Professor H. L. Bray
More Cool Stuff
Click here for my best wishes to the Duke University graduating class of 2020! (Lower resolution version 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!
Click here to see my presentation "Einstein's Greatest Ideas" for the general public of these slides that I gave at Cornell University in 2023.
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.
Hubert Lewis Bray
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 12 Ph.D. graduates (10 in math, 2 in physics) at Duke from 2006
to 2023. 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
On the job market this year:
Yiyue Zhang (Duke
Ph.D. 2021, currently a postdoc at UC-Irvine working with Richard
Schoen). Yiyue (with Sven Hirsh) proved the most general rigidity case
of the case of equality of the Positive Mass Theorem. He is also an
expert on scalar curvature, Ricci curvature, and 2-Ricci curvature. He
and his collaborators also proved new geometric theorems which have
deep implications about the formation of black holes, which was
featured in Quanta Magazine. Click here to read about it.
Bray has also supervised 8 undergraduates who wrote senior theses in
math at Duke, from 2009 to 2021. Among them is Zhenhua Liu (Princeton
Ph.D. expected in 2024) who graduated from Duke in 2019 with highest
honors. His senior
thesis, "Stationary one-sided area-minimizing hypersurfaces with
isolated singularities" foreshadowed the amazing career he is now
having, even as a graduate student.
Another former Duke math major is Daniel Stern, now a professor at Cornell, 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.
These results were further extended by Sven Hirsch, Demetre Kazaras, and Marcus Khuri
who generalized the harmonic functions used above to define a new
useful tool called spacetime harmonic functions. This leads to a new explicit formula
relating the total energy and total momentum of a slice of a spacetime
to the local energy and momentum density of the spacetime on the
spacelike slice, no matter what the second fundamental form of the
slice may be. The Spacetime Positive Mass Theorem follows as a
corollary. They then joined forces with Yiyue Zhang to prove purely geometric comparison theorems
for Riemannian bands involving scalar curvature, Ricci curvature, and
2-Ricci curvature using these same spacetime harmonic functions.
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.
now a professor at Michigan State, was as a postdoc at Duke from 2020
to 2023. During that time, he helped Professor Bray lead his research
group which included Yiyue
Zhang (math Ph.D. 2021), Ben Hamm (physics Ph.D. 2021), Sven Hirsch (math Ph.D. 2023), James Wheeler (physics Ph.D. 2023), Michael Lin (math Ph.D. exp.
2024), and Kai Xu (math Ph.D. exp. 2025). Professor Marcus Khuri (SUNY - Stony Brook) has
also co-supervised the group with Professor Bray since 2020 via weekly zoom meetings.
Professor Bray's other graduate students who have done and continue to
do fascinating work in geometric analysis and mathematical relativity
include Hangjun Xu (math Ph.D. 2014), Mau-Kwong "George" Lam (math
Ph.D. 2011), Graham Cox (math Ph.D. 2011), Jeff Jauregui (math Ph.D. 2010), and Nicholas Robbins (math Ph.D. 2007). A full list of Professor Bray's graduate students is here.
Professor Bray is also very interested in dark matter and its role in the universe. James Wheeler
(physics Ph.D. 2023), now a postdoc at the University of Michigan working with Lydia Bieri, has done fantastic work modeling the universe
since the Big Bang and the resulting power spectrum for the cosmic
microwave background radiation which would be predicted given different
assumptions about the role of dark matter in the early universe. He is
exploring whether or not different, more geometric models of dark
matter can explain the Hubble tension, refering to the discrepancy
between measurements of the Hubble constant via supernovas versus the
cosmic microwave background radiation, the latter of which makes
assumptions about the nature of dark matter. James has also found a
new, mathematically natural definition of black holes in terms of the
abstract boundary of a spacetime and has improved our understanding of
how naked singularities can form in spherically symmetric spacetimes.
James work follows in the footsteps of three other former Ph.D.
students of Professor Bray's who studied dark matter as well: Ben Hamm (physics Ph.D. 2021), Andrew Goetz (math Ph.D. 2015), and Alan Parry (math Ph.D. 2013).
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 at Rice. 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. For more information about Hubert Lewis Bray as a person, click here.
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.