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 Events
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, 3:30pm-4:30pm

Abstract

Let k be a field. A classical result of Manin and Swinnerton-Dyer states that every del Pezzo surface of degree 5, defined over k, is a k-rational variety. It is a standard fact that such a surface is a k-form of the moduli space M_(0,5) of genus 0 curves equipped with 5 ordered points. In this talk, we shall, more generally, consider k-forms 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 k-forms of M_{0,n} are always k-rational if n is odd. On the contrary, if n is even, there exists a field k and a k-form of M_{0,n} which is not (retract) k-rational. 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, 11:00am-12:00pm

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, 1:30pm-2:30pm

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 two-stage 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, 3:00pm-4:00pm

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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