Nicolas is currently an Assistant Professor in the Department of Statistics at the University of Wisconsin-Madison. He finished his PhD in mathematics at Carnegie Mellon University in 2015; his adviser was Dejan Slepčev.
His academic interests lie at the intersection of applied analysis, applied probability, statistics, and machine learning. The main motivation of his research work is to provide mathematical foundations to data analysis and machine learning algorithms that can help provide insights about the methodologies used in practice for the analysis of complex data, as well as help design new algorithms that can tackle the computational bottlenecks of working with large high dimensional data sets. When studying a certain data analysis methodology, his approach is to first seek a well posed continuum analogue that can work as an ideal population level counterpart. The population level methodologies that he typically studies take the form of variational problems or geometric problems on continuum non-parametric settings. Studying these ideal methodologies requires a combination of tools from PDE theory, geometric measure theory, and ODEs in the space of probability measures taken with respect to optimal transport distances.
- Geometric Methods in Optimization and Sampling, Fall 2021. Visiting Scientist.