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 Events
Stanford University
Tue 3 Mar 2015, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
On the topology and index of minimal surfaces
ESB 2012
Tue 3 Mar 2015, 3:30pm-4:30pm

Abstract

We show that for an immersed two-sided minimal surface in R^3, there is a lower bound on the index depending on the genus and number of ends. Using this, we show the nonexistence of an embedded minimal surface in R^3 of index 2, as conjectured by Choe. Moreover, we show that the index of an immersed two-sided minimal surface with embedded ends is bounded from above and below by a linear function of the total curvature of the surface. (This is joint work with Otis Chodosh)

 
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UBC
Tue 3 Mar 2015, 4:00pm
Discrete Math Seminar
ESB 4127
Spectrum in Simplicial Complexes
ESB 4127
Tue 3 Mar 2015, 4:00pm-5:00pm

Abstract

 

Ramanujan graphs are k-regular graphs admitting optimal connectivity properties (namely, optimal expanders). Infinite families of such graphs were first constructed by Lubotzky, Phillips and Sarnak in 1988 by relating the spectrum of a graph with certain representations of GL_2(Q_p). These ideas were generalized to simplical complexes by Lubotzky, Samuels and Vishne in 2005. 
We will present a further generalization, showing that there is a natural way to relate spectral properties of simplicial complexes with certain representations of groups acting on their universal covers. Several results of this connection will be discussed. In particular, we strengthen the spectral properties of the complexes constructed by L-S-V. (Roughly speaking, we show that the complexes constructed by L-S-V have "optimal spectrum in all dimensions".)
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Qingsan Zhu
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, 3:10pm-4:00pm

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 $1/(|a|^2 log|a|)$ 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, 3:15pm-4:15pm

Abstract

We are interested in classifying all finite groups which can act  on a finite CW-complex 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, 3:30pm-4:30pm

Abstract

A Diophantine m-tuple 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 Erdős-Turán 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, 4:00pm-5:00pm

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 4D-Var 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 4D-Var 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.

Note for Attendees

Note SFU downtown venue. Reception at 3:30 pm (light refreshments).
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UBC
Mon 9 Mar 2015, 3:00am
CRG Geometry and Physics Seminar
ESB 4127
The Donaldson-Thomas theory of K3xE via motivic and toric methods
ESB 4127
Mon 9 Mar 2015, 3:00am-4:00pm

Abstract

 Donaldson-Thomas invariants are fundamental deformation invariants of Calabi-Yau threefolds. We describe a recent conjecture of Oberdieck and Pandharipande which predicts that the (three variable) generating function for the Donaldson-Thomas 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, 3:00pm-4:00pm

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 subgrid-scale 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 classifi cation of diff erential equations. By assuming a general functional dependency of the unknown subgrid-scale in terms of the known grid-scale quantities in a system of averaged diff erential equations turns the original unclosed di fferential equations into a class of diff erential equations which is approachable using tools from the classical group classi cation. The result of this procedure yields various forms of local closure ansatzes for the unresolved subgrid scale terms leading the closed diff erential equations having symmetry properties that are related to the original unaveraged diff erential equations.

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