Currently, the departmental research display case showcases the research of Professors Christina TonnesenFriedman and Jeff Jauregui, who both work in the field of differential geometry. Differential geometry is the study of curved shapes that may exist in any number of dimensions.
Professor TonnesenFriedman: The overarching motivation in my research is the classification and explicit construction of Riemannian metrics with properties that generalize the Einstein property. For the first many years of my career I studied this in the realm of Kähler Geometry. I mostly focused on extremal Kähler metrics but I also considered constant scalar curvature metrics, (generalized) Ricci solitons, weakly Bochnerflat metrics, and other Kähler metrics with special geometric properties.
In the last few years I have expanded this interest to include the odddimensional sibling of Kähler geometry, namely Sasakian Geometry.

Professor Jauregui: I work in geometric analysis, emphasizing connections with general relativity. Einstein’s theory of general relativity describes the universe as a spacetime, a fourdimensional continuum describing all points, past, present and future. Gravitational effects manifest through the curvature of spacetime, and thus geometry plays an important role in the theory. My research has involved scalar curvature and has explored connections between mass and geometry, including “quasilocal” mass and the total “ADM” mass of a spacetime.
My current interests include codimensiontwo geometric flows within a spacetime, analyzing limits of sequences of asymptotically flat manifolds, and Bartnik’s quasilocal mass conjectures.

(Please view last year’s display case here.)