Office hours: By appointment
Positive semidefinite matrices are fundamental objects in semidefinite programming, quantum information theory, and spectral graph theory. Despite their widespread utility, analysis and geometry on the PSD cone is often strange, subtle and, occasionally, magical. This course will focus on the properties of such matrices with an eye toward applications.
Often this gives certain phenomena an "operational" interpretation that provides intuition to complement the underlying linear algebra. The style of the course will be to first introduce a classical argument with real numbers and then to explore analogs for PSD matrices.
Mon, Mar 29
PSD matrices [ scribe  video ] 

Wed, Mar 31
Sum of independent random matrices [ scribe  video ] 

Mon, Apr 05
GoldenThompson and the Frobenius inner product [ scribe  video ] 

Wed, Apr 07
Von Neumann's trace inequality and unitarily invariant norms [ scribe  video ] 

Mon, Apr 12
Monotonicity and convexity [ scribe  video ] 

Wed, Apr 14
Joint convexity and the relative entropy [ scribe  video ] 

Mon, Apr 19
Lieb's concavity theorem [ scribe ] 

Wed, Apr 21
Quantum information theory [ scribe  video ] 

Mon, Apr 26
Quantum entropy and strong subadditivity [ scribe  video ] 

Wed, Apr 28
Nonncommutative averages [ scribe  video ] 

Mon, May 03
Semidefinite programming and spectrahedra [ video ] 

Wed, May 05
The cut polytope and SOS cones [ video ] 

Mon, May 10
Symmetric cone factorizations [ scribe ] 

Wed, May 12
Sum of squares degree [ video ] 

Mon, May 17
Pattern matrices and smooth factorization [ scribe  video ] 

Wed, May 19
No lecture 

Mon, May 24
HW#3 discussion 

Wed, May 26
HW#3 discussion 

Wed, Jun 02
Quantum maxentropy approximation 
You may discuss problems with your classmates, but when you write down the solutions, you should do so by yourself. You can use the internet and books for reference material but you should cite every source that you consulted (the name of the book or web page suffices). You should also cite any classmates with whom you discussed solutions. Homework should be typeset.