Lectures by Faculty

Modern Cosmology and the Origin of the Universe

Matias Zaldarriaga
Institute for Advanced Study
February 11, 2015
The last decades have seen great advances
in our understanding of the history of our
universe. I will summarize our current
knowledge, describe some of the puzzles
that still remain and speculate about future
developments in cosmology.
Matias Zaldarriaga has made many influential
and creative contributions to our understanding of the
early universe, particle astrophysics, and cosmology
As a probe of fundamental physics. Much of his work
centers on understanding the clues about the earliest

Remembering Patricia Crone (1945–2015)

Diana Frank, Thomas Frank, Michael Cook, Judith Herrin, Carol Bakhos, Emma Gannagé, Carmela V. Franklin, Robbert Dijkgraaf, Nicola Di Cosmo
October 24, 2015

Patricia Crone, Professor Emerita in the School of Historical Studies, helped to establish the Institute as a recognized center for the pursuit of Islamic culture and history. Crone’s insightful work shed important new light on the critical importance of the Near East—in particular on the cultural, religious, and intellectual history of Islam—in historical studies.

Is the Abstract Mathematics of Topology Applicable to the Real World?

Robert D. MacPherson; Randall D. Kamien; Raúl Rabadán
Hermann Weyl Professor, School of Mathematics; University of Pennsylvania; Columbia University
May 1, 2015
Topology is the only major branch of modern mathematics that wasn't anticipated by the ancient mathematicians. Throughout most of its history, topology has been regarded as strictly abstract mathematics, without applications. However, illustrating Wigner's principle of "the unreasonable effectiveness of mathematics in the natural sciences", topology is now beginning to come up in our understanding of many different real world phenomena.

More on sum-of-squares proofs for planted clique

Avi Wigderson
Herbert H. Maass Professor, School of Mathematics
December 9, 2014

While this talk is a continuation of the one I gave on Tue Nov 25, it will be planned as an independent one. I will not assume knowledge from that talk, and will reintroduce that is needed. (That first lecture gave plenty of background material, and anyone interested can watch it on https://video.ias.edu/csdm/2014/1125-AviWigderson).

Sum-of-squares lower bounds for the planted clique problem

Avi Wigderson
Herbert H. Maass Professor, School of Mathematics
November 25, 2014
Finding large cliques in random graphs and the closely related "planted" clique variant, where a clique of size \(k\) is planted in a random \(G(n,1/2)\) graph, have been the focus of substantial study in algorithm design. Despite much effort, the best known polynomial-time algorithms only solve the problem for \(k = \Theta(\sqrt{n})\). In this paper we study the complexity of the planted clique problem under algorithms from the Sum-Of-Squares hierarchy.