Joel Aaron Tropp (born July 1977 in

Austin, Texas Austin is the capital city of the U.S. state of Texas, as well as the county seat, seat and largest city of Travis County, Texas, Travis County, with portions extending into Hays County, Texas, Hays and Williamson County, Texas, Williamson co ...

) 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 or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...

. 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, sign ...

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 mathematics. ...

, 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 elements are random variables. Many important properties of physical systems can be represented mathemat ...

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. It was founded in 1883 and is the oldest institution in the University of Texas System. With 40,916 undergraduate students, 11,075 ...

, 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. It was founded in 1883 and is the oldest institution in the University of Texas System. With 40,916 undergraduate students, 11,075 ...

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 Anna Catherine Gilbert (born 1972) is an American mathematician who works as the Herman Goldstine Collegiate Professor of Mathematics at the University of Michigan. She also holds a courtesy appointment in electrical engineering and computer sci ...

. He taught at the

University of Michigan , mottoeng = "Arts, Knowledge, Truth" , former_names = Catholepistemiad, or University of Michigania (1817–1821) , budget = $10.3 billion (2021) , endowment = $17 billion (2021)As o ...

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 ...

. 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 factorization of a real or complex matrix. It generalizes the eigendecomposition of a square normal matrix with an orthonormal eigenbasis to any \ m \times n\ matrix. It is related ...

. 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 government on outstanding scientists and engineers in the early stages of their independent research careers. The White ...

(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 signal ...

algorithms. He won the Eighth

Monroe H. Martin Prize The Monroe H. Martin Prize recognizes an outstanding paper in applied mathematics, including numerical analysis, by a young researcher not more than 35 years old and a resident of North America. First awarded in 1975, it is given every 5 years by th ...

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 distinguished ...

"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 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