Joel Aaron Tropp (born July 1977 in

Austin, Texas Austin ( ) is the List of capitals in the United States, capital city of the U.S. state of Texas. It is the county seat and most populous city of Travis County, Texas, Travis County, with portions extending into Hays County, Texas, Hays and W ...

) is the Steele Family Professor of Applied and Computational Mathematics in the Computing and Mathematical Sciences Department at the

California Institute of Technology The California Institute of Technology (branded as Caltech) is a private research university in Pasadena, California, United States. The university is responsible for many modern scientific advancements and is among a small group of institutes ...

. He is known for work on

sparse approximation Sparse approximation (also known as sparse representation) theory deals with sparse solutions for systems of linear equations. Techniques for finding these solutions and exploiting them in applications have found wide use in image processing, signa ...

numerical linear algebra Numerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathemati ...

, and

random matrix theory In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all of its entries are sampled randomly from a probability distribution. Random matrix theory (RMT) is the s ...

Academic biography

Tropp studied at the

University of Texas The University of Texas at Austin (UT Austin, UT, or Texas) is a public research university in Austin, Texas, United States. Founded in 1883, it is the flagship institution of the University of Texas System. With 53,082 students as of fall 2 ...

, where he completed the BS degree in Mathematics and the BA degree in

Plan II Honors The University of Texas at Austin (UT Austin, UT, or Texas) is a public research university in Austin, Texas, United States. Founded in 1883, it is the flagship institution of the University of Texas System. With 53,082 students as of fall 202 ...

in 1999 and the MS and PhD degrees in Computational & Applied Mathematics in 2001 and 2004.Joel A. Tropp, ''curriculum vitae''
. Retrieved August 5, 2014 His dissertation was titled ''Topics in Sparse Approximation'', and his advisers were Inderjit Dhillon and Anna C. Gilbert. He taught at the

University of Michigan The University of Michigan (U-M, U of M, or Michigan) is a public university, public research university in Ann Arbor, Michigan, United States. Founded in 1817, it is the oldest institution of higher education in the state. The University of Mi ...

from 2004 to 2007. He has been on the faculty of the

since 2007.

Research

In his early research, Tropp developed performance guarantees for algorithms for

and

compressed sensing Compressed sensing (also known as compressive sensing, compressive sampling, or sparse sampling) is a signal processing technique for efficiently acquiring and reconstructing a Signal (electronics), signal by finding solutions to Underdetermined s ...

. In 2011, he published a paper on randomized algorithms for computing a truncated

singular value decomposition In linear algebra, the singular value decomposition (SVD) is a Matrix decomposition, factorization of a real number, real or complex number, complex matrix (mathematics), matrix into a rotation, followed by a rescaling followed by another rota ...

. He has also worked in random matrix theory, where he has established a family of results, collectively called ''matrix concentration inequalities'', that includes the matrix Chernoff bound.

Awards and honors

Tropp was a recipient of the

Presidential Early Career Award for Scientists and Engineers The Presidential Early Career Award for Scientists and Engineers (PECASE) is the highest honor bestowed by the United States federal government on outstanding scientists and engineers in the early stages of their independent research careers. T ...

(PECASE) in 2008. In 2010, he was awarded an

Alfred P. Sloan Research Fellowship The Sloan Research Fellowships are awarded annually by the Alfred P. Sloan Foundation since 1955 to "provide support and recognition to early-career scientists and scholars". This program is one of the oldest of its kind in the United States. ...

in Mathematics, and he received the Sixth Vasil A. Popov Prize in approximation theory for his work on

Matching Pursuit Matching pursuit (MP) is a sparse approximation algorithm which finds the "best matching" projections of multidimensional data onto the span of an over-complete (i.e., redundant) dictionary D. The basic idea is to approximately represent a sign ...

algorithms. He won the Eighth Monroe H. Martin Prize in applied mathematics in 2011 for work on sparse optimization. He was recognized as a Thomson Reuters Highly Cited Researcher in Computer Science for the years 2014, 2015, and 2016. In 2019 he was named a

SIAM Fellow The SIAM Fellowship is an award and fellowship that recognizes outstanding members of the Society for Industrial and Applied Mathematics (SIAM). The goal of the program is to: *honor SIAM members who are recognized by their peers as distinguishe ...

"for contributions to signal processing, data analysis, and randomized linear algebra".

References

External links

Joel A. Tropp professional home page
{{DEFAULTSORT:Tropp, Joel Aaron 1977 births Living people University of Texas at Austin alumni California Institute of Technology faculty 20th-century American mathematicians Sloan Research Fellows Fellows of the Society for Industrial and Applied Mathematics Mathematicians from Texas 21st-century American mathematicians University of Michigan faculty Recipients of the Presidential Early Career Award for Scientists and Engineers