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 Events
Tel Aviv University
Mon 21 Sep 2020, 8:00am
Algebraic Groups and Related Structures
Online: link available at https://researchseminars.org/ or from Zinovy Reichstein
Galois cohomology of real reductive groups
Online: link available at https://researchseminars.org/ or from Zinovy Reichstein
Mon 21 Sep 2020, 8:00am-9:00am

Abstract

Using ideas of Kac and Vinberg, we give a simple combinatorial method of computing the Galois cohomology of semisimple groups over the field R of real numbers. I will explain the method by the examples of simple groups of type E_7 (both adjoint and simply connected). This is joint work with Dmitry A. Timashev, Moscow. Preprint available at  http://arxiv.org/abs/2008.11763
 
 
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Geoff Schiebinger
Department of Mathematics, UBC
Mon 21 Sep 2020, 3:00pm
Institute of Applied Mathematics
Zoom meeting
Towards a mathematical theory of developmental biology: Analyzing developmental processes with optimal transport
Zoom meeting
Mon 21 Sep 2020, 3:00pm-4:00pm

Abstract

 https://ubc.zoom.us/j/63318122194?pwd=RUV2RVZVZUtxV0FvdWhOaDBJbzVrQT09
Meeting ID: 633 1812 2194
Passcode: 141447
 
Abstract. This talk focuses on estimating temporal couplings of stochastic processes with optimal transport (OT), motivated by applications in developmental biology and cellular reprogramming. For nearly a century, the prevailing mathematical theory of developmental biology has been based on Waddington's `epigenetic landscape’ – a potential energy surface that determines trajectories of cellular development. Now, with the advent of high-throughput measurement technologies like single cell RNA-sequencing (scRNA-seq), the prospect of charting this landscape is within reach. This holds tremendous potential for diverse applications from regenerative medicine (e.g. cellular reprogramming) to agriculture (e.g. predicting impacts of climate change on crops or growing artificial meat). While the problem of recovering the landscape is inherently nonconvex, we demonstrate that the ‘laws on paths’ induced by this potential energy surface can be recovered using convex optimization. Our approach provides a general framework for investigating cellular differentiation.
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Northwestern University
Wed 23 Sep 2020, 2:05pm
Mathematical Biology Seminar
Zoom - contact organizer (abuttens at math ubc ca) for meeting id
Modeling and measuring cell dynamics in zebrafish-skin patterns
Zoom - contact organizer (abuttens at math ubc ca) for meeting id
Wed 23 Sep 2020, 2:05pm-3:05pm

Abstract

Wild-type zebrafish (Danio rerio) are characterized by black and yellow stripes, which form on their body and fins due to the self-organization of thousands of pigment cells. Mutant zebrafish and sibling species in the Danio genus, on the other hand, feature altered, variable patterns, including spots and labyrinth curves. The longterm goal of my work is to better link genotype, cell behavior, and phenotype by helping to identify the specific alterations to cell interactions that lead to these different fish patterns. Using a phenomenological approach, we develop agent-based models for cell interactions and simulate pattern formation on growing domains. In this talk, I will overview our models and highlight some topological techniques that allow us to quantitatively compare our simulations to in vivo images. I will also discuss current directions and open questions related to taking a more mechanistic and quantitative approach to describing cell behavior in zebrafish.

Note for Attendees

 Dr. Volkening will also deliver the Rising Stars colloquium on Oct 30, 2020.
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UBC and Technion
Wed 23 Sep 2020, 3:00pm
Probability Seminar
https://ubc.zoom.us/s/67941158154?pwd=TDRjdm1ta2Fxbi9tVjJyaWdKb3A5QT09
Scaling limits of uniform spanning trees in three dimensions
https://ubc.zoom.us/s/67941158154?pwd=TDRjdm1ta2Fxbi9tVjJyaWdKb3A5QT09
Wed 23 Sep 2020, 3:00pm-4:30pm

Abstract

Wilson's algorithm allows efficient sampling of the uniform spanning tree (UST) by using loop-erased random walks. This connection gives a tractable method to study the UST. The strategy has been fruitful for scaling limits of the UST in the planar case and high dimensions. However, three-dimensional scaling limits are far from understood. This talk is about recent advances in this problem when we describe the UST as a metric measure space. Our main result is on the existence of sub-sequential scaling limits and convergence under dyadic scalings with respect to a Gromov-Hausdorff-type topology. We will also discuss some properties of the limit tree.

This is joint work with Omer Angel, David Croydon, and Daisuke Shiraishi.
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