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 Events
Brown
Mon 16 Jan 2017, 3:00pm SPECIAL
Institute of Applied Mathematics
ESB 2012
Functional interpretation for transverse arches of human foot
ESB 2012
Mon 16 Jan 2017, 3:00pm-4:00pm

Abstract

Fossil record indicates that the emergence of arches in human ancestral feet coincided with a transition from an arboreal to a terrestrial lifestyle. Propulsive forces exerted during walking and running load the foot under bending, which is distinct from those experienced during arboreal locomotion. I will present mathematical models with varying levels of detail to illustrate a simple function of the transverse arch. Just as we curve a dollar bill in the transverse direction to stiffen it while inserting it in a vending machine, the transverse arch of the human foot stiffens it for bending deformations. A fundamental interplay of geometry and mechanics underlies this stiffening -- curvature couples the soft out-of-plane bending mode to the stiff in-plane stretching deformation. In addition to presenting a functional interpretation of the transverse arch of the foot, this study also identifies a classification of flat feet based on the skeletal geometry and mechanics.

Note for Attendees

Reception before the talk in ESB 4133 (PIMS lounge). This is the annual IAM alumni lecture. 
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San Francisco State University
Mon 16 Jan 2017, 3:00pm
Algebraic Geometry Seminar
MATX 1102
Double Ramification Cycles and Tautological Relations
MATX 1102
Mon 16 Jan 2017, 3:00pm-4:00pm

Abstract

Tautological relations are certain equations in the Chow ring of the moduli space of curves.  I will discuss a family of such relations, first conjectured by A. Pixton, that arises by studying moduli spaces of ramified covers of the projective line.  These relations can be used to recover a number of well-known facts about the moduli space of curves, as well as to generate very special equations known as topological recursion relations.  This is joint work with various subsets of S. Grushevsky, F. Janda, X. Wang, and D. Zakharov.

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San Francisco State University
Mon 16 Jan 2017, 4:15pm
Algebraic Geometry Seminar
MATX 1102
Genus-One Landau-Ginzburg/Calabi-Yau Correspondence
MATX 1102
Mon 16 Jan 2017, 4:15pm-5:15pm

Abstract

First suggested by Witten in the early 1990's, the Landau-Ginzburg/Calabi-Yau correspondence studies a relationship between spaces of maps from curves to the quintic 3-fold (the Calabi-Yau side) and spaces of curves along with 5th roots of their canonical bundle (the Landau-Ginzburg side). The correspondence was put on a firm mathematical footing in 2008 when Chiodo and Ruan proved a precise statement for the case of genus-zero curves, along with an explicit conjecture for the higher-genus correspondence. In this talk, I will begin by describing the motivation and the mathematical formulation of the LG/CY correspondence, and I will report on recent work with Shuai Guo that verifies the higher-genus correspondence in the case of genus-one curves.

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Ben Adcock
Department of Mathematics, SFU
Tue 17 Jan 2017, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Sparse polynomial approximation of high-dimensional functions
ESB 4133 (PIMS Lounge)
Tue 17 Jan 2017, 12:30pm-1:30pm

Abstract

Many problems in scientific computing require the approximation of smooth, high-dimensional functions from limited amounts of data.  For  instance, a typical problem in uncertainty quantification involves identifying the parameter dependence of the output of a computational model. Complex physical systems involve models with multiple parameters, resulting in multivariate functions of many variables. Although the amount of data may be large, the curse of dimensionality
essentially prohibits collecting or processing sufficient data to approximate the unknown function using classical techniques.

In this talk, I will give an overview of the approximation of smooth, high-dimensional functions using sparse polynomial expansions.  I will focus on the application of techniques from compressed sensing to this problem, and discuss the extent to which such approaches overcome the curse of dimensionality. If time, I will also discuss several extensions, including dealing with corrupted and/or unstructured data, the effect of model error and incorporating additional information such as gradient data. I will also highlight several challenges and open problems.

This is joint work with Casie Bao, Simone Brugiapaglia and Yi Sui (SFU).
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Kseniya Garaschuk and Eric Cytrynbaum
University of the Fraser Valley and UBC
Tue 17 Jan 2017, 12:30pm
Lunch Series on Teaching & Learning
Irving K. Barber Learning Ctr Room 461
Collaborative exams in large university courses
Irving K. Barber Learning Ctr Room 461
Tue 17 Jan 2017, 12:30pm-1:30pm

Abstract

As we use more and more group work in our classes, should we consider introducing it into our assessments? One model that has been used are so-called two-stage assessments, where students first complete and turn in the questions individually and then, working in small groups, answer the same questions again. This technique was first introduced in the UBC Faculty of Science in 2009 and is now being used in at least 20 science courses. 
 
In this session, we will discuss a study of feasibility and effectiveness of two-stage quizzes as introduced into two mathematics courses at UBC with a total of 834 students. We examine both short and long term retention resulting from introducing group assessments, we analyze results of collaborative learning based on question type and group composition. Finally, we present student and instructor feedback as well as discuss future directions of implementation and research. 
 
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UBC Math
Tue 17 Jan 2017, 4:00pm SPECIAL
Probability Seminar
ESB 2012
Boundary Harnack principle for diffusions
ESB 2012
Tue 17 Jan 2017, 4:00pm-5:00pm

Abstract

 The boundary Harnack principle (BHP) is a fundamental tool to understand the behaviour of positive harmonic functions near the boundary of a domain. For instance, the BHP implies a concrete description of the Martin boundary of a domain in geometric terms. Other applications of BHP include Carleson estimate, Fatou's theorem, and heat kernel estimates for diffusions killed upon exiting a domain. In this talk, I will discuss a recent extension of BHP that provides new examples of diffusions satisfying BHP even in  R^n.
 
This is joint work with Martin Barlow.
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UBC Math
Wed 18 Jan 2017, 3:00pm SPECIAL
Department Colloquium
ESB 2012 (note special day)
Stability of elliptic Harnack inequality
ESB 2012 (note special day)
Wed 18 Jan 2017, 3:00pm-4:00pm

Abstract

Harnack inequalities have proved to be a powerful tool in PDE (regularity estimates), geometry (geometric flows) and probability (heat kernel estimates). In the early 1990s Grigor'yan and Saloff-Coste gave a characterisation of the parabolic Harnack inequality (PHI). This characterisation implies that PHI is stable under perturbations (quasi-isometries). In this talk, I will provide an introduction to Harnack inequalities and discuss the stability of elliptic Harnack inequality. 

This is joint work with Martin Barlow.

Note for Attendees

Tea and cookies will be served before this special colloquium.
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Columbia University
Thu 19 Jan 2017, 3:30pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012 or ESB 4133
Scaling limits of open ASEP and ferromagnetic Glauber dynamics
ESB 2012 or ESB 4133
Thu 19 Jan 2017, 3:30pm-4:30pm

Abstract

 
We discuss two recent scaling limit results for discrete dynamics converging to stochastic PDEs. The first is the asymmetric simple exclusion process in contact with sources and sinks at boundaries, called Open ASEP.  We prove that under weakly asymmetric scaling the height function converges to the KPZ equation with Neumann boundary conditions. The second is the Glauber dynamics of the Blume-Capel model (a generalization of Ising model), in two dimensions with Kac potential. We prove that the averaged spin field converges to the stochastic quantization equations. The main purpose of this talk is to discuss the general issues one needs to address when passing from discrete to continuum, the common challenge in the proofs of such scaling limit theorems, and how we overcome these difficulties in the two specific models. (Based on joint works with Ivan Corwin and Hendrik Weber)
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Columbia University
Fri 20 Jan 2017, 3:00pm SPECIAL
Department Colloquium
ESB 2012
Singular Stochastic Partial Differential Equations - How do they arise and what do they mean?
ESB 2012
Fri 20 Jan 2017, 3:00pm-4:00pm

Abstract

 
Systems with random fluctuations are ubiquitous in the real world. Stochastic PDEs are default models for these random systems, just as PDEs are default models for deterministic systems. However, a large class of such stochastic PDEs were poorly understood until very recently: the presence of very singular random forcing as well as nonlinearities render it challenging to interpret what one even means by a ``solution". The recent breakthroughs by M. Hairer, M. Gubinelli and other researchers including the speaker not only established solution theories for these singular SPDEs, but also led to an explosion of new questions. These include scaling limits of random microscopic models, development of numerical schemes, ergodicity of random dynamical systems and a new approach to quantum field theory. In this talk we will discuss the main ideas of the recent solution theories of singular SPDEs, and how these SPDEs arise as limits of various important physical models.
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