Ancient Human Genomes Suggest Three Ancestral Populations for Present-Day Europeans

Johannes Krause
Professor of Archaeology and Paleogenetics at the University of Tübingen and Director of the Max Plank Institute for the Science of Human History in Jena
March 19, 2015
In this lecture, Krause explores the methods used to investigate European population history about the time of agricultural transition. Using genome data, Krause explains how at least three ancestral groups, the Hunter-Gathers, the Early Farmers and the Ancient North Eurasians, contributed genetic material to present-day Europeans. Krause also discusses these three ancestral populations discovered from this data and explores their connection to present-day Europeans.

Late Beethoven and American Modernism

Fred Sherry and Sebastian Currier
March 20, 2015
The pianist Peter Serkin and cellist Fred Sherry are both known for their brilliant renderings of classical repertoire, as well as for their passionate advocacy and electrifying performances of contemporary music. They will present Beethoven's last two cellos sonatas, as well as solo works by the American modernist composers Babbitt, Wourinen, and Carter.

Random walks that find perfect objects and the Lovász local lemma

Dimitris Achlioptas
University of California, Santa Cruz
March 23, 2015
At the heart of every local search algorithm is a directed graph on candidate solutions (states) such that every unsatisfactory state has at least one outgoing arc. In stochastic local search the hope is that a random walk will reach a satisfactory state (sink) quickly. We give a general algorithmic local lemma by establishing a sufficient condition for this to be true. Our work is inspired by Moser's entropic method proof of the Lovász Local Lemma (LLL) for satisfiability and completely bypasses the Probabilistic Method formulation of the LLL.

Decoupling in harmonic analysis and applications to number theory

Jean Bourgain
IBM von Neumann Professor, School of Mathematics
March 23, 2015
Decoupling inequalities in harmonic analysis permit to bound the Fourier transform of measures carried by hyper surfaces by certain square functions defined using the geometry of the hyper surface. The original motivation has to do with issues in PDE, such as smoothing for the wave equation and Strichartz inequalities for the Schrodinger equation on tori. It turns out however that these decoupling inequalities have surprizing number theoretical consequences,on which we will mainly focus.

Framed motives of algebraic varieties (after V. Voevodsky)

Ivan Panin
Steklov Institute of Mathematics, St. Petersburg; Member, School of Mathematics
March 25, 2015
This is joint work with G .Garkusha. Using the machinery of framed sheaves developed by Voevodsky, a triangulated category of framed motives is introduced and studied. To any smooth algebraic variety $X$, the framed motive $M_{fr}(X)$ is associated in that category. Theorem. The bispectrum \[( M_{fr} X, M_{fr}(X)(1), M_{fr}(X)(2), ... ),\] each term of which is a twisted framed motive of $X$, has motivic homotopy type of the suspension bispectrum of $X$. (this result is an $A^1$-homotopy analog of a theorem due to G.Segal).

Intelligent learning: similarity control and knowledge transfer

Vladimir Vapnik
Columbia University
March 30, 2015
During last fifty years a strong machine learning theory has been developed. This theory includes: 1. The necessary and sufficient conditions for consistency of learning processes. 2. The bounds on the rate of convergence which in general cannot be improved. 3. The new inductive principle (SRM) which always achieves the smallest risk. 4. The effective algorithms, (such as SVM), that realize consistency property of SRM principle.