Mathematics Dept.
  Events
UBC
Mon 18 Nov 2019, 3:00pm
Algebraic Geometry Seminar
MATH 225
Biregular Cremona transformations of the plane
MATH 225
Mon 18 Nov 2019, 3:00pm-5:00pm

Abstract

We study the birational self-maps of the projective plane that induce bijections on the k-rational points for a given field k. These form a subgroup BCr_2(k) inside the Cremona group. The elements of BCr_2(k) are called Biregular Cremona transformations. We show that BCr_2(k) is not finitely-generated under a mild hypothesis on the field k. When k is a finite field, we study the possible permutations induced on the k-rational points of the plane. This is joint work with Kuan-Wen Lai, Masahiro Nakahara and Susanna Zimmermann.
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Parisa Sarmadi
Department of Mechanical Engineering, UBC
Mon 18 Nov 2019, 4:00pm
CEME 2202
Fluids Seminar: Visco-Plastically Lubricated Multi-Layer Flows with Application to Transport in Pipelines
CEME 2202
Mon 18 Nov 2019, 4:00pm-5:00pm

Details

Abstract: We introduce a novel triple layer core-annular method. The method has broad application in lubricated transport of heavy viscous oils to reduce the frictional pressure gradient and ensure the continued flow. In this method, we purposefully positioned a shaped unyielded visco-plastic fluid (skin layer) at the interfaces to eliminate interfacial instabilities. Specifically, the skin layer is shaped which allows for lubrication force to develop as the core rises under the action of transverse buoyancy forces due to density differences between layers. In this talk, we address the feasibility of the method. Also, we show how to sculpt the interface in a very controlled way for a desirable interface. Finally, we give an overview of 3D triple-layer computations and the buoyant motion of the core.

Bio: Parisa is a graduate research assistant and teaching fellow in the Department of Mechanical Engineering at UBC. She works on “visco-plastically lubricated multi-layer flows” under supervision of Prof. Ian Frigaard at UBC and Prof. Sarah Hormozi at Ohio University.

 

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Nick Dexter
Department of Mathematics, SFU
Tue 19 Nov 2019, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS lounge)
Practical Approximation in High Dimension with ReLU Deep Neural Networks
ESB 4133 (PIMS lounge)
Tue 19 Nov 2019, 12:30pm-1:30pm

Abstract

Deep learning (DL) is transforming whole industries as complicated decision-making processes are being automated by neural networks trained on real-world data. Yet as these tools are increasingly being applied to critical problems in medicine, science, and engineering, many questions about their stability, reliability, and approximation capabilities remain. Such questions include: how many data points are sufficient to train a neural network on simple approximation tasks, and how robust are these trained architectures to noise in the data? In this work we seek to quantify the capabilities of deep neural networks (DNNs), both theoretically and numerically. Recently published results show that these architectures allow for the same convergence rates as best-in-class schemes, e.g., h,p-adaptive finite element and spectral approximations. Our own analysis confirms that DNNs afford the same sample complexity estimates as compressed sensing (CS) on sparse polynomial approximation problems. In exploring the approximation capabilities of DNNs, we also present numerical experiments on a series of simple tests in high-dimensional function approximation, with comparisons to results achieved with CS on the same problems. Our numerical experiments show that standard methods of training and initialization often yield DNNs which fail to achieve the rates of convergence suggested by theory. We conclude with a discussion of the conditioning of the DL problem.

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

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UBC
Tue 19 Nov 2019, 4:00pm
Discrete Math Seminar
ESB 4127
The e-positivity of chromatic symmetric functions
ESB 4127
Tue 19 Nov 2019, 4:00pm-5:00pm

Abstract

The chromatic polynomial was generalized to the chromatic symmetric function by Stanley in his seminal 1995 paper. This function is currently experiencing a flourishing renaissance, in particular the study of the positivity of chromatic symmetric functions when expanded into the basis of elementary symmetric functions, that is, e-positivity.
 
In this talk we approach the question of e-positivity from various angles. Most pertinently we resolve the 1995 statement of Stanley that no known graph exists that is not contractible to the claw, and whose chromatic symmetric function is not e-positive.
 
This is joint work with Soojin Cho, Samantha Dahlberg, Angele Foley and Adrian She, and no prior knowledge is assumed.
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University of Alberta
Wed 20 Nov 2019, 2:45pm SPECIAL
Mathematical Biology Seminar
ESB 4133
Navigating the Flow: The homing of sea turtles.
ESB 4133
Wed 20 Nov 2019, 2:45pm-3:45pm

Abstract

The green sea turtle Chelonia midas travels for thousands of miles from the coast of Brazil to a small island in the Atlantic Ocean, Ascension Island. There the turtles lay their eggs into the warm sand on the beach. It is a classic scientific challenge to understand the navigational skills of the turtles and several orienteering mechanisms are discussed, such as geomagnetic information, chemotaxis, Atlantic flow patterns etc.

In this talk I will present a mathematical model for the homing of sea turtles and discuss how it can be used to identify the navigational mechanisms of sea turtles.

(joint work with K.J. Painter).

Note for Attendees

 This is Part I of a special "Double Feature" Math Biology Seminar on November 20, 2019.
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Thomas Hockenhull
University of Glasgow
Wed 20 Nov 2019, 2:45pm
Topology and related seminars
ESB Room 4127 (PIMS)
Koszul duality and Knot Floer homology
ESB Room 4127 (PIMS)
Wed 20 Nov 2019, 2:45pm-3:45pm

Abstract

‘Koszul duality’ is a phenomenon which algebraists are fond of, and has previously been studied in the context of '(bordered) Heegaard Floer homology' by Lipshitz, Ozsváth and Thurston. In this talk, I shall discuss an occurrence of Koszul duality which links older constructions in Heegaard Floer homology with the bordered Heegaard Floer homology of three-manifolds with torus boundary. I shan’t assume any existing knowledge of Koszul duality or any form of Heegaard Floer homology.
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Professor Eric Climent
IMFT, INP, UPS Toulouse, France
Wed 20 Nov 2019, 4:00pm
CEME 2202
Fluids Seminar: Preferential accumulation and vertical migration of phytoplankton cells in turbulence
CEME 2202
Wed 20 Nov 2019, 4:00pm-5:00pm

Details

Abstract: Many phytoplankton species are motile, propelling themselves through water with velocities ranging from 10 to 1000 microns per second. Daily, phytoplankton needs to migrate vertically from and towards the ocean surface for light and to find nutrients such as dissolved oxygen. To travel through the water column, they need to fight against gravity (by swimming) and fluid turbulence which can make their journey longer.

The spatial distribution of unicellular organisms in the Ocean is observed to be heterogeneous. This communication demonstrates that heterogeneity can be generated ex novo at the smallest scales of turbulent flows via an active coupling between motility and hydrodynamic shear, and stands in direct contrast with the aforementioned mechanism that considers phytoplankton cells to act as passive tracers. It is often observed that cells migrate across the water column as chains. The purpose of our study is to elaborate on this observation as a potential benefit to swim as a chain in turbulence.

We carried out numerical simulations of the coupled system of homogeneous isotropic turbulence and gyrotactic cell trajectories through Lagrangian tracking. Realistic flows are obtained by randomly forcing large-scale fluid motions and solving Navier-Stokes equations through direct numerical simulations for the resultant turbulent motion. This flow is seeded with hundreds of thousands of cells and statistical analysis is carried out to find out the physical mechanisms.

References

               Chain formation can enhance the vertical migration of phytoplankton through turbulence. S. Lovecchio, E. Climent, R. Stocker and W. M. Durham (2019) accepted in Sciences advance

               Turbulent fluid acceleration generates clusters of gyrotactic microorganisms. F. De Lillo, M. Cencini, W.M. Durham, Barry, R. Stocker, E. Climent and G. Boffetta (2014). Physical Review Letters – 112, 044502.

               Turbulence drives microscale patches of motile phytoplankton. W. M. Durham, E. Climent, M. Barry, F. De Lillo G. Boffetta, M. Cencini and R. Stocker. Nature Communications (2013) – 4:2148.

               Gyrotaxis in a steady vortical flow. W.M. Durham, E. Climent and R. Stocker. (2011). Physical Review Letters – 106, 238102.

Bio:

Eric Climent is a full professor at University of Toulouse, France, and the current head of the Fluid Mechanics Institute in Toulouse that counts about 200 researchers in the field of Fluid Mechanics. Eric graduated his Master degree in 1993 and PhD degree in 1996 from University of Toulouse. From 1998 to 2007, he was an Associate professor at University of Strasbourg and University of Toulouse. From 1999 to 2003, he spent about 1 year and a half at Brown University as a visiting professor. His main area of research is the multi-scale modelling and numerical simulation of dispersed phase flows (bubbles, droplets and rigid particles) with potentially additional effects as chemical reactions, magnetic forces, interface properties and biological interactions.

 

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Colorado Stat
Wed 20 Nov 2019, 4:10pm SPECIAL
Mathematical Biology Seminar
ESB 4133
Cell Shape and Cell State: Some experimental investigations
ESB 4133
Wed 20 Nov 2019, 4:10pm-5:00pm

Abstract

 Different types of cells, i.e. from different tissues, typically look quite different from each other. Even when cultured on two-dimensional surfaces like glass slides or tissue culture polystyrene under identical conditions, cells adopt different shapes. These shapes are in general functions of the cytoskeletal properties of those cells, itself a subset of what we can call the “state” of the cell. Experimental evidence over several decades has indicated that for some cell types, imposed changes in shape lead to changes in cellular differentiation and other properties. Conversely there is increasing evidence that some changes in cell state can lead to stereotypical changes in cell shape. We have developed a large number of morphological parameters to quantify cell shape and cytoskeletal morphology. Using these parameters to quantify morphologies of different cell lines, as well as cells in different experimental conditions, we show that quantifiers of cell shape and cytoskeletal texture can be used to discriminate between different cell states. A neural network is able to correctly classify different cell states with high accuracy. Using projections of the data to lower-dimensional shape space, we find that we can distinguish between similar and dissimilar changes in shape.  We use this method to identify similarities in shape changes between breast cancer and osteosarcoma cell lines accompanying the acquisition of invasive characteristics. Our data indicates that cellular morphology is a powerful and sensitive window into the physiological state of the cell, and underline the need to develop mechanistic models that relate cell state to cell shape.  

Note for Attendees

 This is Part II of a special "Double Feature" Math-Biology Seminar on Nov 20, 2019. It will follow directly after the PIMS Tea.
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Massachusetts Institute of Technology
Thu 21 Nov 2019, 3:30pm
Number Theory Seminar
MATX 1102
A database of p-adic tori
MATX 1102
Thu 21 Nov 2019, 3:30pm-5:00pm

Abstract

Maximal tori in reductive groups form the foundation for many constructions in $p$-adic representation theory. Many of these constructions place constraints on the tori involved, requiring that they split over unramified or tamely ramified extensions of the ground field. When the residue characteristic is small, wild tori occur even for groups of small rank. Such tori complicate standard tools used to construct representations, such as Bruhat-Tits buildings, Néron models and the Moy-Prasad filtration. In an effort to aid in the study of representations in small characteristic, I will present an early version of an online database of p-adic tori.
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Dept of Mathematics, University of Cincinnati
Fri 22 Nov 2019, 3:00pm
Department Colloquium
ESB 1012
Microswimmers propelled by helical flagella: Modeling, Simulations & Analysis
ESB 1012
Fri 22 Nov 2019, 3:00pm-3:50pm

Abstract

 Swimming bacteria with helical flagella are self-propelled micro-swimmers in nature, and the swimming strategies of such bacteria vary depending on the number and the position of flagella on the cell body. In this talk, I will introduce two microorganisms, multi-flagellated E. coli and single-flagellated Vibrio A. The Kirchhoff rod theory is used to model the elastic helical flagella and the rod-shaped cell body is represented by a hollow ellipsoid that can translate and rotate as a neutrally buoyant rigid body interacting with a surrounding fluid. The hydrodynamic interaction between the fluid and the bacteria is described by the regularized version of Stokes flow. I will focus on how bacteria can swim and reorient swimming course for survival and how Mathematics can help to understand the swimming mechanism of such bacteria.

Keywords: Fluid-structure interaction, Bacterial flagellar propulsion, Polymorphic transformation, Buckling instability

Note for Attendees

Refreshments are served at 2:30pm in ESB 4133 PIMS lounge before the Colloquium.
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