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 Events
Hong Kong University of Science and Technology
Wed 1 Oct 2014, 3:00pm
Probability Seminar
ESB 2012
Solving the high-dimensional Markowitz Optimization Problem: a tale of sparse solutions
ESB 2012
Wed 1 Oct 2014, 3:00pm-4:00pm

Abstract

We consider the high-dimensional Markowitz optimization problem. A new approach combining sparse regression and estimation of optimal returns based on random matrix theory is proposed to solve the problem. We prove that under some sparsity assumptions on the underlying optimal portfolio, our novel approach asymptotically yields the theoretical optimal return, and in the meanwhile satisfies the risk constraint. To the best of our knowledge, this is the first method that can achieve these two goals simultaneously in the high-dimensional setting. We further conduct simulation and empirical studies to compare our method with some benchmark methods, including the equally weighted portfolio, the bootstrap-corrected method by Bai et al. (2009) and the covariance-shrinkage method by Ledoit and Wolf (2004). The results demonstrate substantial advantage of our method, which attains high level of returns while keeping the risk well controlled by the given constraint.

Based on joint work with Mengmeng Ao and Yingying Li.

 
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UBC
Wed 1 Oct 2014, 3:15pm
Topology and related seminars
ESB 4133 (may move to Thursday)
The Status of the Farrell-Jones conjecture
ESB 4133 (may move to Thursday)
Wed 1 Oct 2014, 3:15pm-4:15pm

Abstract

In the beginning of this talk I will use the Farrell-Jones conjecture to express the K-theory of R[Z^2] in Terms of the K-theory of R. Geometric conditions on a Group that imply the conjecture will be mentioned . The class of Groups for which the conjecture is known is quite large I will define it and mention some interesting open cases.
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Université Pierre et Marie Curie
Thu 2 Oct 2014, 3:30pm
Number Theory Seminar
room MATH 126
Points of small height on abelian varieties over function fields
room MATH 126
Thu 2 Oct 2014, 3:30pm-4:30pm

Abstract

An old conjecture of Lang (for elliptic curves) generalized by Silverman, asserts that the Néron-Tate height of a rational point of an abelian variety defined over a number field can be bounded below linearly in terms of the Faltings height of the underlying abelian variety. We shall explore the function field analogue of this problem.
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Université Paris-Sud
Thu 2 Oct 2014, 4:00pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
ESB 4133 (PIMS lounge)
Large Time behavior for the cubic Szego évolution
ESB 4133 (PIMS lounge)
Thu 2 Oct 2014, 4:00pm-5:00pm

Abstract

The cubic Szegö equation is an Hamiltonian evolution on periodic functions with nonnegative Fourier modes, arising as a normal form for the large time behavior of a nonlinear wave equation on the circle. It defines a flow on every Sobolev space with enough regularity. In this talk, I will give the main arguments for the proof of the following theorem. The trajectories of the cubic Szegö equation are almost periodic in the Sobolev energy space, but
are generically unbounded in every more regular Sobolev space.This is a joint work with Sandrine Grellier and Zaher Hani.

Note for Attendees

 Please note unusual time and room.
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UBC
Fri 3 Oct 2014, 3:00pm
Department Colloquium
MATH ANNEX 1100
Recent developments for Ricci flow on non-compact manifolds.
MATH ANNEX 1100
Fri 3 Oct 2014, 3:00pm-4:00pm

Abstract

The Ricci flow is one of the most important equations in geometric analysis, and has been used to solve deep problems in topology and geometry. Through a system of local parabolic PDE's, the flow governs the evolution of a Riemannian metric tensor in space, and it's general theory is fundamentally based on the assumption that the metric is complete with bounded sectional curvatures. I will give an overview of the general theory, then discuss the problem of flowing unbounded curvature metrics on non-compact manifolds. I will then discuss recent results for U(n) invariant Kahler metrics on C^n, and connections to Yau's uniformization conjecture. The talk is based in part on joint work with L.F. Tam and K.F Li.

Note for Attendees

Refreshments will be served at 2:45pm in the Math Lounge area, MATH 125 before the colloquium.
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Director of Institute for Pure & Applied Mathematics, UCLA, Los Angeles
Mon 6 Oct 2014, 3:00pm SPECIAL
Institute of Applied Mathematics
LSK 460
From PDEs to Information Science and Back
LSK 460
Mon 6 Oct 2014, 3:00pm-4:00pm

Abstract

 The arrival of massive amounts of data from imaging, sensors, computation and the internet brought with it significant challenges for information science. New methods for analysis and manipulation of big data have come from many scientific disciplines. The first focus of this presentation is the application of ideas from PDEs, such as variational principles and numerical diffusion, to image and data analysis. Examples include denoising, segmentation, inpainting and texture extraction for images. The second focus is the development of new ideas in information science, such as wavelets, soft-thresholding, sparsity and compressed sensing. The subsequent application of these ideas to PDEs and numerical computation is the third focus of this talk. Examples include wavelet analysis for turbulent flows, the use of soft-thresholding in computation of PDEs with multi-scale features, and the construction of “compressed modes” (modes that are compactly supported in space) for density functional theory and other PDEs that come from variational principles.

Russel Caflisch is a Professor in the Mathematics Department at UCLA and has a joint appointment in the Department of Materials Science and Engineering. He received his PhD from the Courant Institute at New York University in 1978 and has also held faculty positions at Stanford and NYU. He is currently the director of the Institute for Pure & Applied Mathematics (IPAM), and the Editor-In-Chief for the journal Multiscale Modeling and Simulation. He was a Sloan Foundation Research Fellow, and a fellow of the Society for Industrial and Applied Mathematics, the American Mathematical Society, and the American Academy of the Arts and Sciences. Caflisch’s expertise includes a wide range of topics in applied mathematics, including PDEs, fluid dynamics, plasma physics, materials science, Monte Carlo methods, and computational finance.

Note for Attendees

Refreshments start 15 minutes before the talk in the IAM Lounge, Room 306 of the LSK building. 
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Kansas State
Mon 6 Oct 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)
Mirror symmetry for the punctured plane
ESB 4127 (host: UBC)
Mon 6 Oct 2014, 3:00pm-4:00pm

Abstract

Homological mirror symmetry initially concerned Calabi-Yau 3-folds and, from that point, rapidly expanded to incorporate local Calabi-Yau's and Fano varieties. In this talk, I will discuss joint work with Ludmil Katzarkov and Maxim Kontsevich on extending this correspondence further to include quasi-affine toric varieties, the most basic example of which is a punctured plane. The complex side of the correspondence, or B-model, remains the derived category of coherent sheaves of the variety. On the mirror side, the A-model is a partially wrapped Fukaya category on the cotangent bundle of the torus. The key ingredient is the wrapping Hamiltonian which is defined as a distance^2 function away from a mirror non-compact Lagrangian skeleton. I will explain the geometric intuition for the case of the punctured plane and discuss elements of the proof for the general case.

 

Note for Attendees

  Note: Today we have a double-header again. Talk one: Gabriel Kerr 15:00-16:00. Talk two: Charlie Beil: 16:30-17:30. Coffee and cookies in between the two talks.
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Bristol
Mon 6 Oct 2014, 4:30pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)
Nonlocality and the central geometry of dimer algebras
ESB 4127 (host: UBC)
Mon 6 Oct 2014, 4:30pm-5:30pm

Abstract

A dimer algebra is a type of quiver algebra whose quiver embeds in a torus, with homotopy-like relations.  Dimer algebras with the cancellation property are Calabi-Yau algebras, and their centers are 3-dimensional Gorenstein singularities.  Non-cancellative dimer algebras, on the other hand, are not Calabi-Yau, and their centers are nonnoetherian.  In contrast to their cancellative counterparts, very little is known about these algebras, despite the fact that almost all dimer algebras are non-cancellative.  I will describe how their centers are also 3-dimensional singularities, but with the strange property that they contain positive dimensional 'smeared-out' points.  Furthermore, I will describe how this nonlocal geometry is reflected in the homology of certain vertex simple representations.

Note for Attendees

 Note: Today we have a double-header again. Talk one: Gabriel Kerr 15:00-16:00. Talk two: Charlie Beil: 16:30-17:30. Coffee and cookies in between the two talks.
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UBC
Tue 7 Oct 2014, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Analytical properties for the Navier-Stokes equations and applications
ESB 2012
Tue 7 Oct 2014, 3:30pm-4:30pm

Abstract

Strong solutions to the 3D Navier-Stokes equations are known to exist locally-in-time and are real analytic. Providing lower bounds for their analyticity radius is important as this length scale plays an important role in turbulent phenomenologies and can be used to establish blow-up criteria. In this talk we discuss one approach to estimating analyticity radii and a related conditional regularity criteria.
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Simon Fraser University
Wed 8 Oct 2014, 3:00pm
Probability Seminar
ESB 2012 Oct 7th update: This seminar has been canceled.
Modelling and simulating systems with state-dependent diffusion
ESB 2012 Oct 7th update: This seminar has been canceled.
Wed 8 Oct 2014, 3:00pm-4:00pm

Abstract

We propose a framework for modelling stochastic systems with state-dependent diffusion coefficients. Rather than specifying dynamics through a state-dependent drift and diffusion coefficients, assuming detailed balance we specify an equilibrium probability density and a state-dependent diffusion coefficient. We argue that our framework is more natural from the modelling point of view and has a distinct advantage in situations where either the equilibrium probability density or the diffusion coefficient is discontinuous. We introduce a numerical method for simulating dynamics in our framework that samples from the equilibrium probability density exactly and elegantly handles discontinuities in the coefficients. This is joint work with Xin Yang.
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UAlberta
Wed 8 Oct 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UAlberta)
False Theta Functions and Logarithmic CFT
ESB 4127 (host: UAlberta)
Wed 8 Oct 2014, 3:00pm-4:00pm

Abstract

 A two-dimensional conformal field theory (CFT) is constructed from the representations of a vertex operator algebra. The Verlinde formula tells us much information about the fusion ring of modules in terms of the modular data of characters and this formula is known to be true if the vertex algebra is sufficiently nice, meaning essentially that the representation category is semi-simple and that there are only finitely many simple modules. Information about this relation is already included in the asymptotic behavior of characters. A conformal field theory/vertex algebra with modules that are not completely reducible is called logarithmic. In this case not much is known concerning the Verlinde formula. False theta functions appear frequently in characters of such theories. In this talk, I will introduce false theta functions, explain that they have a modular-like behavior and will relate their asymptotic behavior to fusion rings. Asymptotics are subtle and both wall-crossing and a relation to the D-brane fusion ring of minimal string theory will appear. The results presented are joint work with Antun Milas and Simon Wood.
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George Bluman
Mathematics, UBC
Wed 8 Oct 2014, 3:30pm
Symmetries and Differential Equations Seminar
MATH 126
Some Recent Developments in Finding Systematically Conservation Laws and Nonlocal Symmetries for PDEs
MATH 126
Wed 8 Oct 2014, 3:30pm-4:30pm

Abstract

This will be an introduction on recent developments in symmetries and PDEs by the speaker and collaborators.  It will be based on the article with the same title as this talk by the speaker and Zhengzheng Yang, in Similarity and Symmetry Methods: Applications in Elasticity and Mechanics in Materials (J-F Ganghoffer, I Mladenov, Editors), Lecture Notes in Applied and Computational Mechanics 73, pp. 1-59 (2014).
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UBC
Thu 9 Oct 2014, 1:00pm
Graduate Student Seminar
Math 225
Universality in statistical mechanics
Math 225
Thu 9 Oct 2014, 1:00pm-1:45pm

Abstract

I will talk about the concept of universality as it arises in critical phenomena from the point of view of probability. I will also briefly discuss why the Brownian motion is so cool.

Note for Attendees

 Pizza and pop will be provided.
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Harvard University
Thu 9 Oct 2014, 3:30pm
Number Theory Seminar
room MATH 126
Rational points on hyperelliptic curves
room MATH 126
Thu 9 Oct 2014, 3:30pm-4:30pm

Abstract

I will define hyperelliptic curves, and describe three families of curves of each genus n ≥ 2. I will then discuss results of Bhargava, Poonen, Stoll, Shankar and Wang, which show that most curves in these families have the minimal number of rational points.
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Harvard University
Fri 10 Oct 2014, 3:00pm
Department Colloquium
ESB 2012 (PIMS)
The rank of elliptic curves (PIMS-UBC Distinguished Colloquium)
ESB 2012 (PIMS)
Fri 10 Oct 2014, 3:00pm-4:00pm

Abstract

After quadratic equations in two variables come cubic equations, or elliptic curves. The set of rational points on an elliptic curve has the structure of a finitely generated abelian group. I will recall the basic theory of elliptic curves, then discuss the conjecture of Birch and Swinnerton-Dyer, which attempts to predict the rank of the group of rational points from the number of solutions (mod p) for all primes p. I will also discuss some recent results on the average rank, due to Manjul Bhargava and his collaborators.

Note for Attendees

Coffee, tea and cookies served at 2:30pm in the PIMS Lounge, ESB 4133.
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Toulouse
Tue 14 Oct 2014, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
On the blow-up speed for modified critical nonlinear Schrödinger equations
ESB 2012
Tue 14 Oct 2014, 3:30pm-4:30pm

Abstract

So far, only two blow-up regimes have been studied for NLS equations: the pseudo-conformal regime, where the blow-up speed is like $|t| ^{-1}$ and the log-log regime where the blow-up speed is like $|t|^{-1/2}$ with a log-log correction.

In this talk, we consider the nonlinear Schrodinger with a double power nonlinearity where one of the power is L2 critical and the other one is L2-subcritical. We construct a minimal mass blowing up solution whose blow-up speed is  neither the log-log speed nor the pseudo-conformal speed, but is of the type $|t|^{-s}$ with $s$ varying between $1/2$ and $1$ depending on the subcritical power. This is based on a joint work with Yvan Martel and Pierre Raphael.














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Simon Fraser University
Wed 15 Oct 2014, 3:00pm
Probability Seminar
ESB 2012
Modelling and simulating systems with state-dependent diffusion
ESB 2012
Wed 15 Oct 2014, 3:00pm-4:00pm

Abstract

We propose a framework for modelling stochastic systems with state-dependent diffusion coefficients. Rather than specifying dynamics through a state-dependent drift and diffusion coefficients, assuming detailed balance we specify an equilibrium probability density and a state-dependent diffusion coefficient. We argue that our framework is more natural from the modelling point of view and has a distinct advantage in situations where either the equilibrium probability density or the diffusion coefficient is discontinuous. We introduce a numerical method for simulating dynamics in our framework that samples from the equilibrium probability density exactly and elegantly handles discontinuities in the coefficients. This is joint work with Xin Yang.
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Man Chuen Cheng
UBC
Wed 15 Oct 2014, 3:15pm
Topology and related seminars
ESB 4133
The space of almost commuting tuples of unitary matrices
ESB 4133
Wed 15 Oct 2014, 3:15pm-4:15pm

Abstract

Let G be a Lie group. The space Hom(Z^n,G) of commuting n-tuples in G was extensively studied over the last few years. Two related generalizations of this space are the space of almost commuting tuples, in the sense that the commutator of every pair of elements in each tuple is in the center of G, and the space of homomorphisms Hom(Gamma, G) from a central extension Gamma of a free abelian group by a free abelian group to G.

In this talk, I will describe the structures of these spaces and the relations between them in the case G=U(m). I will also discuss questions such as the number of path components and the rational homotopy type of these spaces.

This is joint work with Adem.

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Buhe Eerdun
Mathematics, UBC
Wed 15 Oct 2014, 3:30pm
Symmetries and Differential Equations Seminar
Math 125
Applications of some methods for the construction of conservation laws for PDEs
Math 125
Wed 15 Oct 2014, 3:30pm-4:30pm

Abstract

We briefly review some methods for the construction of conservation laws for PDEs. These methods include the classical Nöther's theorem applicable to any variational system, symmetry action on known conservation laws, an auxiliary equations method, linearizing operator approach (use of a symmetry/adjoint symmetry pair) and, most generally, the direct method applicable essentially to any PDE system. In particular, we will exhibit examples for some of the above methods and applications of conservation laws.
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University of Goettingen
Thu 16 Oct 2014, 12:00pm
Mathematics of Information and Applications Seminar
ESB 4133 (PIMS Lounge)
Suprema of Chaos Processes and the Restricted Isometry Property
ESB 4133 (PIMS Lounge)
Thu 16 Oct 2014, 12:00pm-1:00pm

Abstract

The theory of compressed sensing considers the following problem: Let A be an m x n matrix and let x be an s-sparse vector in n dimensions, i.e., all but s of its entries vanish. One seeks to recover x uniquely and efficiently from linear measurements y = Ax, although m is much less than n. A sufficient condition to ensure that this is possible is the Restricted Isometry Property (RIP). A is said to have the RIP, if its restriction to any small subset of the columns acts almost like an isometry.

 
In this talk, we study two classes of matrices with respect to the RIP: First, we consider matrices A which represent the convolution with a random vector followed by a restriction to an arbitrary fixed set of entries. We focus on the scenario of a Rademacher vector, i.e., a vector whose entries are independent random signs, but also discuss the case of independent subgaussian entries. Second, we study Gabor synthesis matrices, that is, matrices consisting of time-frequency shifts of a such vectors.
 
In both cases, this question can be reduced to estimating a supremum of random variables taken over an indexing set of matrices. Random variables of this type are closely related to suprema of chaos processes. Using generic chaining techniques, we derive a bound for its moments in terms of concepts from the theory of empirical processes. As a consequence, we obtain that matrices from both classes under consideration have the RIP with high probability if the embedding dimension satisfies m > Cs log^4(n). This bound exhibits optimal dependence on s, while previous works had only obtained a suboptimal scaling of s^(3/2).
 
This is joint work with Shahar Mendelson and Holger Rauhut.
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UBC
Thu 16 Oct 2014, 2:00pm
Number Theory Seminar
room MATH 126
Euler systems and p-adic L-functions (note different seminar time)
room MATH 126
Thu 16 Oct 2014, 2:00pm-3:00pm

Abstract

An Euler system is a collection of global arithmetic objects, most notably global cohomology classes arising from geometry, which are related to L-functions and can be made to vary in p-adic families. The talk will mainly focus on the Euler system of Hegneer points that played a key role in the seminal work of Gross–Zagier and Kolyvagin on the Birch and Swinnerton–Dyer Conjecture. We will present a construction of anticyclotomic p-adic Rankin–Selberg L-functions and discuss some related reciprocity laws in the spirit of Kato.
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Doug Nychka
Director of the Institute for Mathematics Applied to Geosciences of the US National Center for Atmospheric Research
Thu 16 Oct 2014, 4:00pm
Scientific Computation and Applied & Industrial Mathematics
Michael Smith Labs, Room 102
Reconstructing carbon dioxide for the last 2000 years: a hierarchical success story
Michael Smith Labs, Room 102
Thu 16 Oct 2014, 4:00pm-5:00pm

Abstract

Knowledge of atmospheric carbon dioxide (CO2) concentrations in the past are important to provide an understanding of how the Earth's carbon cycle varies over time. This project combines ice core CO2 concentrations, from Law Dome, Antarctica and a physically based forward model to infer CO2 concentrations on an annual basis. Here the forward model connects concentrations at given time to their depth in the ice core sample and an interesting feature of this analysis is a more complete characterization of the uncertainty in "inverting" this relationship. In particular, Monte Carlo based ensembles are particularly useful for assessing the size of the decrease in CO2 around 1600 AD. This reconstruction problem, also known as an inverse problem, is used to illustrate a general statistical approach where observational information is limited and characterizing the uncertainty in the results is important. These methods, known as Bayesian hierarchical models, have become a mainstay of data analysis for complex problems and have wide application in the geosciences. 

This work is in collaboration with  Eugene Wahl (NOAA), David Anderson  (NOAA) and Catherine Truding.

Note for Attendees

The Thursday talk is preceded by coffee, tea, cookies (15:30 pm -16:00 pm) in Room 101.
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Thu 16 Oct 2014, 5:20pm
Thu 16 Oct 2014, 5:20pm-10:00am

Details

 
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UCLA
Fri 17 Oct 2014, 3:00pm SPECIAL
Harmonic Analysis Seminar
Math 126
An approach to pointwise ergodic theorems
Math 126
Fri 17 Oct 2014, 3:00pm-4:00pm

Abstract


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UBC
Mon 20 Oct 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)
Donaldson-Thomas theory of local elliptic surfaces via the topological vertex
ESB 4127 (host: UBC)
Mon 20 Oct 2014, 3:00pm-4:00pm

Abstract

Donaldson-Thomas (DT) invariants of a Calabi-Yau threefold X are fundamental quantum invariants given by (weighted) Euler characteristics of the Hilbert schemes of X. We compute these invariants for the case where X is a so-called local elliptic surface --- it is the total space of the canonical line bundle over an elliptic surface. We find that the generating functions for the invariants admit a nice product structure. We introduce a new technique which allows us to use the topological vertex in this computation --- a tool which previously could only be used for toric threefolds. As a by product, we discover surprising new identities for the topological vertex. This is joint work with Martijn Kool, with an assist from Ben Young. 

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Yonsei University, visiting UC-Irvine
Mon 20 Oct 2014, 3:00pm
Harmonic Analysis Seminar
Math 204
Oscillatory integrals and Newton polyhedra
Math 204
Mon 20 Oct 2014, 3:00pm-4:00pm

Abstract


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Mark Schmidt
Computer Science, UBC
Tue 21 Oct 2014, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS lounge)
Minimizing Finite Sums with the Stochastic Average Gradient
ESB 4133 (PIMS lounge)
Tue 21 Oct 2014, 12:30pm-1:30pm

Abstract

We propose the stochastic average gradient (SAG) method for optimizing the sum of a finite number of smooth convex functions. Like stochastic gradient (SG) methods, the SAG method's iteration cost is independent of the number of terms in the sum. However, by incorporating a memory of previous gradient values the SAG method achieves a faster convergence rate than black-box SG methods. Specifically, under standard assumptions the convergence rate is improved from O(1/k) to a linear convergence rate of the form O(p^k) for some p < 1. Further, in many cases the convergence rate of the new method is also faster than black-box deterministic gradient methods, in terms of the number of gradient evaluations. Beyond these theoretical results, the algorithm also has a variety of appealing practical properties: it supports regularization and sparse datasets, it allows an adaptive step-size and has a termination criterion, it allows mini-batches, and its performance can be further improved by non-uniform sampling. Numerical experiments indicate that the new algorithm often dramatically outperforms existing SG and deterministic gradient methods, and that the performance may be further improved through the use of non-uniform sampling strategies.

Note for Attendees

Sushi will be provided.
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Tingting Huan
UBC
Tue 21 Oct 2014, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Traveling fronts to reaction diffusion equations with fractional Laplacian
ESB 2012
Tue 21 Oct 2014, 3:30pm-4:30pm

Abstract

We show the nonexistence of traveling fronts in the combustion model with fractional Laplacian (-\Delta)^s when s\in(0,1/2]. Our method can be used to give a direct and simple proof of the nonexistence of traveling fronts for the usual Fisher-KPP nonlinearity. Also we prove the existence and nonexistence of traveling waves solutions for different ranges of the fractional power s for the generalized Fisher-KPP type model. 
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Eva Czabarka
University of South Carolina
Tue 21 Oct 2014, 4:00pm
Discrete Math Seminar
ESB 4127
Mixed orthogonal arrays and more - part Sperner families
ESB 4127
Tue 21 Oct 2014, 4:00pm-5:00pm

Abstract

Sperner's theorem from 1928 states that the greatest number subsets of an n-element set such that no subset contains another (in other words the largest chain is length 1), is \binom{n}{\lfloor n/2\rfloor}. This result has many generalizations since: L-Sperner families are families where the largest chain is of length at most L, M-part families are families where there is no chain of length 2 where the increase of a chain is contained in a fixed M-partition of the underlying set, etc. Mixed orthogonal arrays are designs introduced by statisticians for designing experiments, so that factors potentially influential to the outcome occur simultaneously in a regular manner. We show that these distant topics have a strong connection (in particular mixed ortogonal arrays and homogeneous M-part (L_1,...,L_M)-Sperner families correspond to each other), and provide constructions for mixed orthogonal arrays. Joint work with H Aydinian and L.A. Szekely.
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UAlberta
Wed 22 Oct 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UAlberta)
Equivalences of derived categories of double mirrors
ESB 4127 (host: UAlberta)
Wed 22 Oct 2014, 3:00pm-4:00pm

Abstract

Given a Calabi-Yau complete intersection in a toric Fano variety, there are various ways to construct the mirror. Sometimes these mirrors are isomorphic and sometimes they are not. These distinct 'double' mirrors should be equivalent in some way if they all have a shot at being the 'correct' mirror in some setting of mirror symmetry. We will discuss the Batyrev-Borisov and Berglund-Hübsch-Krawitz construction and the double mirrors which arise, as well as their relationship through variation of geometric invariant theory quotients, Landau-Ginzburg models, and derived equivalence. This is joint work with Tyler Kelly.
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Tom Hutchcroft
UBC
Wed 22 Oct 2014, 3:00pm
Probability Seminar
ESB 2012
Unimodular hyperbolic triangulations
ESB 2012
Wed 22 Oct 2014, 3:00pm-4:00pm

Abstract

For deterministic bounded degree triangulations, circle packing has proven a powerful tool for studying random walk via geometric arguments. In this talk, I will discuss extensions and analogues for random triangulations without the assumption of bounded degree. In particular, I will show that the circle packing type (hyperbolic or Euclidean) is determined by the expected degree at the root and that, in the hyperbolic case, the geometric boundary given by the circle packing coincides with the Poisson boundary of the random walk. No specialised knowledge will be assumed and I will review the main examples.
Joint work with Omer Angel, Asaf Nachmias and Gourab Ray.
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UBC
Wed 22 Oct 2014, 3:00pm
Undergraduate Colloquium
MATH 203
The Art in Problem Solving
MATH 203
Wed 22 Oct 2014, 3:00pm-4:00pm

Abstract

The scope of what constitutes a math problem is far wider than "how many apples are left in the basket if..." or "prove the equation has at least one real root." Math problems can be seen in everything from the development of bone structures through the bending of light due to massive objects; math is everywhere. By going through a few projects I've recently had the fortune of working on, I want to highlight a few of the beautiful ways mathematical thinking finds its way into solving real-world problems including: using physical modelling in designing devices for water filtration by electrodialysis, implementing formal asymptotic analysis to predict the behaviour of a fusion reactor, and writing numerical methods to provide a proof-of-concept for a new method of mass spectrometry. Just as there is art in expressing the world through imagery and poetry, so there is in analyzing problems appropriately and making use of such analysis.  No prior knowledge is expected: all the problems presented will include the relevant background information.
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UBC
Wed 22 Oct 2014, 3:15pm
Topology and related seminars
ESB 4133
Generalized torsion in knot groups
ESB 4133
Wed 22 Oct 2014, 3:15pm-4:15pm

Abstract

Classical knot groups, that is fundamental groups of knot complements in 3-space, are known to be torsion-free.  However, we show that for many knots, their groups contain generalized torsion: a nontrivial element such that some product of conjugates of that element equals the identity.  One example (the hyperbilic knot 5_2) was discovered with the aid of a Python program written by the USRA student Geoff Naylor.  Other examples include torus knots, algebraic knots in the sense of Milnor (arising from singularities of complex curves) and satellites of knots whose groups contain generalized torsion.  Although all knot groups are left-orderable, the existence of generalized torsion is an obstruction to their being bi-orderable.
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Abdul Kara
University of the Witwatersrand, Johannesburg
Wed 22 Oct 2014, 3:30pm
Symmetries and Differential Equations Seminar
MATH 126
Symmetry structures of manifolds
MATH 126
Wed 22 Oct 2014, 3:30pm-4:30pm

Abstract

We study the Noether and Lie symmetries that arise from the Euler-Lagrange equations, i.e., the ‘geodesic’ equations, related to manifolds that arise from a metric. In particular and as one of the examples, we present some peculiarities associated with the ASD Ricci-flat metric which depends on the `second heavenly equation'. It is noted, in general, that the Killing vectors are contained in the Noether symmetries generated by the Lagrangian of the geodesic equations. Specifically, a number of symmetries which are Noether and not Killing vectors are independent of the arc length variable ‘s’.
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Foster Tom
UBC
Thu 23 Oct 2014, 12:30pm
Graduate Student Seminar
Math 225
The probabilistic method
Math 225
Thu 23 Oct 2014, 12:30pm-1:45pm

Abstract

The probabilistic method, pioneered by Paul Erdős, is a means of proving the existence of a certain object. By describing a random process of choosing objects, if there is a nonzero probability of making a successful choice, then necessarily the desired kind of object exists. We present a problem in discrete math that employs this method.
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Avi Kulkarni
SFU
Thu 23 Oct 2014, 3:30pm
Number Theory Seminar
room ASB 10900 (SFU - IRMACS)
On Jacobians of dimension 2g that decompose into Jacobians of dimension g
room ASB 10900 (SFU - IRMACS)
Thu 23 Oct 2014, 3:30pm-4:30pm

Abstract

Let X be a genus 2g curve defined over an arbitrary field of characteristic not equal to 2 and let J(X) the Jacobian variety of X. We say that a Jacobian variety is decomposable if it is isogenous to a product of abelian varieties. The type of decomposition can by characterized by the type of kernel of the isogeny and the dimensions of the varieties in the product. We consider isogenies with kernel type (Z/2Z)g and products of dimension g Jacobian varieties. Additionally, we insist that the isogeny is polarized. In this talk we describe a family of (non-hyperelliptic) genus 2g curves whose Jacobians are decomposable in this way. We prove that all genus 4 curves whose Jacobian has this decomposition type are either in this family or arise from a different construction considered by Legendre. Joint work with Nils Bruin.
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Department of Mathematics, University of South Carolina
Fri 24 Oct 2014, 3:00pm
Department Colloquium
MATX 1100
A new asymptotic enumeration technique: the Lovasz Local Lemma
MATX 1100
Fri 24 Oct 2014, 3:00pm-4:00pm

Abstract

The lopsided version of the Lovasz Local Lemma gives asymptotically tight lower boundsfor a number of enumeration problems. In the configuration model matching upper bounds are available. In this way a number of asymptotic enumeration results, mostly due to Wormald and McKay, can be proved in an alternative way. A new result is asymptotic enumeration of graphs with respect to degree sequence and girth.  A classical probabilistic result of Paul Erdos showed the existence of graphs with arbitrary large girth and chromatic number. If the degree sequence satisfies some mild conditions, we show that almost all graphs with this degree sequence and prescribed girth have high chromatic number.
This is joint work with Lincoln Lu.

Note for Attendees

Refreshments will be served at 2:45pm in the Math Lounge area, MATH 125 before the colloquium.
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PennState
Mon 27 Oct 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)
Rozansky--Witten-type invariants from symplectic Lie pairs
ESB 4127 (host: UBC)
Mon 27 Oct 2014, 3:00pm-4:00pm

Abstract

 In 1997, Rozansky and Witten built new finite-type invariants of 3-manifolds from hyperkahler manifolds. It was later shown by Kontsevich and Kapranov that those invariants only depend on the holomorphic symplectic structure of the hyperkahler manifolds. Indeed Kapranov proved that these invariants may be considered as an analogue of Chern-Simons type invariants, where the Atiyah class of the underlying complex manifold plays the role of  Lie bracket. In this talk, we introduce symplectic structures on "Lie pairs" of (real or complex) algebroids, encompassing homogeneous symplectic spaces, symplectic manifolds with a $\mathfrak g$-action and holomorphic symplectic manifolds. We show that to each such symplectic Lie pair are associated Rozansky-Witten-type invariants of three-manifolds. This is a joint work with Yannick Voglaire.
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Wes Maciejewski
UBC, Dept of Mathematics & CWSEI
Tue 28 Oct 2014, 12:30pm
Lunch Series on Teaching & Learning
MATH 126
Do we know how students view mathematics and how they study it?
MATH 126
Tue 28 Oct 2014, 12:30pm-1:30pm

Abstract

It has long been known that the way a student views the subject they study affects the approach they take to studying
the subject. This, in turn, affects their performance in the subject. It seems, then, that the improvement of student
outcomes not only requires addressing the approach a student takes to study, but also their view of the subject. In this presentation, I will present results from a series of surveys intended to explore two separate, but related questions:
1. Do math instructors actually know how their students view math?
2. What approaches to study do students take and how do these relate to their achievement?
The crucial aspect of this work is that the data gathered was analysed by course year. It turns out that the answers to both questions above are different for lower and upper-year courses.
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Mingfeng Zhao
Tue 28 Oct 2014, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Traveling waves involving fractional Laplacians
ESB 2012
Tue 28 Oct 2014, 3:30pm-4:30pm

Abstract

In this talk, we will discuss the existence of the traveling wave solution for the Allen-Cahn equation involving the fractional Laplacians. Based on the existence of the standing waves for the balanced Allen-Cahn equation, we will use the continuity method to obtain the existence of the traveling waves for unbalanced Allen-Cahn equation. The key ingredient is the the bound of the traveling speed in terms of the potential. Some open questions will be discussed.
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Eindhoven University of Technology
Wed 29 Oct 2014, 3:00pm
Probability Seminar
ESB 2012
Degree distribution of shortest path trees and bias in network sampling algorithms
ESB 2012
Wed 29 Oct 2014, 3:00pm-4:00pm

Abstract

In this talk, we investigate the degree distribution of shortest path trees of various weighted network models. The aim of many empirical studies is to determine the degree distribution of a network with unknown structure by using trace-route sampling. We derive the limiting degree distribution of the shortest path tree from a single source on various random network models with edge weights: the configuration model and r-regular graphs with i.i.d. power law degrees and i.i.d. edge weights, the complete graph with edge weights that are powers of i.i.d. exponential random variables. We use these results to shed light on an empirically observed bias in network sampling methods.
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University of Utah
Wed 29 Oct 2014, 3:15pm
Topology and related seminars
ESB 4133
Constructing aspherical manifolds with a given fundamental group
ESB 4133
Wed 29 Oct 2014, 3:15pm-4:15pm

Abstract

While an aspherical complex is determined up to homotopy by its fundamental group, there are many geometrically different aspherical manifolds with the same fundamental group. For instance, the punctured torus and the pair of pants look quite different, but both have the same fundamental group F_2. I will discuss constructions of aspherical manifolds for a given fundamental group, talk about the smallest dimension of such a manifold for a given group and describe some geometric invariants that distinguish different aspherical manifolds with the same fundamental group. I will discuss this for right angled Artin groups (joint work with Mike Davis, Boris Okun and Kevin Schreve) and possibly also for duality groups.
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Abdul Kara
Witwatersrand University, Johannesburg
Wed 29 Oct 2014, 3:30pm
Symmetries and Differential Equations Seminar
Math 125
Symmetry structures of manifolds
Math 125
Wed 29 Oct 2014, 3:30pm-4:30pm

Abstract

We study the Noether and Lie symmetries that arise from the Euler-Lagrange equations, i.e., the ‘geodesic’ equations, related to manifolds that arise from a metric. In particular and as one of the examples, we present some peculiarities associated with the ASD Ricci-flat metric which depends on the `second heavenly equation'. It is noted, in general, that the Killing vectors are contained in the Noether symmetries generated by the Lagrangian of the geodesic equations. Specifically, a number of symmetries which are Noether and not Killing vectors are independent of the arc length variable ‘s’.
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Emory University
Thu 30 Oct 2014, 3:30pm
Number Theory Seminar
room MATH 126
Hasse principles over function fields of p-adic curves
room MATH 126
Thu 30 Oct 2014, 3:30pm-4:30pm

Abstract

 Obstructions to the Hasse principle for the existence of rational points on principal homogeneous spaces under connected linear algebraic groups over a number fi eld are well understood. Similar questions of Hasse principle have been studied over more general fi elds, particularly, function fields of curves over complete discrete valued fields. There are several positive results in this direction for connected linear algebraic groups which are rational, thanks to the patching techniques developed by Harbater-Hartmann-Krashen. We shall explain some recent progress and open questions concerning Hasse principle for function fi elds of p-adic curves.
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Univeristy of Michigan
Fri 31 Oct 2014, 3:00pm
Department Colloquium
ESB 2012 (PIMS)
Imaging with waves in complex environments (PIMS-IAM-UBC distinguished colloquium)
ESB 2012 (PIMS)
Fri 31 Oct 2014, 3:00pm-4:00pm

Abstract

The talk is concerned with the application of sensor array imaging in complex environments. The goal of imaging is to estimate the support of remote sources or strong reflectors using time resolved measurements of waves at a collection of sensors (the array). This is a challenging problem when the imaging environment is complex, due to numerous small scale inhomogeneities and/or rough boundaries that scatter the waves. Mathematically we model such complexity (which is necessarily uncertain in applications) using random processes, and thus study imaging in random media. I will focus attention on the application of imaging in random waveguides, which exhibits all the challenges of imaging in random media. I will present a quantitative study of cumulative scattering effects in such waveguides and then explain how we can use such a study to design high fidelity imaging methods.

Note for Attendees

Coffee, tea and cookies served at 2:30pm in the PIMS Lounge, ESB 4133.
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