This week, the Math/Stats Colloquium welcomes Dominique Guillot (Stanford) to talk about “Critical exponents of graphs: Analysis, combinatorics, and statistics”.  Given a positive semidefinite matrix A and a real number a, the entrywise power of A is obtained by taking the ath power of each entry of A.  Whether or not the resulting matrix must be positive semidefinite is a non-trivial problem solved in 1977 by FitzGerald and Horn.  Motivated by applications in statistics, we examine when powering-up matrices having a given structure of zeros preserves positivity.  This talk will discuss the history of the problem, present new results that characterize when entrywise powers preserve positivity, and discuss applications to high-dimensional statistics.  Joint with Apoorva Khare and Bala Rajaratnam (Stanford).

Background: One semester linear algebra and one semester analysis.

• Date: Wed Apr 22
• Time: 3-3:50pm
• Room: MH320
• Snacks: 2:30pm in MH331B

For more information, click here to see the full flyer, suitable for printing and posting.

Hope to see you there!

Upcoming events:

• Mon Apr 27: Math/Stats Teaching Career Day, 3:00-4:15pm, MH320
• Wed Apr 29: Dick Canary, U. Michigan (visiting MSRI)
  “Non-Euclidean sports and the geometry of surfaces”
• Wed May 06: Erica Flapan, Pomona College visiting MSRI
  “Topological and Geometric Symmetries of Molecular Structures”