Abstract: The work is devoted to cooperative and coalitional game-theoretic methods for community detection in networks.The traditional methods for detecting community structure are based on selecting dense subgraphs inside the network.

Abstract: In 1971, Graham and Pollak showed that if $D_T$ is the distance matrix of a tree $T$ on $n$ nodes, then $\det(D_T)$ depends only on $n$, not $T$.

This course will start with gradient based methods in convex optimization starting with gradient descent, proximal point methods and the use of momentum and randomness.

Abstract: In this talk, we will explore a surprising connection between graph theory and convex geometry. We look at graphs whose edge weights are linear forms in $d$ variables.