Math Department Awarded Major NSF Research Training Grant

The Topology and Geometry group in the Department of Mathematics is happy to announce that they are the recipient of a five year $2.5 million Research Training Group grant from the National Science Foundation. The NSF RTG program is aimed at strengthening the nation’s scientific competitiveness by increasing the number of well-prepared U.S. residents who pursue careers in the mathematical sciences. Nationally, roughly 5 RTG grants are awarded each year by the NSF to support efforts to improve research training by involving undergraduate students, graduate students, postdoctoral associates, and faculty members in structured research groups centered on a common research theme.

Geometric Topology and Algebraic Topology are areas of mathematics in which one is trying to understand aspects of the global shape of objects, with tools for doing this coming from various mathematical disciplines. Most classically, the objects of study are curves, surfaces, and higher dimensional analogues of these - manifolds, but modern topology also studies things like the ‘shape’ of algebraic structures like number systems satisfying an associative law. Symmetries, in the guise of group theory, also play a major role. Applications range from the use of curvature and symmetry in mathematical physics to the use of homology theory in the emerging field of topological data analysis.

THE UVA TOPOLOGY GROUP

The University of Virginia has a long and strong legacy of research in topology. The current UVA topology faculty, who will be leading the RTG activities, are as follows.

• Julia Bergner (Professor) studies algebraic and higher categorical structures in- formed by the homotopical methods of algebraic topology.
• Thomas Koberda (Associate Professor) studies geometric group theory, particu- larly groups arising as symmetries on curves and surfaces.
• Slava Krushkal (Professor) works in low-dimensional and geometric topology, with interests including 3 and 4 dimensional manifolds and quantum topology.
• Nicholas Kuhn (Professor) is an algebraic topologist who studies the interplay between stable, unstable, and chromatic homotopy.
• Sara Maloni (Assistant Professor) has interests lying at the intersection of geom- etry and low-dimensional topology, studying deformations of geometric structures.
• Thomas Mark (Professor) studies the differential and symplectic topology of 3 and 4 dimensional manifolds, and developing tools for their study.