“Matrices, (Random) Perturbation, Sparsification, Completion”

Speaker: Van Vu
Percey F. Smith Professor of Mathematics and Professor of Statistics and Data Science, Yale University

Talk summary: We discuss recent studies focusing on the following question: How much does (random) noise perturbe the (most important) spectral parameters of a matrix?

Without randomness, the answer is given by perturbation theory in linear algebra. Randomness, however, changes the picture, somewhat interestingly, to our favor. We have found out that under certain assumptions, data can tolerate random noise much better than expected fromthe classical perturbation theory. These new results, in turn, offer a fresh way to view important problems such as matrix sparsification and matrix completion, leading to new results and analysis. 

Speaker bio: Van Vu is Percey F. Smith Professor of Mathematics and Professor of Statistics and Data science at Yale.  Before joining Yale in 2011, he was Professor of Mathematics at Rutgers and UCSD.  He is the author of over 120 academic papers. His research areas include  additive number theory, combinatorics, random graphs and random matrices.

Vu holds a MA in Mathematics from Etvos Univ. in Budapest, and a PhD in mathematics  from Yale (1998). He did postdoctoral work at IAS (Princeton) and Microsoft Research.  He is the recipient of an NSF Career Award, a Sloan Fellowship, Polya Prize (SIAM), and Fulkerson Prize (AMS).  In 2006, he led the program “Arithmetics Combinatorics” at IAS. 

.