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Click here for my best wishes to the Duke University graduating class of 2020! (Lower resolution version here.)

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Hubert Lewis Bray
Professor Bray 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. Professor Bray has proposed geometric explanations for dark matter which he calls "wave dark matter," which motivate very interesting questions about geometric partial differential equations.

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 8 math Ph.D. graduates at Duke from 2006 to 2017. He is currently supervising two math Ph.D. students and two physics Ph.D. students. His most recent 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.

ON THE JOB MARKET: Yiyue Zhang (math) and Ben Hamm (physics), current 5th year graduate students working with Professory Bray who are doing excellent research and are great teachers too. While each have their own specialties, both have also been exposed to an unusually broad range of research topics across both mathematics and physics.

Yiyue Zhang (Ph.D. candidate in math) has three papers on the arXiv and another on the way. His solo paper is on proving new scalar curvature volume comparison theorems with weak additional hypotheses. With coauthors, he found a new proof of Bishop's volume comparison theorem for Ricci curvature using novel techniques involving singular soap bubbles that work in all dimensions. With Ben Hamm and others, he also collaborated on a paper which defines a new theory between special relativity and general relativity that we are calling flatly foliated relativity, a toy theory of gravity which is easier to understand than general relativity because it does not model gravitational waves. Finally, Yiyue is currently taking the lead writing up a fourth paper (with coauthors) on a new result that generalizes the hyperbolic positive mass theorem in three dimensions.

Ben Hamm (Ph.D. candidate in physics) has two papers on the arXiv and another in progress. His main paper is the first of its kind that shows that an up-and-coming theory of dark matter (wave / fuzzy / scalar field / Bose-Einstein condensate dark matter) is consistent with the observations about spiral galaxies in the universe called the Baryonic Tully-Fisher Relation on the median velocity of stars and the total mass of the galaxies in which they reside. This widely studied model of dark matter has a fundamental constant, the mass of the boson dark matter particle, which Ben and others in our group are in the process of estimating. More generally, Ben is extremely knowledgeable about the area of theoretical astrophysics attempting to relate observations about dark matter to understanding dark matter's true nature.









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.

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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. All of the atoms that make up us and our world, except for hydrogen, helium, and some lithium atoms, were created inside stars which later exploded, the aftermaths of which would have looked something like this.