University of British Columbia

Wed 4 Mar 2015, 3:10pm
Probability Seminar
ESB 2012

An upper bound for the probability of visiting a distant point by critical branching random walk in $Z^4$

ESB 2012
Wed 4 Mar 2015, 3:10pm4:00pm
Abstract
We solve an open question raised by Le Gall and Lin. We study the probability of visiting a distant point $a \in Z^4$ by critical branching random walk starting from the origin. We prove that this probability is bounded by $1/(a^2 loga)$ up to a constant.
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Bilkent University and McMaster University

Wed 4 Mar 2015, 3:15pm
Topology and related seminars
ESB 4133

Finite group actions on homotopy spheres

ESB 4133
Wed 4 Mar 2015, 3:15pm4:15pm
Abstract
We are interested in classifying all finite groups which can act on a finite CWcomplex homotopy equivalent to a sphere, such that all isotropy subgroups are rank one groups, i.e., they do not include Z/pxZ/p for any prime p. The equivalent question for free actions (all isotropy subgroups are trivial) has been answered completely by the works of P.A. Smith and R. Swan. For actions with rank one isotropy, we give a list of group theoretical conditions which guarantee the existence of such actions. Some of these conditions are necessary conditions depending on assumptions on fixed point subspaces. This is a joint work with Ian Hambleton.
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UBC

Thu 5 Mar 2015, 3:30pm
Number Theory Seminar
room MATH 126

Diophantine quadruples

room MATH 126
Thu 5 Mar 2015, 3:30pm4:30pm
Abstract
A Diophantine mtuple is a set A of m positive integers such that ab+1 is a perfect square for every pair a,b of distinct elements of A. We derive an asymptotic formula for the number of Diophantine quadruples whose elements are bounded by x. In doing so, we extend two existing tools in ways that might be of independent interest. The ErdősTurán inequality bounds the discrepancy between the number of elements of a sequence that lie in a particular interval modulo 1 and the expected number; we establish a version of this inequality where the interval is allowed to vary. We also adapt an argument of Hooley on the equidistribution of solutions of polynomial congruences to handle reducible quadratic polynomials. (joint work with Scott Sitar)
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Mathematics, University of Bath

Fri 6 Mar 2015, 4:00pm
SPECIAL
Institute of Applied Mathematics
Canfor Policy Rm 1600, SFU Harbour Centre, Downtown Vancouver

Data Assimilation and Adaptivity

Canfor Policy Rm 1600, SFU Harbour Centre, Downtown Vancouver
Fri 6 Mar 2015, 4:00pm5:00pm
Abstract
Data assimilation is the process of systematically including (often noisy) data into a forecast. It is now widely used in numerical weather prediction and its positive impact on the accuracy of weather forecasts is unquestionable. Indeed improvements in our ability to forecast the weather over the last decade are a reflection on the increasing volume of data available, improved computational methods and (significantly) much improved algorithms for incorporating this data into the forecast. However, many problems remain, including dealing with the sheer volume of the data and the inherent complexity of the weather and climate, understanding the effects of data and model error, and of reducing spurious correlations between the data and the forecast.
In this talk I will give a survey of various techniques that are used operationally to implement data assimilation procedures in weather (and climate) forecasting including the Ensemble Kalman Filter, and the 4DVar method.
I will discuss their various advantages and disadvantages, the nature of the errors and ways to minimise these. In particular I will show that the use of adaptive numerical methods can significantly improve the performance
of the 4DVar method. Hopefully I will show that used carefully Data Assimilation techniques can significantly improve our ability to forecast the weather of Planet Earth.
Joint work with Mike Cullen and Chiara Piccolo at the Met Office.
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UBC

Mon 9 Mar 2015, 3:00am
CRG Geometry and Physics Seminar
ESB 4127

The DonaldsonThomas theory of K3xE via motivic and toric methods

ESB 4127
Mon 9 Mar 2015, 3:00am4:00pm
Abstract
DonaldsonThomas invariants are fundamental deformation invariants of CalabiYau threefolds. We describe a recent conjecture of Oberdieck and Pandharipande which predicts that the (three variable) generating function for the DonaldsonThomas invariants of K3xE (the product of a K3 surface and an elliptic curve) is given by the reciprocal of the Igusa cusp form of weight 10. For each fixed K3 surface of genus g, the conjecture predicts that the corresponding (two variable) generating function is given by a particular meromorphic Jacobi form. We prove the conjecture for K3 surfaces of genus 0 and genus 1. Our computation uses a new technique which mixes motivic and toric methods.
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Wolfgang Pauli Institute and at the UBC Math Department

Mon 9 Mar 2015, 3:00pm
Institute of Applied Mathematics
LSK 460

Invariant turbulence modeling

LSK 460
Mon 9 Mar 2015, 3:00pm4:00pm
Abstract
Numerical weather prediction models can only operate at finite resolution. However, processes below the model resolution have an impact on the processes resolved by the model and therefore cannot be omitted in the model. The proper formulation of subgridscale processes in terms of resolved grid scale quantities is referred to as parameterization. The aim of this talk is to discuss a method for constructing parameterization schemes that preserve invariance properties. The method is based on group classification of differential equations. By assuming a general functional dependency of the unknown subgridscale in terms of the known gridscale quantities in a system of averaged differential equations turns the original unclosed differential equations into a class of differential equations which is approachable using tools from the classical group classication. The result of this procedure yields various forms of local closure ansatzes for the unresolved subgrid scale terms leading the closed differential equations having symmetry properties that are related to the original unaveraged differential equations.
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Mathematics Department, UBC

Tue 10 Mar 2015, 3:30pm
Mathematical Biology Seminar
PIMS Lounge, Earth Sciences Bldg. (ESB) 4th Foolr

MathBio Works in Progress: Spatially Structured Neural Systems

PIMS Lounge, Earth Sciences Bldg. (ESB) 4th Foolr
Tue 10 Mar 2015, 3:30pm4:30pm
Abstract
Scintillating Scotoma is a phenomenon in the visual cortex which may signal the onset of migraine, or may happen for no apparent reason. Initial steps to model this use a stochastic reaction diffusion system. A stochastic version of Turing patterns, called quasipatterns is introduced. This idea is analogous to oscillations sustained by noise in a stochatic ODE setting.
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Colorado State University

Tue 10 Mar 2015, 4:00pm
Discrete Math Seminar
ESB 4127

Nilpotence, Simplicity, and Exotic Geometries.

ESB 4127
Tue 10 Mar 2015, 4:00pm5:00pm
Abstract
In a quantifiable way most groups, rings, and Lie algebras are nilpotent. In fact even the extension of two abelian groups, or two trivial algebras, has enough variation to match the total quantity of all finite groups, resp. finitedimensional algebras. However, our most developed theories concern groups, rings, and algebras that are simple, semisimple, or highly related to simplicity.
In this talk I will demonstrate a simple way to convert questions about nilpotence into questions about simple and semisimple groups and nonassociative rings. The process is recursive and captures new structure in a positive proportion of all products. In fact 4/5 of the 11 million groups of size at most 1000 are explained by this mechanism. I will close with a a surprising characterization of the base case of these recursive techniques: they are products without zerodivisors and thus have storied histories in discrete and differential geometry.
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Note for Attendees
Note SFU downtown venue. Reception at 3:30 pm (light refreshments).