA and ML to biomedical data science. If you’re interested in working together, feel free to reach out at:

andreamarino [at] uvic [dot] ca