Brendan Mallery

I am a 5th year PhD candidate studying mathematics at Tufts University, working with Professors James Murphy and Shuchin Aeron. I obtained a Masters in mathematics from SUNY Albany in 2020, and a B.A. in mathematics and chemistry from Bowdoin College in 2018. For more details, see my CV.

I am broadly interested in applications of optimal transportation to data science and machine learning. I am particularly intersted in developing ideas from sparse-signal processing and representation learning in Wasserstein space. My ongoing projects are:

• Developing theory and algorithms for transport map dictionary learning, for nonlinear dimensionality reduction on probability measure valued data.
• Establishing quantitative regularity results for entropy-regularized optimal transportation, with applications to Wasserstein gradient flows.

In addition to my dissertation work, I am also interested in:

• Modeling and analysis of time-evolving networks;
• Interactions between optimal transport and Ricci curvature;

I was introduced to the first topic through my work at NASA Glenn Research & Goddard Space Flight Centers (2020-2023). I have also published work in topological data analysis and geometric group theory.