Faculty
Piotr Hajlasz
Piotr Hajlasz has been awarded the 2021 Sierpiński Medal by the University of Warsaw together with the Polish Mathematical Society. This international award has been granted to outstanding mathematicians with Polish associations since 1974. Past recipients include Paul Erdős and Benoit Mandelbrot. Hajlasz received this medal for his "contributions to the theory of Sobolev spaces, geometric analysis, and the theory of function spaces". In 1996, Hajlasz generalized Sobolev spaces to general metric spaces. Since then, this subject has been developed by many researchers and as of 2020, the theory of Sobolev spaces on metric spaces has been recognized as a separate area in the Mathematics Subject Classification. Hajlasz has also been named a Fellow of the American Mathematical Society in 2017 for "contributions to analysis in metric spaces, in particular the notion of Sobolev spaces in metric-measure spaces also known as Hajlasz-Sobolev spaces". The theory of Sobolev spaces on metric spaces is a part of a broader area called analysis on metric spaces.
Analysis on metric spaces and quantitative topology is nowadays an active and independent field bringing together researchers from disparate parts of the mathematical spectrum. While classical topology aims to study spaces and functions that are continuous but not smooth, analysis often deals with smooth objects like manifolds and smooth functions. Nonetheless, non-smooth functions such as Sobolev functions have been studied in analysis, but they were defined on smooth objects: domains in Euclidean space, or more generally, Riemannian manifolds. Both the theories of classical topology and analysis have been constantly developed since the nineteenth century, building the framework for contemporary mathematics and its applications. However, in the last thirty years, we have witnessed the emergence of new directions in mathematics--analysis on metric spaces and quantitative topology--leading to new bridges between the distant worlds of non-smooth topology and smooth analysis. These new directions have far-reaching applications to areas as diverse as geometric group theory, nonlinear partial differential equations, and even theoretical computer science. Hajlasz's most recent research project funded by the US National Science Foundation aims at investigating the broad spectrum of problems in analysis on metric spaces and quantitative topology while including other related problems in analysis.
http://www.mathematics.pitt.edu/people/piotr-hajlasz.
Jason DeBlois
Professor DeBlois Takes the Helm as Undergraduate Director
Last September, Jason DeBlois took over as Undergraduate Director from Professor Juan Manfredi. Jason writes, “while I have faced some challenges learning the ropes at a time of high staff turnover, Juan and Paul Gartside (Undergrad Director before Juan) have been very helpful, as has (senior administrator) Carol Miller. And our newly hired academic coordinator Cynthia Romo is already doing a great job: she’s working hard and rapidly mastering the university’s systems. I look forward to working with them and all of you to ensure the undergraduate program’s continued success. The department’s strategic planning process offers a near-term opportunity for your input, as we have identified the undergraduate program as a focus area.”
http://www.mathematics.pitt.edu/people/jason-deblois.