Mathematics Dept.
  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.
hide
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

We consider the critical behaviour of long-range O(n) models
for n greater than or equal to 0.  For n=1,2,3,... these
are phi^4 spin models.  For n=0 it is the weakly self-avoiding walk.
We prove existence of critical exponents for the susceptibility
and the specific heat, below the upper critical dimension.
This is a rigorous version of the epsilon expansion in physics.
The proof is based on a rigorous renormalisation group method
developed in previous work with Bauerschmidt and Brydges.
hide
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.
hide
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.
hide
Felix Schulze
University College, UK
Tue 24 May 2016, 3:30pm
ESB 2012
Ricci flow from metrics with isolated conical singularities
ESB 2012
Tue 24 May 2016, 3:30pm-4:30pm

Details

 
Abstract: Let (M,g_0) be a compact n-dimensional Riemannian manifold with a finite number of singular points, where at each singular point the metric is asymptotic to a cone over a compact (n-1)-dimensional manifold with curvature operator greater or equal to one. We show that there exists a smooth Ricci flow starting from such a metric with curvature decaying like C/t. The initial metric is attained in Gromov-Hausdorff distance and smoothly away from the singular points. To construct this solution, we desingularize the initial metric by glueing in expanding solitons with positive curvature operator, each asymptotic to the cone at the singular point, at a small scale s. Localizing a recent stability result of Deruelle-Lamm for such expanding solutions, we show that there exists a solution from the desingularized initial metric for a uniform time T>0, independent of the glueing scale s. The solution is then obtained by letting s->0. We also show that the so obtained limiting solution has the corresponding expanding soliton as a forward tangent flow at each initial singular point. This is joint work with P. Gianniotis.
hide
Mon 30 May 2016, 11:15am SPECIAL
MATH 126
Mathematics Grad Reception
MATH 126
Mon 30 May 2016, 11:15am-12:45pm

Details

The luncheon and awards presentation will be followed by the Niven Lecture at 1:00pm.
hide
IAS Institute for Advanced Study (UBC Alum and former Math Department faculty member)
Mon 30 May 2016, 1:00pm SPECIAL
UBC Vancouver / Math Annex 1100
Niven Lecture: A glamorous Hollywood star, a renegade composer, and the mathematical development of spread spectrum communications.
UBC Vancouver / Math Annex 1100
Mon 30 May 2016, 1:00pm-2:00pm

Details

Abstract: During World War II Hedy Lamarr, a striking Hollywood actress, together with George Antheil, a radical composer, invented and patented a secret signaling system for the remote control of torpedoes.  The ideas in this patent have since developed into one of the ingredients in modern digital wireless communications.  The unlikely biography of these two characters, along with some of the more modern developments in wireless communications will be described.

Bio: Mark is a UBC alum and former math department faculty member. He is most well known for discovering Intersection Cohomology Theory with Robert MacPherson. Intersection Cohomology has had a profound impact on several areas of math, particularly Representation Theory, Algebraic Topology and Algebraic Geometry.
 

About the Niven Lectures: Ivan Niven was a famous number theorist and expositor; his textbooks won numerous awards, have been translated into many languages and are widely used to this day. Niven was born in Vancouver in 1915, earned his Bachelor’s and Master’s degrees at UBC in 1934 and 1936 and his Ph.D. at the University of Chicago in 1938. He was a faculty member at the University of Oregon from 1947 until his retirement in 1982. The annual Niven Lecture Series, held at UBC since 2005, is funded in part through a generous bequest from Ivan and Betty Niven to the UBC Mathematics Department.

 

hide