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, 3:30pm4:30pm
Details
Abstract: Let (M,g_0) be a compact ndimensional Riemannian manifold with a finite number of singular points, where at each singular point the metric is asymptotic to a cone over a compact (n1)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 GromovHausdorff 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 DeruelleLamm 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.
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Mon 30 May 2016, 11:15am
SPECIAL
MATH 126

Mathematics Grad Reception

MATH 126
Mon 30 May 2016, 11:15am12:45pm
Details
The luncheon and awards presentation will be followed by the Niven Lecture at 1:00pm.
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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, 1:00pm2:00pm
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.
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