Tue, 21 Oct 2008
17:00 -
18:00
L2
Thu, 04 Dec 2008
16:30
16:30
L2
Fri, 03 Oct 2008
10:00 -
17:00
L2
Elastic Stability Workshop
Becca Thomases, Yury Grabovsky, L Mahadevan, Tim Healey, Heinrich Freistühler and Robin Knops
Abstract
The workshop will address current issues related to the stability of solutions in nonlinear elasticity, including local energy minimizers, the stability of growing bodies, global existence for small data, bifurcation and continuation of solutions, and Saint-Venant’s principle.
Fri, 06 Jun 2008
16:30
16:30
L2
Towards the Sato-Tate Conjecture for pairs of elliptic curves
Prof. Michael Harris
(Université Paris VII)
Abstract
Let E be an elliptic curve defined by a cubic equation with rational coefficients.
The Sato-Tate Conjecture is a statistical assertion about the variation of the number of points of E over finite fields. I review some of the main steps in my proof of this conjecture with Clozel, Shepherd-Barron, and Taylor, in the case when E has non-integral j-invariant. Emphasis will be placed on the steps involving moduli spaces of certain Calabi-Yau hypersurfaces with level structure.
If one admits a version of the stable trace formula that should soon be available, the same techniques imply that, when E and E' are two elliptic curves that are not isogenous, then the numbers of their points over finite fields are statistically independent. For reasons that have everything to do with the current limits to our understanding of the Langlands program, the analogous conjectures for three or more non-isogenous elliptic curves are entirely out of reach.
The Sato-Tate Conjecture is a statistical assertion about the variation of the number of points of E over finite fields. I review some of the main steps in my proof of this conjecture with Clozel, Shepherd-Barron, and Taylor, in the case when E has non-integral j-invariant. Emphasis will be placed on the steps involving moduli spaces of certain Calabi-Yau hypersurfaces with level structure.
If one admits a version of the stable trace formula that should soon be available, the same techniques imply that, when E and E' are two elliptic curves that are not isogenous, then the numbers of their points over finite fields are statistically independent. For reasons that have everything to do with the current limits to our understanding of the Langlands program, the analogous conjectures for three or more non-isogenous elliptic curves are entirely out of reach.
Thu, 22 May 2008
17:00
17:00
L2
Manipulating thin-film flows: From patterned substrates to evaporating systems
Howard Stone
(Harvard University, USA)
Abstract
The lecture will describe two variants of thin film flows, one involving wetting and the other involving evaporation. First, describing the spreading of mostly wetting liquid droplets on surfaces decorated with assemblies of micron-size cylindrical posts arranged in regular arrays. A variety of deterministic final shapes of the spreading droplets are obtained, including octagons, squares, hexagons and cricles. Dynamic considerations provide a "shape" diagram and suggest rules for control. It is then shown how these ideas can be used to explore (and control) splashing and to create polygonal hydraulic jumps. Second, the evaporation of volatile liquid drops is considered. Using experiments and theory it is shown how the sense of the internal circulation depends on the ratio of the liquid and substrate conductivities. The internal motions control the deposition patterns and so may impact various printing processes. These ideas are then applied to colloid deposition porous media.