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 Events
University of Washington
Mon 27 Jan 2020, 3:00pm
Algebraic Geometry Seminar
MATH 225
Variation of Instability in Invariant Theory
MATH 225
Mon 27 Jan 2020, 3:00pm-4:00pm

Abstract

 Mumford's GIT quotient is one way to construct moduli spaces that parametrize classes of algebro-geometric objects. It turns out there is an interesting structure on the set of unstable points discarded in the GIT quotients. In this talk I would aim to describe:  

1. the stratification of the unstable points and its variation caused by different choices of linearizations;  

2. a wall and chamber decomposition analogous to Variation of Geometric Invariant Theory Quotient;

3. examples and results in the case of projective toric varieties.
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Jim Varah
Department of Computer Science, UBC
Tue 28 Jan 2020, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS lounge)
Seminar: Error Bounds for Symmetric Iterative Methods from Minimal Polynomials
ESB 4133 (PIMS lounge)
Tue 28 Jan 2020, 12:30pm-1:30pm

Abstract

Error bounds for the conjugate gradient method using minimal polynomials are well known. What are less well known are comparable bounds for indefinite systems using minimal polynomials over two intervals. The key result goes back to Akhieser, with significant enhancements by Fischer.

We gratefully acknowledge generous financial support for the SCAIM seminar by PIMS and the IAM.

Note for Attendees

A light lunch (pizza) will be served.
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Yakine Bahri
University of Victoria
Tue 28 Jan 2020, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
PIMS Lounge, ESB
Self-similar blow-up profiles for slightly supercritical nonlinear Schrödinger equations
PIMS Lounge, ESB
Tue 28 Jan 2020, 3:30pm-4:30pm

Abstract

We construct radially symmetric self-similar blow-up profiles for the mass supercritical nonlinear Schrödinger equation with nonlinear exponent close to the mass critical case and for any space dimension. These profiles bifurcate from the ground state solitary wave. In this talk, we present the argument which relies on the matched asymptotics method and we derive an exponentially smallness condition on the Sobolev critical exponent as conjectured by Sulem and Sulem in 1997.

This is a joint work with Yvan Martel and Pierre Raphaël.
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Sumreen Javed
UBC Pharmaceutical Sciences
Wed 29 Jan 2020, 1:45pm
Mathematical Biology Seminar
ESB 4133
Role of Invadopodia in Tumor Dissemination through the Lymphatic System
ESB 4133
Wed 29 Jan 2020, 1:45pm-2:45pm

Abstract

Breast cancer remains the second leading cause of cancer-related death with metastasis accounting around 90% of the total deaths. Specialized subcellular structures termed invadopodia play a critical role in metastasis, aiding tumor cell dissemination to distant sites. Invadopodia have documented roles in aiding tumor cells movement into (intravasation) and out of (extravasation) the blood vessels. While movement through the hematogenous system is well characterised, we are limited in our understanding of dissemination through the lymphatics. In this study we explore the role of invadopodia in aiding tumor cells invasion through the lymphatics. To impair invadopodia formation, knockout (KO) of key invadopodial regulatory protein Tks5 was performed in human breast cancer cells MDA-MB-231. Invadopodia formation in Tks5-KO cells was found to be completely abolished. We assessed cell invasion across a lymphatic monolayer and found a significant reduction in lymphatic invasion for Tks5-KO cells. Next, using transendothelial electrical resistance (TEER) we measured lymphatic tight junction integrity and found that control cells were able to reduce lymphatic tight junctions but this was significantly impaired in Tks5-KO. Overall, the inability of Tks5-KO cells to form invadopodia compromised their ability to invade through the lymphatics suggesting that invadopodia aid tumor cells invasion through the lymphatic system. Current studies are expanding on this work to better understand the role of invadopodia in lymphatic dissemination through the use of live cell imaging and bioluminescent imaging of progression and lymphatic invasion in mice.

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University of Copenhagen
Wed 29 Jan 2020, 3:15pm
Topology and related seminars
ESB 4127
String topology of finite groups of Lie type
ESB 4127
Wed 29 Jan 2020, 3:15pm-4:15pm

Abstract

In this talk, I will discuss a surprising connection between finite groups of Lie type and string topology of classifying spaces of compact connected Lie groups recently discovered by Jesper Grodal and myself: the cohomology of a finite group of Lie type is a module over the cohomology of the free loop space of the classifying space of the corresponding compact Lie group when the latter cohomology groups are equipped with a string topological multiplication. This module structure provides in particular a new perspective towards the Tezuka conjecture asserting that under certain conditions, the cohomologies of the two objects are isomorphic.
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UBC
Wed 29 Jan 2020, 3:15pm
Probability Seminar
PIMS lounge
A bridge between elliptic and parabolic Harnack inequalities
PIMS lounge
Wed 29 Jan 2020, 3:15pm-4:05pm

Abstract

The notion of conformal walk dimension serves as a bridge between elliptic and parabolic Harnack inequalities. The importance of this notion is due to the fact that the finiteness of the conformal walk dimension characterizes the elliptic Harnack inequality. 
 
Roughly speaking, the conformal walk dimension is the infimum of all possible values of the walk dimension that can be attained by a time-change of the process and by a quasisymmetric change of the metric. Two natural questions arise (a) What are the possible values of the conformal walk dimension? (b) When is the infimum attained? In this talk, I will explain the answer to (a), and mention partial progress towards (b). 
 
This talk is based on joint work with Naotaka Kajino.
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