## Andromeda's Dust

Bruce Draine

Princeton University

October 7, 2014

Bruce Draine

Princeton University

October 7, 2014

Stefan Schreieder

University of Bonn

October 8, 2014

What are the possible Hodge numbers of a smooth complex projective variety? We construct enough varieties to show that many of the Hodge numbers can take all possible values satisfying the constraints given by Hodge theory. For example, there are varieties such that a Hodge number \(h^{p,0}\) is big and the intermediate Hodge numbers \(h^{i,p-i}\) are small.

Santosh Vempala

Georgia Institute of Technology

October 13, 2014

Computing the volume of a convex body in n-dimensional space is an ancient, basic and difficult problem (#P-hard for explicit polytopes and exponential lower bounds for deterministic algorithms in the oracle model). We present a new algorithm, whose complexity grows as \(n^3\) for any well-rounded convex body (any body can be rounded by an affine transformation). This improves the previous best Lo-Ve algorithm from 2003 by a factor of \(n\), and bypasses the famous KLS hyperplane conjecture, which appeared essential to achieving such complexity.

Richard Hain

Institute for Advanced Study

October 13, 2014

Please see agenda here: https://www.math.ias.edu/wfgp/agenda1

Francis Brown

Institute for Advanced Study

October 13, 2014

Please see agenda here: https://www.math.ias.edu/wfgp/agenda1

Joseph Ayoub

University of Zurich

October 13, 2014

Please see agenda here: https://www.math.ias.edu/wfgp/agenda1

Hélène Esnault

FU Berlin

October 13, 2014

Please see agenda here: https://www.math.ias.edu/wfgp/agenda1

October 13, 2014

Dragan Huterer

University of Michigan

October 14, 2014

Patrick Brosnan

Institute for Advanced Study

October 14, 2014

Please see agenda here: https://www.math.ias.edu/wfgp/agenda1