Scientific

A Bratteli-Vershik model for $\mathbb{Z^2}$ actions, or how cohomology can help us make dynamical systems

Speaker: 
Ian Putnam
Date: 
Thu, May 21, 2020
Location: 
Zoom
Conference: 
Pacific Dynamics Seminar
Abstract: 

The Bratteli-Vershik model is a method of producing minimal actions of the integers on a Cantor set. It was given by myself, Rich Herman and Chris Skau, building on seminal ideas of Anatoly Vershik, over 30 years ago. Rather disappointingly and surprisingly, there isn't a good version for $\mathbb{Z}^2$ actions. I'll report on a new outlook on the problem and recent progress with Thierry Giordano (Ottawa) and Christian Skau (Trondheim). The new outlook focuses on the model as an answer to the question: which cohomological invariants can arise from such actions? I will not assume any familiarity with either the original model or the cohomology. The first half of the talk will be a gentle introduction to the $\mathbb{Z}$-case and the second half will deal with how to adapt the question to get an answer for $\mathbb{Z}^2$

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Binocular Rivalry; Modeling by Network Structure

Speaker: 
Marty Golubitsky
Date: 
Wed, May 20, 2020
Location: 
Zoom
Conference: 
Mathematical Biology Seminar
CRG: 
Abstract: 

Binocular rivalry explores the question of how the brain copes with contradictory information. A subject is shown two different pictures – one to each eye. What images does the subject perceive? Results from rivalry experiments usually lead to alternation of percepts and are often surprising. Hugh Wilson proposed modeling rivalry in the brain by using structured networks of differential equations. We use Wilson networks as modeling devices and equivariant Hopf bifurcation as a tool to both post-dict and predict experimentally observed percepts. This work is joint with Casey Diekman, Zhong-Lin Lu, Tyler McMillen, Ian Stewart, Yunjiao Wang, and Yukai Zhao.

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Bratteli-Vershik models for Cantor and Borel dynamical systems

Speaker: 
Bratteli-Vershik models for Cantor and Borel dynamical systems
Date: 
Tue, May 19, 2020
Location: 
Zoom
Conference: 
University of Utah Seminar in Ergodic Theory
CRG: 
Abstract: 

In this talk we will introduce Bratteli diagrams and Vershik maps. Herman-Putnam-Skau proved that for every minimal Cantor dynamical system there exists a Bratteli-Vershik model. We will discuss the proof of this theorem, some of its applications and recent developments. We will also discuss Bratteli-Vershik models for Borel dynamical systems (Bezuglyi-Dooley-Kwiatkowski). Finally, we will briefly talk about connections between Bratteli diagrams and flows on translation surfaces (Lindsey-Treviño).

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Veech's Criterion for a process to be prime

Speaker: 
Jon Chaika
Date: 
Thu, May 14, 2020
Location: 
Zoom
Conference: 
University of Utah Seminar in Ergodic Theory
CRG: 
Abstract: 

This talk will present Veech's criterion for an ergodic probability measure preserving system to be prime. It will define factors of measure preserving systems, prime and self-joinings and provide examples. It uses disintegration of measures, the ergodic decomposition and Haar's Theorem. It will state these results and have examples of disintegration of measures and the ergodic decomposition, but wont discuss their proofs.

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Gaps of saddle connection directions for some branched covers of tori

Speaker: 
Anthony Sanchez
Date: 
Thu, May 14, 2020
Location: 
Zoom
Conference: 
Pacific Dynamics Seminar
Abstract: 

TBA

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Real-time modelling of the COVID-19 epidemic: perspectives from British Columbia

Speaker: 
Caroline Colijn
Daniel Coombs
Date: 
Thu, May 14, 2020
Location: 
Zoom
Conference: 
bcCOVID-19group public seminar
Abstract: 

The COVID-19 global pandemic has led to unprecedented public interest in mathematical modelling as a tool to understand the dynamics of disease spread and predict the impact of public health interventions. In this pair of talks, we will describe how mathematical models are being used, with particular reference to the British Columbia epidemic.

In the first talk, Prof. Caroline Colijn (Dept. of Mathematics, Simon Fraser University) will outline the key features of the British Columbia data and focus on how modelling has allowed us to estimate the effectiveness of the provincial response. In the second talk, Prof. Daniel Coombs (Dept. of Mathematics and Inst. of Applied Mathematics, University of British Columbia) will describe forward-looking modelling approaches that can provide some guidance as the province moves towards partial de-escalation of measures. Each talk will be 30 mins in length and followed by a question and discussion period.

For more details on the group's work and to contact the team, please visit https://bccovid-19group.ca/

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Factors of Gibbs measures on subshifts (2 of 2)

Speaker: 
Sophie MacDonald
Date: 
Thu, May 7, 2020
Location: 
Zoom
Conference: 
Pacific Dynamics Seminar
Abstract: 

Classical results of Dobrushin and Lanford-Ruelle establish, in rough terms, that for a local energy function on a subshift without too much long-range order, the translation-invariant Gibbs measures are precisely the equilibrium measures. There are multiple definitions of a Gibbs measure in the literature, which do not always coincide. We will discuss two of these definitions, one introduced by Capocaccia and the other used by Dobrushin-Lanford-Ruelle, and outline a proof (available at arxiv.org/abs/2003.05532) that they are equivalent.

We will also discuss forthcoming work, in which we show that Gibbsianness is preserved by pushforward through a certain kind of almost invertible factor map. As an application in one dimension, we show that for a sufficiently regular potential, any equilibrium measure on an irreducible sofic shift is Gibbs. As far as we know, this is the first reasonably general result of the Lanford-Ruelle type for a class of subshifts without the topological Markov property.

Joint work with Luísa Borsato, with extensive advice from Brian Marcus and Tom Meyerovitch.

This lecture was given in two parts. The video on this page was given as a follow up to a pre-recorded video.

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What is epithelial-mesenchymal plasticity and why is it important for metastasis?

Speaker: 
Herbert Levine
Date: 
Wed, May 6, 2020
Location: 
Zoom
University of British Columbia, Vancouver, Canada
Conference: 
Mathematical Biology Seminar
CRG: 
Abstract: 

Until very recently most cancer biologists operated with the assumption that the most common route to metastasis involved cells of the primary tumor transforming to a motile single-cell phenotype via complete EMT (the epithelial-mesenchymal transition). This change allowed them to migrate individually to distant organs, eventually leading to clonal growths in other locations. But, a new more nuanced picture has been emerging, based on advanced measurements and on computational systems biology approaches. It has now been realized that cells can readily adopt states with hybrid properties, use these properties to move collectively and cooperatively, and reach distant niches as highly metastatic clusters. This talk will focus on the accumulating evidence for this revised perspective, the role of biological physics theory in instigating this whole line of investigation, and on open questions currently under investigation.

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Rigidity of Geodesic Planes in Hyberbolic Manifolds

Speaker: 
Osama Khalil
Date: 
Tue, May 5, 2020
Location: 
Zoom
Conference: 
University of Utah Seminar in Ergodic Theory
CRG: 
Abstract: 

TBA

Subject: 
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Factors of Gibbs measures on subshifts (1 of 2)

Speaker: 
Sophie MacDonald
Date: 
Thu, May 7, 2020
Location: 
Zoom
Conference: 
Pacific Dynamics Seminar
Abstract: 

Classical results of Dobrushin and Lanford-Ruelle establish, in rough terms, that for a local energy function on a subshift without too much long-range order, the translation-invariant Gibbs measures are precisely the equilibrium measures. There are multiple definitions of a Gibbs measure in the literature, which do not always coincide. We will discuss two of these definitions, one introduced by Capocaccia and the other used by Dobrushin-Lanford-Ruelle, and outline a proof (available at [arxiv.org/abs/2003.05532]) that they are equivalent.

We will also discuss forthcoming work, in which we show that Gibbsianness is preserved by pushforward through a certain kind of almost invertible factor map. As an application in one dimension, we show that for a sufficiently regular potential, any equilibrium measure on an irreducible sofic shift is Gibbs. As far as we know, this is the first reasonably general result of the Lanford-Ruelle type for a class of subshifts without the topological Markov property.

Joint work with Luísa Borsato, with extensive advice from Brian Marcus and Tom Meyerovitch.

This lecture was given in two parts. The video on this page was distributed as a pre-recorded session ahead of a second live lecture.

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