## Higher order curvatures and isoperimetric inequalities

Yi Wang

Member, School of Mathematics

October 1, 2014

Yi Wang

Member, School of Mathematics

October 1, 2014

John Lesieutre

Member, School of Mathematics

October 1, 2014

Joanna Nelson

Member, School of Mathematics

October 1, 2014

Runpu Zong

Member, School of Mathematics

October 1, 2014

Nadya Gurevich

Ben-Gurion University of the Negev

October 2, 2014

We consider a Rankin-Selberg integral representation of a cuspidal (not necessarily generic) representation of the exceptional group \(G_2\). Although the integral unfolds with a non-unique model, it turns out to be Eulerian and represents the standard \(L\)-function of degree 7. We discuss a general approach to the integrals with non-unique models. The integral can be used to describe the representations of \(G_2\) for which the (twisted) \(L\)-function has a pole as functorial lifts. This is a joint work with Avner Segal.

Rotem Oshman

Tel Aviv University

October 6, 2014

In distributed systems, communication between the participants in the computation is usually the most expensive part of the computation. Theoretical models of distributed systems usually reflect this by neglecting the cost of local computation, and charging only for messages sent between the participants; in particular, we usually assume that the computation proceeds in rounds, and in each round each participant can send only a limited number of bits. We are interested in characterizing the number of rounds required to perform various tasks.

Claire Voisin

Centre national de la recherche scientifique; Distinguished Visiting Professor, School of Mathematics

October 6, 2014

My talk will be a broad introduction to what is the (mostly conjectural) higher dimensional generalization of Abel's theorem on divisors on Riemann surfaces, namely, the relationship between the structure of the group of algebraic cycles on a complex projective variety and the complexity of its so-called Hodge structures.

Yuval Filmus

Member, School of Mathematics

October 7, 2014

Monotone submodular maximization over a matroid (MSMM) is a fundamental optimization problem generalizing Maximum Coverage and MAX-SAT. Maximum Coverage is NP-hard to approximate better than \(1-1/e\), an approximation ratio obtained by the greedy algorithm. The performance of the greedy algorithm deteriorates to \(1/2\) on the more general problem of MAX-SAT. Recently, Vondrak et al. designed a sophisticated algorithm attaining the optimal approximation ratio \(1-1/e\) for MSMM.

Kieran O'Grady

Sapienza - Università di Roma; Member, School of Mathematics

October 7, 2014

Beauville and Voisin proved that decomposable cycles (intersections of divisors) on a projective K3 surface span a 1-dimensional subspace of the (infinite-dimensional) group of 0-cycles modulo rational equivalence. I will address the following question: what is the rank of the group of decomposable 0-cycles of a smooth projective variety? Beauville and Voisin also proved a refinement of the result mentioned above, namely a decomposition (modulo rational equivalence) of the small diagonal in the cube of a K3.

John Lesieutre

Member, School of Mathematics

October 7, 2014

I will explain how infinite sequences of flops give rise to some interesting phenomena: first, an infinite set of smooth projective varieties that have equivalent derived categories but are not isomorphic; second, a pseudoeffective divisor for which the asymptotic multiplicity along a certain subvariety is infinite, in the relative setting.