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 Events
Utah
Mon 3 Apr 2017, 3:00pm SPECIAL
Institute of Applied Mathematics
ESB 2012
Extending the Theory of Composites to Other Areas of Science
ESB 2012
Mon 3 Apr 2017, 3:00pm-4:00pm

Abstract

 

Note for Attendees

Reception precedes the talk in ESB 4133 (the PIMS lounge). This is in the IAM/PIMS distinguished colloquium series. 
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Rice
Mon 3 Apr 2017, 3:00pm
Algebraic Geometry Seminar
MATX 1102
Riemann-Hilbert problems in Donaldson-Thomas theory
MATX 1102
Mon 3 Apr 2017, 3:00pm-4:00pm

Abstract

Recently Bridgeland has introduced the notion of a BPS structure, which is meant to encode the output of unrefined Donaldson-Thomas theory. He studied an associated Riemann-Hilbert problem and found a relation with Gromov-Witten invariants in the case of the conifold. In this talk I will try to give an overview of this work, ending with some potential new directions to explore.

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Rongrong Wang
Department of Mathematics, UBC
Tue 4 Apr 2017, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Frequency down-extrapolation and its application to seismic inversion
ESB 4133 (PIMS Lounge)
Tue 4 Apr 2017, 12:30pm-1:30pm

Abstract

In this talk, we examine two methods for frequency extrapolation. Frequency extrapolation is the problem of utilizing data processing techniques to obtain the entire spectrum of an objective signal while only a middle band is sampled. This problem is well-posed for signals with special structures, such as those with a few non-zeros. The study is motivated by seismic inversion. Due to physical constraints, data obtained from a seismic survey is severely limiting in both the low and high frequency extent for the purposes of inversion. In particular, the missing low frequencies are known to be extremely essential, because when missing, most inversion algorithms are very likely to get stuck in local minima. In the numerical section, I will demonstrate the efficacy of the proposed methods in manufacturing low frequencies with real seismic examples and visualized inversion results.
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Columbia University
Tue 4 Apr 2017, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012 (PIMS)
Regularity of the Gauss curvature flow
ESB 2012 (PIMS)
Tue 4 Apr 2017, 3:30pm-4:30pm

Abstract

We will discuss about the regularity of the Gauss curvature flow: the optimal C^{1,\frac{1}{n-1}} regularity of degenerate solutions with flat sides and the interior C^{\infty} regularity of strictly convex solutions. 
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Purdue University
Wed 5 Apr 2017, 3:00pm
Probability Seminar
ESB 2012
Littlewood-Paley Estimates for LÚvy Processes
ESB 2012
Wed 5 Apr 2017, 3:00pm-4:00pm

Abstract

L^p inequalities for certain Littlewood-Paley functionals arising from  Lévy processes will be discussed. These are motivated by applications to the L^p boundedness of Fourier multiples which give L^p regularity of solutions to some non-local operators, including the fractional Laplacian.  Non-local operates have been extensively studied in recent years by researchers in analysis, probability and PDE.  The relevant Fourier multiples have been studied using the deep sharp martingale transform inequalities of Burkholder.  The proofs here, although not sharp, are completely elementary and use nothing more than Itô’s formula and arguments similar to those for the classical case of the Laplacian.
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Statistics and Actuarial Science, SFU
Wed 5 Apr 2017, 3:00pm SPECIAL
ESB 5104 (PIMS)
BC Data Science Colloquium: High dimensional statistical inference
ESB 5104 (PIMS)
Wed 5 Apr 2017, 3:00pm-4:15pm

Details

Penalized regression methods permit data analysts to fit models with more adjustable parameters than data points by imposing strong prior assumptions on the relationships between variables. As a result classical tools of uncertainty assessment no longer work. I have been involved in one approach to uncertainty assessment for problems of this sort. I will try to summarize the issues and contrast the current approaches.
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McMaster University
Wed 5 Apr 2017, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
Group actions on homology 3-spheres
ESB 4133 (PIMS Lounge)
Wed 5 Apr 2017, 3:15pm-4:15pm

Abstract

I will discuss finite group actions on integral or rational homology 3-spheres. The main examples for this talk are the Brieskorn integral homology 3-spheres M(p,q,r) arising from isolated singularities, which bound smooth 4-manifolds with definite intersection forms. In addition, there are special infinite families of Brieskorn homology 3-spheres which can be realized as boundaries of smooth contractible 4-manifolds. We ask whether the free periodic actions on Brieskorn spheres extend to smooth actions with isolated fixed points on one of these associated 4-manifolds.
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UC Berkeley and MPI Leipzig
Fri 7 Apr 2017, 3:00pm
Department Colloquium
ESB 2012
Sixty-four Curves of Degree Six
ESB 2012
Fri 7 Apr 2017, 3:00pm-4:00pm

Abstract

 
This lecture is an invitation to real algebraic geometry, along with computational aspects, ranging from bitangents and K3 surfaces to eigenvectors and ranks of tensors. We present an experimental study - with many pictures - of smooth curves of degree six in the real plane. The number 64 refers to rigid isotopy types in the Rokhlin-Nikulin classification.
 

Note for Attendees

Refreshments will be served at 2:45 p.m. in PIMS lounge before this colloquium
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Faculty of Mathematics, TU Chemnitz, Germany
Tue 11 Apr 2017, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Total Variation Image Reconstruction on Smooth Surfaces
ESB 4133 (PIMS Lounge)
Tue 11 Apr 2017, 12:30pm-1:30pm

Abstract

We present an analog of the total variation image reconstruction approach by Rudin, Osher, Fatemi (1992) for images defined on smooth surfaces, together with a proper analytical framework. The problem is defined in terms of quantities intrinsic to the surface and it is therefore independent of the parametrization.  It is shown that the Fenchel predual of the total variation problem is a quadratic optimization problem for the vector-valued predual variable with pointwise constraints on the surface. The predual problem is solved using a function space interior point method, and discretized by conforming Raviart-Thomas finite elements on a triangulation of the surface.  As in the flat case, the predual variable serves as an edge detector.  Numerical examples including denoising and un-erasing problems with both gray-scale and color images on complex 3D geometries are presented. 
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U.C. Santa Barbara
Tue 11 Apr 2017, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Min-max minimal hypersurfaces with free boundary
ESB 2012
Tue 11 Apr 2017, 3:30pm-4:30pm

Abstract

I will present a joint work with Martin Li. Minimal surfaces with free boundary are natural critical points of the area functional in compact smooth manifolds with boundary. In this talk, I will describe a general existence theory for minimal surfaces with free boundary. In particular, I will show the existence of a smooth embedded minimal hypersurface with free boundary in any compact smooth Euclidean domain. The minimal surfaces with free boundary were constructed using the min-max method. I will explain the basic ideas behind the min-max theory as well as our new contributions.
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UBC
Wed 12 Apr 2017, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
Proving Yuzvinsky's conjecture: an instance of applying topology to combinatorics
ESB 4133 (PIMS Lounge)
Wed 12 Apr 2017, 3:15pm-4:15pm

Abstract

The fact that |xy| = |x| |y| for real, complex, quaternion and octonion numbers x and y leads to the open question of finding all possible maps f: R^r X R^s ---> R^n  satisfying |f(x,y)| = |x| |y| for each x in R^r and y in R^s. For example, that no such f can exist when r=s=n=16 was a celebrated result in classical algebra.
When the components of f(x,y) are required to be bilinear forms in the components of x and y with integer coefficients, one can crudely encode f by a colored matrix M of r rows and s columns, using n colors but avoiding certain "forbidden configurations". In 1981, S. Yuzvinsky conjectured that the chromatic number for this kind of coloring of M should be given by a certain function of r and s already familiar to topologists. In this talk I shall prove his conjecture for a majority of values of r and s, including the case of square matrices r=s. I shall explain how each step in my combinatorial proof was indeed suggested by topological considerations.
This talk is dedicated to the memory of professor Erhard Luft (1933-2017).
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Thomas McCormick
Operations and Logistics Division, Sauder School of Business, UBC
Tue 18 Apr 2017, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Computing closest vectors in zonotopal lattices
ESB 4133 (PIMS Lounge)
Tue 18 Apr 2017, 12:30pm-1:30pm

Abstract

A lattice L is the set of vectors arising from integer linear combinations of given basis vectors in R^n. Given some vector x, the Closest Vector Problem (CVP) is to find a vector v in L of minimum l_2-norm distance to x. CVP is a fundamental problem for lattices with many applications, and it is in general NP Hard. 
A zonotopal lattice is given as the set of integer points {v | Mv = 0} when M is a totally unimodular matrix. We show how to adapt the Cancel and Tighten algorithm of Karzanov and McCormick to solve CVP for zonotopal lattices in O(n^3) time via the Seymour decomposition of totally unimodular matrices. The algorithm uses the decomposition to reduce the problem to a series of subproblems that are piecewise linear convex circulation and co-circulation network flow problems.

by
Britta Peis, Robert Scheidweiler (RWTH Aachen)
S. Thomas McCormick (UBC Sauder)
Frank Vallentin (Cologne)
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Computer Science Department, UBC, Vancouver
Wed 19 Apr 2017, 3:00pm
ESB 2012
Counting independent sets: not up to the tree threshold, but down to the root
ESB 2012
Wed 19 Apr 2017, 3:00pm-4:00pm

Details

The independence polynomial has been widely studied in algebraic graph theory, in statistical physics, and in algorithms for counting and sampling problems. Seminal results of Weitz (2006) and Sly (2010) have shown that in bounded-degree graphs the independence polynomial can be efficiently approximated if the argument is real, positive and below a certain threshold, whereas above that threshold the polynomial is hard to approximate. Furthermore, this threshold exactly corresponds to a phase transition in physics, which demarcates the region within which the Gibbs measure has correlation decay.
 
We consider the problem of computing the independence polynomial with a negative (or even complex) argument, whose magnitude is less than the smallest magnitude of any root of the polynomial. We show that there is a fully-polynomial-time approximation scheme (FPTAS) for such an argument. This result actually holds much more generally for the multivariate independence polynomial, in which each vertex has its own activity. Our proof uses a novel multivariate form of the correlation decay technique.
 
This FPTAS can be used to give a constructive algorithm for the Lovasz Local Lemma in probabilistic combinatorics.
 
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UniversitÚ catholique de Louvain
Wed 19 Apr 2017, 3:15pm
Topology and related seminars
ESB 4133
Cosimplicial models for embedding spaces of manifolds and manifold calculus.
ESB 4133
Wed 19 Apr 2017, 3:15pm-4:15pm

Abstract

 TBA
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Paul Tupper
Department of Mathematics, SFU
Tue 25 Apr 2017, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
From Distance to Diversity: Extending the Concept of a Metric Space
ESB 4133 (PIMS Lounge)
Tue 25 Apr 2017, 12:30pm-1:30pm

Abstract


One important construction in the theory of metric spaces is the tight span. The tight span of a metric space can be thought of as a generalization of the idea of a convex hull in linear spaces and is the basis for much work in the study and visualization of finite metric spaces. Motivated by problems in phylogenetics, we have developed a generalization of the concept of metric spaces, which we call diversities. In a diversity, every subset of points in the space corresponds to a number, not just pairs, and there is a more general version of the triangle inequality. Besides encompassing a number of interesting examples as special cases, diversities have a natural tight span construction with corresponding theory. I will give an introduction to tight span theory for metric spaces and then show how it extends to our theory of diversities. I will conclude by demonstrating the relation between diversities and Steiner tree packing in graphs. This is joint work with David Bryant (University of Otago, New Zealand).

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UBC
Wed 26 Apr 2017, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
Mod 2 homology operations for spectral Lie algebras
ESB 4133 (PIMS Lounge)
Wed 26 Apr 2017, 3:15pm-4:15pm

Abstract

The Goodwillie derivatives of the identity functor on pointed spaces form an operad in spectra that is  very closely related to the Lie operad. I will describe the mod 2 homology operations for algebras over this operad. This talk will not assume prior knowledge of either operads or Goodwillie calculus. Sadly, due to time constraints, it also won't explain any Goodwillie calculus! (Instead I will start from a combinatorial description of the derivatives of the identity functor.)
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Ecole Normale SupÚrieure de Lyon
Thu 27 Apr 2017, 3:30pm
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
ESB 4127
Iterated extensions and p-adic dynamical systems
ESB 4127
Thu 27 Apr 2017, 3:30pm-5:00pm

Abstract

Let K be a field and let P be a polynomial. What can we say about the field generated by the roots of P and of all its iterates? I will discuss some questions motivated by this general problem when K is a p-adic field. Along the way, we'll see Coleman power series, p-adic dynamical systems and a little bit of p-adic Hodge theory.

(This talk is part of the PIMS focus semester on the mod p Langlands program).
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