Jeff Jauregui, Graduate Student

Contact Info:

Office Location:	025 Physics Bldg
Office Phone:	(919)-660-2832
Email Address:

Education:

MA, Mathematics	Duke University	2006
BS, Mathematics and Physics	Harvey Mudd College	2005

Specialties:

Geometry
Mathematical Physics

Research Interests: General Relativity, geometric flows

Almost a century after its introduction, General Relativity continues to produce many interesting geometric problems. Some of the major results in the past few decades are the positive mass theorem and the Penrose inequality, both of which estimate the mass of a spacetime in terms of its geometry. Currently I am studying related inequalities which use curvature data to sharpen the bounds.

The Yamabe Invariant of a smooth manifold is a number, defined geometrically, whose value takes on topological significance. Yamabe invariants have the potential to provide a deeper understanding of the topology of closed 3-manifolds, but they are often very difficult to compute. Recently many surprising connections have been made between Yamabe-like problems and problems in General Relativity. Much of what I study touches on such connections, especially the idea of inverse mean curvature flow.

Selected Talks

1. Yamabe Invariants and Ricci Flow, October 22, 2007, Duke Geometry Seminar    

Recent Grant Support

• NSF Graduate Research Fellowship, National Science Foundation, 2006/08-2009/08.      
• James B. Duke Fellowship, Duke University Graduate School, 2005/09-2009/05.