Uniform words are primitive (cont'd)

Doron Puder
Member, School of Mathematics
September 30, 2014
Let \(G\) be a finite group, and let \(a\), \(b\), \(c\),... be independent random elements of \(G\), chosen at uniform distribution.
What is the distribution of the element obtained by a fixed word in the letters \(a\), \(b\), \(c\),..., such as \(ab\), \(a^2\), or \(aba^{-2}b^{-1}\)? More concretely, do these new random elements have uniform distribution?

In general, a word \(w\) in the free group \(F_k\) is called uniform if it induces the uniform distribution on every finite group \(G\). So which words are uniform?

Tropical currents

June Huh
Princeton University; Veblen Fellow, School of Mathematics
September 30, 2014
I will outline a construction of "tropical current", a positive closed current associated to a tropical variety. I will state basic properties of tropical currents, and discuss how tropical currents are related to a version of Hodge conjecture for positive currents. This is an ongoing joint work with Farhad Babaee.