Up Close and Far Away: Artists, Memorialization, and Uganda’s Troubled Past

Sidney Kasfir
Professor Emerita, Emory University
December 10, 2012

In the past ten years, the term “heritage” in African art studies has gone from being a cliché used only by cultural bureaucrats to a burgeoning academic growth industry, brought into being by studies of collective memory or national trauma in relation to both historical and invented pasts. In this lecture, Sidney Kasfir, Professor Emerita at Emory University, asserts that one of the important ways heritage is given substance as an idea is through memorialization, both through public monuments and smaller-scale artworks. In Buganda, a long-embattled African kingdom, these works of art and architecture give substance to memories of greatness, on the one hand, and victimhood, suffering, and loss, on the other.

Combinatorial PCPs with Short Proofs

Or Meir
Institute for Advanced Study
December 11, 2012

The PCP theorem (Arora et. al., J. ACM 45(1,3)) asserts the existence of proofs that can be verified by reading a very small part of the proof. Since the discovery of the theorem, there has been a considerable work on improving the theorem in terms of the length of the proofs, culminating in the construction of PCPs of quasi-linear length, by Ben-Sasson and Sudan (SICOMP 38(2)) and Dinur (J. ACM 54(3)).

Quantum Beauty

Frank Wilczek
Herman Feshbach Professor of Physics, Massachusetts Institute of Technology
December 11, 2012

Does the world embody beautiful ideas? This is a question that people have thought about for a long time. Pythagoras and Plato intuited that the world should embody beautiful ideas; Newton and Maxwell demonstrated how the world could embody beautiful ideas, in specific impressive cases. Finally in the twentieth century in modern physics, and especially in quantum physics, we find a definitive answer: Yes! The world does embody beautiful ideas.

Universality in Mean Curvature Flow Neckpinches

Gang Zhou
University of Illinois at Urbana-Champaign
December 12, 2012

This is from joint works with D. Knopf and I. M. Sigal. In this talk I will present a new strategy in studying neckpinching of mean curvature flow. Different from previous results, we do not use backward heat kernel, entropy estimates or subsequent convergence, instead we apply almost precise estimates, invented in the past few years, to obtain the first result on asymmetric surface.

Local Global Principles for Galois Cohomology

Julia Hartmann
RWTH Aachen University; Member, School of Mathematics, IAS
December 13, 2012

We consider Galois cohomology groups over function fields F of curves that are defined over a complete discretely valued field.
Motivated by work of Kato and others for n=3, we show that local-global principles hold for
$H^n(F, Z/mZ(n-1))$ for all n>1.
In the case n=1, a local-global principle need not hold. Instead, we will see that the obstruction to a local-global principle for $H^1(F,G)$, a Tate-Shafarevich set, can be described explicitly for many (not necessarily abelian) linear algebraic groups G.

The SOS (aka Lassere/Positivestellensatz/Sum-of-Squares) System Series

Raghu Meka (1) and Avi Wigderson (2)
DIMACS (1) and Professor, School of Mathematics, IAS (2)
December 18, 2012

We will give an overview of this system, which has been at the center of recent algorithmic and proof complexity developments. We will give the definitions of the system (as a proof system for polynomial inequalities, and as an SDP-based algorithm), and basic upper and lower bounds for it. In particular we'll explain the recent SOS-proof of the hypercontractive inequality for the noisy hypercube of Barak et al., as well as the degree lower bounds for proving Tseitin and Knapsack tautologies of Grigoriev.

On Bilinear Complexity

Pavel Hrubes
University of Washington
January 14, 2013

For a set of polynomials F, we define their bilinear complexity as the smallest k so that F lies in an ideal generated by k bilinear polynomials. The main open problem is to estimate the bilinear complexity of the single polynomial $\sum_{i,j}x_i^2 y_j^2$. This question is related to the classical sum-of-squares problem as well as to problems in arithmetic circuit complexity. We will focus on related sets of polynomials and prove some lower and upper bounds on their bilinear complexity.