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 Events
Andreas Stathopoulos
Computer Science, College of William and Mary
Mon 25 Feb 2019, 12:30pm SPECIAL
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS lounge)
(SCAIM) Seminar: State-of-the-Art SVD for Big Data
ESB 4133 (PIMS lounge)
Mon 25 Feb 2019, 12:30pm-1:30pm

Abstract

The singular value decomposition (SVD) is one of the core computations of today's scientific applications and data analysis tools. The main goal is to compute a compact representation of a high dimensional operator, a matrix, or a set of data that best resembles the original in its most important features. Thus, SVD is widely used in scientific computing and machine learning, including low rank factorizations, graph learning, unsupervised learning, compression and analysis of images and text.

The popularity of the SVD has resulted in an increased diversity of methods and implementations that exploit specific features of the input data (e.g., dense/sparse matrix, data distributed among the computing devices, data from queries or batch access, spectral decay) and certain constraints on the computed solutions (e.g., few/many number of singular values and singular vectors computed, targeted part of the spectrum, accuracy). The use of the proper method and the customization of the settings can significantly reduce the cost.

In this talk, we'll overview the most relevant methods in terms of computing cost and accuracy (direct methods, iterative methods, online methods), including the most recent advances in randomized and online SVD solvers. We present what parameters have the biggest impact on the computational cost and the quality of the solution, and some intuition for their tuning. Finally, we discuss the current state of the software on widely used platforms (MATLAB, Python's numpy/scipy and R) as well as high-performance solvers with support for multicore, GPU, and distributed memory.

Note for Attendees

A light lunch will be served.
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Francesco DiPlinio
University of Virginia
Mon 25 Feb 2019, 3:00pm
Harmonic Analysis Seminar
MATH 126
Directional operators and the multiplier problem for the polygon
MATH 126
Mon 25 Feb 2019, 3:00pm-4:00pm

Abstract

I will discuss two recent results obtained in collaboration with I. Parissis (U Basque Country).  The first is a sharp L^2 estimate for the maximal averaging operator associated to sets of directions from algebraic sets in R^n of arbitrary codimension. The proof uses a new scheme of polynomial partitioning on manifolds which extends ideas by Larry Guth.
 

The second result is a sharp L^4 estimate for the Fourier multiplier associated to a polygon of N sides in R^2, and a sharp form of the two parameter Meyer's lemma. These results improve on the usual ones obtained via weighted norm inequalities and rely on a novel Carleson measure estimate for directional square functions of time-frequency nature.
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UBC
Mon 25 Feb 2019, 4:00pm
Algebraic Geometry Seminar
MATH 126
The motivic weight of the stack of bundles
MATH 126
Mon 25 Feb 2019, 4:00pm-5:00pm

Abstract

I will talk about a new approach to computing the motivic weight of the stack of G-bundles on a curve. The idea is to associate a motivic weight to certain ind-schemes, such as the affine Grassmannian and the scheme of maps X -> G, where X is an affine curve, using Bittner's calculus of 6 operations. I hope that this will eventually lead to a proof of a conjectural formula for the motivic weight of the stack of bundles in terms of special values of Kapranov's zeta function.
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Bartek Protas
Department of Mathematics & Statistics, McMaster University
Tue 26 Feb 2019, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS lounge)
(SCAIM) Seminar: Proving Fundamental Bounds in Hydrodynamis Using Variational Optimization Methods
ESB 4133 (PIMS lounge)
Tue 26 Feb 2019, 12:30pm-1:30pm

Abstract

In the presentation we will discuss our research program concerning the study of extreme vortex events in viscous incompressible flows. These vortex states arise as the flows saturating certain fundamental mathematical estimates, such as the bounds on the maximum enstrophy growth in 3D (Lu & Doering, 2008). They are therefore intimately related to the question of singularity formation in the 3D Navier-Stokes system, known as the hydrodynamic blow-up problem. We demonstrate how new insights concerning such questions can be obtained by formulating them as variational PDE optimization problems which can be solved computationally using suitable discrete gradient flows. More specifically, such an optimization formulation allows one to identify "extreme" initial data which, subject to certain constraints, leads to the most singular flow evolution.  In offering a systematic approach to finding flow solutions which may saturate known estimates, the proposed paradigm provides a bridge between mathematical analysis and scientific computation. In particular, it makes it possible to determine whether or not certain mathematical estimates are "sharp", in the sense that they can be realized by actual vector fields, or if these estimates may still be improved. In the presentation we will review a number of results concerning 2D and 3D flows characterized by the maximum possible growth of different Sobolev norms of the solutions.  Even when extreme initial data is used, high-resolution computations for the 3D Navier-Stokes system reveals no tendency for singularity formation in finite time.

[Joint work with Diego Ayala, Dongfang Yun and Di Kang]

Note for Attendees

A light lunch will be served.
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Université de Nantes
Wed 27 Feb 2019, 2:45pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
Lagrangian cocores generates the wrapped Fukaya category
ESB 4133 (PIMS Lounge)
Wed 27 Feb 2019, 2:45pm-3:45pm

Abstract

The Fukaya category of a Weinstein manifolds W algebraically package all Lagrangian submanifolds of W into an A-infinity category. In this talk I will motivate why studying Lagragian submanifolds in symplectic manifolds is relevant and then I will give an overview of the definition of wrapped Fukaya categories. I will explain a theorem stating that for Weinstein manifolds a particular finite collection of Lagrangians generates this category. Finally we will see some element of the proof and applications of this generation criterion. This is joint work with G. Dimitroglou-Rizell, P. Ghiggini and R. Golovko.
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James Johnson
Department of Cellular and Physiological Sciences, UBC
Wed 27 Feb 2019, 2:45pm
Mathematical Biology Seminar
ESB 4127
Biological problems on multiple time scales related to the local feedback actions of insulin on pancreatic beta-cells that could benefit from mathematical modelling
ESB 4127
Wed 27 Feb 2019, 2:45pm-3:45pm

Abstract

Insulin is an essential hormone that regulates nutrient homeostasis. Insufficient insulin results in diabetes, one of the most prevalent and costly diseases. Although the primary actions of insulin are to induce glucose uptake and metabolism in distant tissues, including muscle, fat and liver, the insulin secreting pancreatic beta-cells contain a high number of insulin receptors and known to respond to the hormone. On a minute-to-minute time-scale, insulin has been reported to have negative feedback effects on its own secretion, and we have data suggesting that the actions of insulin may be context-dependent, potentially depending on the ambient glucose levels (which are primarily controlled by glucose). Insulin has also been reported to have positive effects on its own synthesis and on the survival of the beta-cells over a timescale of months. Within beta-cells, insulin production is inherently stressful and exerts a negative effect on beta-cell proliferation that is most pronounced at a young age. We have also recently found that single beta-cells can exist in ‘bursting’ states of elevated insulin production that account for a significant proportion of the previous described heterogeneity in this cell type. Thus, using a variety of experimental approaches, we seek to understand context-dependent insulin feedback signalling on single beta-cells and their collective populations and we are interested in collaborating to build quantitative and testable models that could be used to explain the pathogenesis of diabetes. We also interested in expanding models to include other tissues and other soluble factors that are also relevant in nutrient homeostasis and diabetes.

 
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UBC
Wed 27 Feb 2019, 3:00pm
Probability Seminar
ESB 1012
Optimal Transport by Stopping Times
ESB 1012
Wed 27 Feb 2019, 3:00pm-4:00pm

Abstract

Optimal transport (OT) problems, initiated by G. Monge 200 years ago and refined by L. Kantorovich in the 1940’s, provide --among other things-- a quantitative way for measuring correlations between probability distributions.  Martingale optimal transports (MOT) and their Skorokhod embeddings in Brownian motion lead to optimal transport by stopping time (OTST) problems. These are important variations on OT, with applications to financial mathematics and probability theory. In OTST, one specifies a stochastic state process and a cost, and minimizes the expected cost over stopping times with a given state distribution.

In this talk, I will focus on the case where the state process is d-dimensional Brownian motion and the cost is given by the Euclidean distance. I will discuss new results involving dual variational principles, their attainment, as well as characterizations of the optimal stopping times as a hitting time of barriers given by solutions of corresponding obstacle problems. I will also discuss how these results generalize for other processes and costs and relate them to other aspects of probability theory. This talk is based on joint work with Nassif Ghoussoub, Young-Heon Kim and Tongseok Lim.
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