Video Lectures

What brought about the current chaos in the Middle East? Did the machinations of the Cold War exhaust the region leaving it unable to develop new relationships between governor and governed? As Americans, how much should we criticize our role or...

Reed-Muller codes encode an $m$-variate polynomial of degree $r$ by evaluating it on all points in $\{0,1\}^m$. Its distance is $2^{m-r}$ and so it cannot correct more than that many errors/erasures in the worst case. For random errors one may hope...

A. Venkatesh asked us the question, in the context of torsion automorphic forms: Does the Standard Conjecture (of Grothendieck's) of Künneth type hold with mod p coefficients? We first review the geometric and number-theoretic contexts in which this...

The dichotomy between overtwisted and tight contact structures has been central to the classification of contact structures in dimension 3. Ozsvath-Szabo's contact invariant in Heegaard Floer homology proved to be an efficient tool to distinguish...

In this talk we will discuss further the existence of knot complements with essential surfaces of unbounded Euler characteristics. More precisely, we show the existence of a knot with an essential tangle decomposition for any number of strings. We...

We study the number of nodal domains of toral Laplace eigenfunctions. Following Nazarov-Sodin's results for random fields and Bourgain's de-randomisation procedure we establish a precise asymptotic result for "generic" eigenfunctions. Our main...

A spectral gap on a noncompact Riemannian manifold is an asymptotic strip free of resonances (poles of the meromorphic continuation of the resolvent of the Laplacian). The existence of such gap implies exponential decay of linear waves, modulo a...

We characterize all complex-valued (Lebesgue) integrable functions $f$ on $[0,1]^m$ such that $f$ vanishes when integrated over the product of $m$ measurable sets which partition $[0,1]$ and have prescribed Lebesgue measures $\alpha_1,\ldots,\alpha...

McDuff and Schlenk studied an embedding capacity function, which describes when a 4-dimensional ellipsoid can symplectically embed into a 4-ball. The graph of this function includes an infinite staircase determined by the odd index Fibonacci numbers...

The Institute for Advanced Study and Nautilus are pleased to present a special edition of Categorically Not!, the conversation series exploring the common ground of art, science and politics, April 14 at Wolfensohn Hall on the Institute campus (1...