The Age of Networks

Jennifer Chayes
Distinguished Scientist and Managing Director Microsoft Research New England and New York City
November 8, 2013

In this talk, Jennifer Chayes, Distinguished Scientist and Managing Director of Microsoft Research New England and New York City, looks quite generally at some of the models we are using to describe ­networks, processes we are studying on the networks, ­algorithms we have devised for the networks, and finally, methods we are developing to indirectly infer network structure from measured data. In particular, she discusses models and techniques that cut across many disciplinary boundaries.

cdh methods in K-theory and Hochschild homology

Charles Weibel
Rutgers University; Member, School of Mathematics
November 11, 2013

This is intended to be a survey talk, accessible to a general mathematical audience. The cdh topology was created by Voevodsky to extend motivic cohomology from smooth varieties to singular varieties, assuming resolution of singularities (for example complex varieties). The slogan is that every variety is locally smooth in this topology. Adapting this to algebraic K-theory has led to several breakthroughs in computation, and clarified connections between the "singular" part of K-theory and Hodge theory.

Hypermatrix Algebra, their spectral decomposition and applications

Edinah Gnang
Institute for Advanced Study; Member, School of Mathematics
November 12, 2013

In this talk we will present an overview of the hypermatrix generalization of matrix algebra proposed by Mesner and Bhattacharya in 1990. We will discuss a spectral theorem for hypermatrices deduced from this algebra as well as connections with other tensor spectral decompositions. Finally if time permits we will discuss some applications and related open problems.

Rethinking Barbarian Invasions through Genomic History

Patrick Geary
School of Historical Studies
November 13, 2013
Historians have debated for centuries the magnitude, nature, and impact of population movements from the borders of the Roman Empire into its heart between the fourth and seventh centuries. In recent years, geneticists have begun to attempt to provide clarity to these questions through the analysis of the biological data contained in the human genome.

Independence of \(\ell\) and local terms

Martin Olsson
University of California, Berkeley
November 14, 2013
Let \(k\) be an algebraically closed field and let \(c:C\rightarrow X\times X\) be a correspondence. Let \(\ell \) be a prime invertible in \(k\) and let \(K\in D^b_c(X, \overline {\mathbb Q}_\ell )\) be a complex. An action of \(c\) on \(K\) is by definition a map \(u:c_1^*K\rightarrow c_2^!K\). For such an action one can define for each proper component \(Z\) of the fixed point scheme of \(c\) a local term \(\text{lt}_Z(K, u)\in \overline {\mathbb Q}_\ell \).