Abstract:  In modern applications of graph algorithms, where the graphs of interest are large and dynamic, it is unrealistic to assume that an input representation contains the full information of a graph being studied.

Abstract: We study the sum of squares (*SOS*) representation of polynomials, i.e. f = \sum_{i\in s} c_i f_i^2 , where c_i are field elements and f_i(x_1,\ldots,x_n) are polynomials.

Abstract:  How should one divide $m$ goods between $n$ agents, given the utility each agent has when allocated a subset of goods?

Talk will be held on Zoom.