## Time, space and monotone circuits

Christopher Beck

Member, School of Mathematics

September 29, 2014

Christopher Beck

Member, School of Mathematics

September 29, 2014

Doron Puder

Member, School of Mathematics

September 29, 2014

Bin Xu

Member, School of Mathematics

September 29, 2014

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?

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?

János Kollár

Princeton University; Member, School of Mathematics

September 30, 2014

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.

Mansi M. Kasliwal

Carnegie Institution for Science (& California Institute of Technology)

September 30, 2014

Mark Andrea de Cataldo

Stony Brook University; Member, School of Mathematics

October 1, 2014

I will discuss some of the topology of the fibers of proper toric maps and a combinatorial invariant that comes out of this picture. Joint with Luca Migliorini and Mircea Mustata.

Giulia Saccà

Member, School of Mathematics

October 1, 2014

Michael Magee

Member, School of Mathematics

October 1, 2014