Dr. Grigoris Paouris, assistant professor of mathematics at Texas A&M University, has been selected to receive a 2012 National Science Foundation (NSF) Faculty Early Career Development (CAREER) Award in support of his research on the underlying geometry of high-dimensional probability measures.

Paouris' project, "Geometry of Measures in High Dimensions," is a continuing grant funded through the Division of Mathematical Sciences through May 2017. His long-term research goal is to investigate the properties of high-dimensional probability measures in order to understand the geometry that serves as its underpinning -- knowledge which has broad implications in a variety of mathematical fields, from classical analysis to probability theory.

A member of the Texas A&M Department of Mathematics faculty since 2008, Paouris is a leading expert in the area of functional analysis with emphasis on convex geometry. He has spent the last decade examining how the volume of a convex region in high-dimensional space relates to the area of its cross-sectional slices -- work that has significant applications to statistical physics, computer science and learning theory. Arguably one of the department's fastest rising stars, he recently was named a 2011 Sloan Research Fellow of the Alfred P. Sloan Foundation -- one of only 21 mathematicians nationwide to earn selection.

"Following his Sloan Fellowship with an NSF CAREER award this year is a feat that places Dr. Paouris into a stellar group," says Dr. Emil J. Straube, professor and head of the Texas A&M Department of Mathematics. "We are fortunate to have him here.

"Dr. Paouris is one of the outstanding young faculty members that the department hired under the university's reinvestment program. This talented young cohort has brought in several Sloan Fellowships and CAREER awards during the last few years."

Paouris' grant is one of 11 CAREER awards announced thus far in 2012 across the overall Texas A&M campus, which currently boasts six in the Dwight Look College of Engineering, three in the College of Science (Paouris' as well as one each to Dr. Helmut Katzgraber in the Department of Physics and Astronomy and to Dr. Wenshe Liu in the Department of Chemistry), one in the College of Agriculture and Life Sciences and one in the Texas A&M University Health Science Center.

Paouris' NSF-funded work will continue to focus on high-dimensional measures and, in particular, on their tendency to congregate around typical forms -- a relatively new discovery. His proposal is dedicated to the investigation of these phenomena as well as to advancing theory that already has seen significant application in probability, combinatorics, mathematical physics and informatics, with the recurrent theme being that of extending known results to a much broader setting without any assumptions on "randomness." Paouris hopes that any progress in the direction of this proposal will be of great significance to every field interested in high-dimensional phenomena.

"This is a rapidly developing new field full of challenging questions and with many interactions between various fields," Paouris says. "The CAREER grant gives me the opportunity to communicate with and learn from specialists in other fields, to strengthen these interactions and to collaborate with many young talented scientists -- a fascinating perspective that I optimistically predict will be quite challenging and fruitful."

Paouris says the main goal of this research program is to reveal and quantify the structure, or geometry, of high-dimensional measures. Although the primary focus is on log-concave measures, which are of particular interest to the statistical mechanics, he says that results for general high-dimensional measures have already appeared, indicating there is more to be discovered. He notes these encouraging results have been initiated at least in part as a result of questions posed from computer science and random algorithmic theory -- issues of widespread theoretical importance, given that they lie at the intersection of probability theory, convexity and functional analysis.

NSF established the CAREER program to support junior faculty within the context of their overall career development, combining in a single program the support of research and education of the highest quality and in the broadest sense.

Through this program, the NSF emphasizes the importance on the early development of academic careers dedicated to stimulating the discovery process in which the excitement of research is enhanced by inspired teaching and enthusiastic learning.

For more on the NSF and the CAREER program, visit http://www.nsf.gov/funding/pgm_summ.jsp?pims_id=503214.

Click here to learn more about Paouris and his research.


Contact: Shana K. Hutchins, (979) 862-1237 or shutchins@science.tamu.edu or Dr. Grigoris Paouris, (979) 845-1474 or grigoris@math.tamu.edu

Hutchins Shana

  • Dr. Grigoris Paouris

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