University of Paris 6

Mon 9 May 2016, 3:30pm
SPECIAL
Algebraic Groups and Related Structures
Math Annex 1102

On the rationality of forms of moduli spaces of marked curves

Math Annex 1102
Mon 9 May 2016, 3:30pm4:30pm
Abstract
Let k be a field. A classical result of Manin and SwinnertonDyer states that every del Pezzo surface of degree 5, defined over k, is a krational variety. It is a standard fact that such a surface is a kform of the moduli space M_(0,5) of genus 0 curves equipped with 5 ordered points. In this talk, we shall, more generally, consider kforms of the moduli spaces M_{g,n} of curves of genus g, with n marked points. These are, in most cases, moduli spaces for genus g curves, equipped with an embedding of a fixed degree n 'etale algebra. The main result is that kforms of M_{0,n} are always krational if n is odd. On the contrary, if n is even, there exists a field k and a kform of M_{0,n} which is not (retract) krational. Results in higher genus will also be discussed. This is joint work with Zinovy Reichstein.
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UBC Math

Wed 11 May 2016, 11:00am
Probability Seminar
ESB 2012

Critical exponents for O(n) models

ESB 2012
Wed 11 May 2016, 11:00am12:00pm
Abstract
TBA
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IMPA and Uppsala University

Wed 11 May 2016, 1:30pm
Probability Seminar
ESB 2012

Sharpness of the phase transition for continuum percolation on R^2

ESB 2012
Wed 11 May 2016, 1:30pm2:30pm
Abstract
Many complex systems involving a large number of independent variables have come to be very well understood. One such example is Bernoulli percolation on a planar lattice. However, how to adapt the techniques to closely related models, such as continuum percolation in $\mathbb{R}^2$, may be far from obvious. We will describe some techniques of this kind that recently has been developed for Poisson Boolean percolation. We will focus on a certain twostage construction that allows for a reduction to the discrete setting, where a larger arsenal of techniques is available for the study of phenomena such as sharp thresholds and noise sensitivity. Joint work with Vincent Tassion and Augusto Teixeira.
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Tel Aviv University

Wed 11 May 2016, 3:00pm
Probability Seminar
ESB 2012

Slightly subcritical hypercube percolation

ESB 2012
Wed 11 May 2016, 3:00pm4:00pm
Abstract
We will present some recent results about bond percolation on the hypercube {0,1}^m in the "slightly" subcritical phase, that is, just below the critical percolation scaling window. We estimate the size, diameter and mixing time of the largest components. A difficulty that arises only in the subcritical phase is that the cluster of the largest size does not attain the largest possible diameter. Therefore, we are able to analyze rather accurately the cluster of largest diameter, but not the cluster of largest size, leaving some interesting open problems.
Joint work with Tim Hulshof.
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