The standard \(L\)-function for \(G_2\): a "new way"

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.

The communication complexity of distributed subgraph detection

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.

Hodge theory, coniveau and algebraic cycles

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.

Monotone submodular maximization over a matroid

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.

Chow rings and modified diagonals

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.

Two counterexamples arising from infinite sequences of flops

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.