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# UCLA professors Andrea Ghez, Terence Tao honored by Royal Swedish Academy of Sciences

Two internationally renowned UCLA professors — Andrea Ghez, a professor of physics and astronomy, and Terence Tao, a professor of mathematics — have been awarded the Crafoord Prize by the Royal Swedish Academy of Sciences.

The prize, which recognizes extraordinary achievements in mathematics, astronomy and other fields, is among the most prestigious honors in science.

Ghez and Germany’s Reinhard Genzel share the 2012 Crafoord Prize in Astronomy for their research on stars orbiting the center of the Milky Way galaxy indicating the presence of a supermassive black hole. The two, working independently of one another, have discovered "the most reliable evidence to date that supermassive black holes really exist," the Royal Swedish Academy of Sciences announced, saying their research "allows astronomers to better investigate gravity and explore the limitations of the theory of relativity."

Tao shares the 2012 Crafoord Prize in Mathematics with Princeton University’s Jean Bourgain for their "brilliant and groundbreaking work in harmonic analysis, partial differential equations, ergodic theory, number theory, combinatorics, functional analysis and theoretical computer science," the academy said. "Their deep mathematical erudition and exceptional problem-solving ability have enabled them to discover many new and fruitful connections and to make fundamental contributions to current research in several branches of mathematics... They have developed and used the toolbox of analysis in groundbreaking and surprising ways." Tao and Bourgain also have worked independently of each other.

"Andrea Ghez and Terry Tao are two of UCLA’s true superstars — indeed, two of the world’s intellectual superstars," said Joseph Rudnick, dean of the UCLA Division of Physical Sciences. "Of course, we knew this long before they were honored by the Royal Swedish Academy of Sciences, but we are delighted to see that Andrea and Terry have both been awarded the Crafoord** **Prize on the same day."

Since 1995, Ghez has used the Keck Observatory, which sits atop Hawaii’s dormant Mauna Kea volcano, to study the rotational center of the Milky Way and the movement of hundreds of stars close to this galactic center.

"I am really thrilled that the research done at UCLA has been recognized with this award," said Ghez, who holds UCLA’s Lauren B. Leichtman and Arthur E. Levine Chair in Astrophysics. "This research was possible thanks to the W.M. Keck Observatory, which houses the two largest telescopes in the world; they have enabled us to achieve the tremendous progress that we have made in correcting the distorting effects of the Earth’s atmosphere with high–angular resolution imaging. The most recent technology of adaptive optics is now opening up new horizons and allowing us to learn even more about this black hole at the center of our galaxy — how it was formed, how it grows and how to correctly describe the properties of space and time in the vicinity of such an exotic object."

Ghez added that she is "delighted to be the first woman to be awarded this prize" and that she especially enjoys "being a role model to women science students."

Tao said that we are living in a "golden age for mathematics" and that mathematics has become much more collaborative and interdisciplinary than in the past.

"We use math all the time without even knowing it," said Tao, who holds the James and Carol Collins Chair in the UCLA College of Letters and Science. "When we use Google, for example, to find a Web page, there is a lot of powerful mathematics that we take for granted occurring behind the scenes."

Speaking about his approach to solving mathematical problems, Tao said, "If I don’t understand something properly, every single component, it really bugs me. I don’t like accepting things at face value." He also said he learns much from the feedback he receives from other mathematicians on his mathematics blog.

Ghez, who was selected as a 2008 MacArthur Fellow , among many other prestigious honors, uses novel, ground-based telescopic techniques to identify thousands of new star systems and illuminate the role of supermassive black holes in the evolution of galaxies.

In 1998, she answered one of astronomy’s most important questions, showing that a monstrous black hole resides at the center of our Milky Way galaxy, some 26,000 light-years away from Earth, with a mass more than 3 million times that of the sun. The question had been a subject of raging debate among astronomers for more than a quarter of a century.

One reason astronomers had been unable to determine whether a black hole was at the galactic center is that the Earth’s atmosphere distorts the images of stars.

Ghez used a technique she refined known as speckle interferometry, which involves taking thousands of very quick, high-resolution snapshots that correct for these distortions. She has developed algorithms — specific computer commands based on sophisticated mathematics — and software for analyzing the data.

While traditional imaging techniques at the center of the galaxy cause the stars closest to the galactic center to look fuzzy and indecipherable, Ghez’s technique improves the resolution by a factor of at least 20.

In 2000, Ghez and colleagues reported that for the first time, astronomers had seen stars accelerate around a supermassive black hole. Their research demonstrated that three stars had accelerated by more than 250,000 mph a year as they orbited the black hole at the center of the Milky Way. They also reported, based on five years of measurements, that the star closest to the black hole had turned a corner in its orbit.

"We are actually seeing stars begin to curve in their orbits," she said at the time. "One of these stars may complete its orbit around the supermassive black hole in as little as 15 years."

In 2003, Ghez reported that the case for the Milky Way’s black hole had been strengthened substantially and that all of the proposed alternatives could be excluded.

In 2005, she and her colleagues took the first clear picture of the center of the Milky Way, including the area surrounding the black hole, using laser guide star adaptive optics technology at Hawaii’s Keck Observatory.

Compared with the earlier approach of speckle imaging, adaptive optics is much more powerful, allowing astronomers to correct the distorting effects of the Earth’s atmosphere in real time, as opposed to post-processing, and to do so much more effectively. With this technology at the Keck Observatory, Ghez and her colleagues have revealed many surprises about the environment surrounding supermassive black holes, discovering young stars where none were expected and seeing a lack of old stars where many were anticipated. These observations are challenging our notions about how supermassive black holes and their host galaxies grow over time.

Black holes are collapsed stars so dense that nothing can escape their gravitational pull, not even light. They cannot be seen directly, but their influence on nearby stars is visible and provides a signature, Ghez said.

Tao, the first faculty member in UCLA’s history to win the prestigious Fields Medal , often described as the "Nobel Prize in mathematics," is widely considered one of the world’s leading mathematicians.

Tao has received numerous national and international honors, including a MacArthur Fellowship and the National Science Foundation’s Alan T. Waterman Award , the highest honor the NSF bestows. He was named among the " Best Brains in Science " by Discover magazine, which praised him as "one of the most prolific and esteemed mathematicians in the nation," and was honored as one of science’s " Brilliant 10 " by Popular Science magazine, which called him "math’s great uniter," to whom "the traditional boundaries between different mathematical fields don’t seem to exist."

"Terry is like Mozart; mathematics just flows out of him," said John Garnett, a professor and former chair of mathematics at UCLA, "except without Mozart’s personality problems; everyone likes him. Mathematicians with Terry’s talent appear only once in a generation. Terry can unravel an enormously complicated mathematical problem and reduce it to something very simple."

Discover magazine praised Tao’s research on prime numbers, conducted with Ben Green, a professor of mathematics at the University of Bristol in England, as one of the 100 most important discoveries in all of science for 2004. A number is prime if it is larger than one and divisible by only itself and one. The primes begin with 2, 3, 5, 7, 11, 13 and 17.

Euclid proved that the number of primes is infinite. Tao and Green proved that the set of prime numbers contains infinitely many progressions of all finite lengths. An example of an equally spaced progression of primes, of length three and space four, is 3, 7, 11; the largest known progression of prime numbers is length 23, with each of the numbers containing 16 digits. Green and Tao’s discovery reveals that somewhere in the prime numbers, there is a progression of length 100, one of length 1,000, and one of every other finite length, and that there are an infinite number of such progressions in the primes.

To prove this, Tao and Green spent two years analyzing all four proofs of a theorem named for Hungarian mathematician Endre Szemerédi. Very few mathematicians understand all four proofs, and Szemerédi’s theorem does not apply to prime numbers.

"We took Szemerédi’s theorem and goosed it so that it handles primes," Tao said. "To do that, we borrowed from each of the four proofs to build an extended version of Szemerédi’s theorem. Every time Ben and I got stuck, there was always an idea from one of the four proofs that we could somehow shoehorn into our argument."

Tao is also well-known for his work on the "Kakeya conjecture," a perplexing set of five problems in harmonic analysis. One of Tao’s proofs extends more than 50 pages, in which he and two colleagues obtained the most precise known estimate of the size of a particular geometric dimension in Euclidean space. The issue involves the most space-efficient way to fully rotate an object in three dimensions, a question of interest to theoretical mathematicians.

Tao and colleagues Allen Knutson at UC Berkeley and Chris Woodward at Rutgers University solved an old problem (proving a conjecture proposed by former UCLA professor Alfred Horn) for which they developed a method that also solved longstanding problems in algebraic geometry and representation theory.

Speaking of this work, Tao has said, "Other mathematicians gave the impression that the puzzle required so much effort that it was not worth making the attempt, that first you have to understand this 100-page paper and that 100-page paper before even starting. We used a different approach to solve a key missing gap."

Tao found a surprising result to an applied mathematics problem involving image processing with California Institute of Technology mathematician Emmanuel Candčs; their collaboration was forged while they were taking their children to UCLA’s Fernald Child Care Center. Chan said that Tao and Candčs’ work is providing important insights into how to compress images, which has applications for medical imaging.

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