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 Events
PennState
Mon 27 Oct 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)
Rozansky--Witten-type invariants from symplectic Lie pairs
ESB 4127 (host: UBC)
Mon 27 Oct 2014, 3:00pm-4:00pm

Abstract

 In 1997, Rozansky and Witten built new finite-type invariants of 3-manifolds from hyperkahler manifolds. It was later shown by Kontsevich and Kapranov that those invariants only depend on the holomorphic symplectic structure of the hyperkahler manifolds. Indeed Kapranov proved that these invariants may be considered as an analogue of Chern-Simons type invariants, where the Atiyah class of the underlying complex manifold plays the role of  Lie bracket. In this talk, we introduce symplectic structures on "Lie pairs" of (real or complex) algebroids, encompassing homogeneous symplectic spaces, symplectic manifolds with a $\mathfrak g$-action and holomorphic symplectic manifolds. We show that to each such symplectic Lie pair are associated Rozansky-Witten-type invariants of three-manifolds. This is a joint work with Yannick Voglaire.
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Wes Maciejewski
UBC, Dept of Mathematics & CWSEI
Tue 28 Oct 2014, 12:30pm
Lunch Series on Teaching & Learning
MATH 126
Do we know how students view mathematics and how they study it?
MATH 126
Tue 28 Oct 2014, 12:30pm-1:30pm

Abstract

It has long been known that the way a student views the subject they study affects the approach they take to studying
the subject. This, in turn, affects their performance in the subject. It seems, then, that the improvement of student
outcomes not only requires addressing the approach a student takes to study, but also their view of the subject. In this presentation, I will present results from a series of surveys intended to explore two separate, but related questions:
1. Do math instructors actually know how their students view math?
2. What approaches to study do students take and how do these relate to their achievement?
The crucial aspect of this work is that the data gathered was analysed by course year. It turns out that the answers to both questions above are different for lower and upper-year courses.
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Mingfeng Zhao
Tue 28 Oct 2014, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Traveling waves involving fractional Laplacians
ESB 2012
Tue 28 Oct 2014, 3:30pm-4:30pm

Abstract

In this talk, we will discuss the existence of the traveling wave solution for the Allen-Cahn equation involving the fractional Laplacians. Based on the existence of the standing waves for the balanced Allen-Cahn equation, we will use the continuity method to obtain the existence of the traveling waves for unbalanced Allen-Cahn equation. The key ingredient is the the bound of the traveling speed in terms of the potential. Some open questions will be discussed.
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Eindhoven University of Technology
Wed 29 Oct 2014, 3:00pm
Probability Seminar
ESB 2012
Degree distribution of shortest path trees and bias in network sampling algorithms
ESB 2012
Wed 29 Oct 2014, 3:00pm-4:00pm

Abstract

In this talk, we investigate the degree distribution of shortest path trees of various weighted network models. The aim of many empirical studies is to determine the degree distribution of a network with unknown structure by using trace-route sampling. We derive the limiting degree distribution of the shortest path tree from a single source on various random network models with edge weights: the configuration model and r-regular graphs with i.i.d. power law degrees and i.i.d. edge weights, the complete graph with edge weights that are powers of i.i.d. exponential random variables. We use these results to shed light on an empirically observed bias in network sampling methods.
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University of Utah
Wed 29 Oct 2014, 3:15pm
Topology and related seminars
ESB 4133
Constructing aspherical manifolds with a given fundamental group
ESB 4133
Wed 29 Oct 2014, 3:15pm-4:15pm

Abstract

While an aspherical complex is determined up to homotopy by its fundamental group, there are many geometrically different aspherical manifolds with the same fundamental group. For instance, the punctured torus and the pair of pants look quite different, but both have the same fundamental group F_2. I will discuss constructions of aspherical manifolds for a given fundamental group, talk about the smallest dimension of such a manifold for a given group and describe some geometric invariants that distinguish different aspherical manifolds with the same fundamental group. I will discuss this for right angled Artin groups (joint work with Mike Davis, Boris Okun and Kevin Schreve) and possibly also for duality groups.
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Abdul Kara
Witwatersrand University, Johannesburg
Wed 29 Oct 2014, 3:30pm
Symmetries and Differential Equations Seminar
Math 125
Symmetry structures of manifolds
Math 125
Wed 29 Oct 2014, 3:30pm-4:30pm

Abstract

We study the Noether and Lie symmetries that arise from the Euler-Lagrange equations, i.e., the ‘geodesic’ equations, related to manifolds that arise from a metric. In particular and as one of the examples, we present some peculiarities associated with the ASD Ricci-flat metric which depends on the `second heavenly equation'. It is noted, in general, that the Killing vectors are contained in the Noether symmetries generated by the Lagrangian of the geodesic equations. Specifically, a number of symmetries which are Noether and not Killing vectors are independent of the arc length variable ‘s’.
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Emory University
Thu 30 Oct 2014, 3:30pm
Number Theory Seminar
room MATH 126
Hasse principles over function fields of p-adic curves
room MATH 126
Thu 30 Oct 2014, 3:30pm-4:30pm

Abstract

 Obstructions to the Hasse principle for the existence of rational points on principal homogeneous spaces under connected linear algebraic groups over a number fi eld are well understood. Similar questions of Hasse principle have been studied over more general fi elds, particularly, function fields of curves over complete discrete valued fields. There are several positive results in this direction for connected linear algebraic groups which are rational, thanks to the patching techniques developed by Harbater-Hartmann-Krashen. We shall explain some recent progress and open questions concerning Hasse principle for function fi elds of p-adic curves.
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Univeristy of Michigan
Fri 31 Oct 2014, 3:00pm
Department Colloquium
ESB 2012 (PIMS)
Imaging with waves in complex environments (PIMS-IAM-UBC distinguished colloquium)
ESB 2012 (PIMS)
Fri 31 Oct 2014, 3:00pm-4:00pm

Abstract

The talk is concerned with the application of sensor array imaging in complex environments. The goal of imaging is to estimate the support of remote sources or strong reflectors using time resolved measurements of waves at a collection of sensors (the array). This is a challenging problem when the imaging environment is complex, due to numerous small scale inhomogeneities and/or rough boundaries that scatter the waves. Mathematically we model such complexity (which is necessarily uncertain in applications) using random processes, and thus study imaging in random media. I will focus attention on the application of imaging in random waveguides, which exhibits all the challenges of imaging in random media. I will present a quantitative study of cumulative scattering effects in such waveguides and then explain how we can use such a study to design high fidelity imaging methods.

Note for Attendees

Coffee, tea and cookies served at 2:30pm in the PIMS Lounge, ESB 4133.
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