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Click here for my best wishes to the Duke University graduating class of 2020! (Lower resolution version here.)
Click here to see our Pi Day celebration in 2022 (pie eating contest, digits of pi recitation contest, and pieing of 4 math professors) hosted by The Lyceum, our interdisciplinary math social club. Thanks to Fayfay Ning, the Lyceum president, for organizing this event!

Hubert Lewis Bray
Professor Bray's research uses differential geometry to understand general relativity, and general relativity to motivate interesting problems in differential geometry. In 2001, he published his proof of the Riemannian Penrose Conjecture about the mass of black holes using geometric ideas related to minimal surfaces, scalar curvature, conformal geometry, geometric flows, and harmonic functions. He is also interested in the large-scale unexplained curvature of the universe, otherwise known as dark matter, which makes up most of the mass of galaxies. This motivates very interesting questions about geometric partial differential equations and the dynamics of spiral galaxies.

Professor Bray received his Ph.D. in mathematics from Stanford University in 1997 under the direction of Richard Schoen. He then spent one year as an NSF postdoc at Harvard supervised by S.-T. Yau, before going to MIT where he was an instructor, an assistant professor, and an associate professor. Professor Bray accepted an associate professorship at Columbia in 2003 and a full professorship at Duke in 2004, where he resides today as a professor of mathematics and physics. He has been married since 2004 and has six children.

Professor Bray has supervised 10 Ph.D. graduates (9 in math, 1 in physics) at Duke from 2006 to 2021. His 2017 Ph.D. graduate, Henri Roesch, proved a Null Penrose Conjecture, open since 1973, as his thesis. While the physical motivation about the mass of black holes is the same as for the Riemannian Penrose Conjecture, the geometry involved is almost unrecognizably different, and may be viewed as a fundamental result about the geometries of light cones and other null hypersurfaces in curved spacetimes.

Professor Bray has also supervised 8 undergraduates who wrote senior theses in math at Duke, from 2009 to 2021. Among them is Daniel Stern who wrote his 2014 senior thesis on classifying general relativity type actions of a certain form from a geometric perspective.  Daniel's 2019 paper "Scalar curvature and harmonic maps to S^1" represents a new technique for understanding scalar curvature, a fundamental concept in geometric analysis, and hence has been very influential in the field. Among many other applications, this new approach has led to new explicit formulas for the total mass of asymptotically flat and asymptotically hyperbolic 3-manifolds, which yield the corresponding versions of the Positive Mass Theorem as corollaries.

Three recommended books that students can read to get into some of these subjects are

"Differential Geometry" by John Oprea (for undergraduates), "Semi-Riemannian Geometry" by Barrett O'Neill (for graduate students), and "Geometric Relativity" by Dan Lee (for advanced graduate students). Professor Lee collaborated with Professor Bray on the proof of the Riemannian Penrose Conjecture in dimensions less than eight as a postdoc at Duke from 2005 to 2008.

Hubert Lewis Bray (1970 - ) is named after his dad's dad, Hubert Evelyn Bray (1889 - 1978), who was also a mathematician. The original Hubert Bray received the first Ph.D. awarded by Rice University in 1918 and joined the faculty of the mathematics department thereafter. He was chairman from 1935 to 1957, secretary of the faculty from 1935 to 1959, and chairman of the Committee on Outdoor Sports from 1920 to 1959, a job analogous to being the athletic director today. He was initially asked to serve in this job in 1920 because, as a mathematician, he could be trusted to reliably average the multiple stop watches used to determine the track times at Rice track meets. Upon his first retirement in 1959 he was named "Trustees' Distinguished Professor of Mathematics" for his long service to Rice. He continued to teach classes until 1970 at age 81. His grandson, Hubert Lewis Bray, attended Rice as an undergraduate from 1988 to 1992 and won the Hubert E. Bray Prize in Mathematics, awarded annually to the outstanding junior mathematics major. This 1927 photo captures some of the history of the Rice Mathematics Department, showing the entire department - faculty, staff, and graduate students - all 11 of them, including Mandelbrojt who was visiting as a guest lecturer. From left to right: E.R.C. Miles, David Widder, Miss Alice Dean , S. Mandelbrojt (visiting from France), Nat Edmondson, Arthur Copeland, H.E. Bray, May Hickey (Maria), G.C. Evans (namesake for Evans Hall, the math building at UC Berkeley), R. N. Haskell, and J. Gergen, then a graduate student, who later became department chairman at Duke from 1937 to 1966. In this photo, Hubert Evelyn Bray (seated) and Jess Nealy, the head football coach, appear together with the Cotton Bowl Trophy. This video reflects on the first one hundred years of Rice University.

The above image shows a small section of the Veil Nebula, as it was observed by the NASA/ESA Hubble Space Telescope. This section of the outer shell of the famous supernova remnant is in a region known as NGC 6960 or, more colloquially, the Witch's Broom Nebula. Many of the atoms that make up our world were created inside stars which later exploded, the aftermaths of which would have looked something like this.