##### Events
Andy Wathen
Mathematical Institute, Oxford University
Tue 6 Sep 2016, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
A preconditioner with guaranteed rapid convergence for nonsymmetric real Toeplitz systems and its application for time-dependent PDE problems
ESB 4133 (PIMS Lounge)
Tue 6 Sep 2016, 12:30pm-1:30pm

#### Abstract

Descriptive convergence estimates or bounds for Krylov subspace iterative methods for nonsymmetric matrix systems are keenly desired but remain elusive. In the case of symmetric (self-adjoint) matrices, bounds based on eigenvalues can be usefully descriptive of observed convergence; an important consequence is that there are rigorous criteria for what constitutes a good preconditioner for symmetric matrices. For nonsymmetric matrices preconditioning must generally be
heuristically motivated.

Such comments apply quite generally, however there is one class of nonsymmetric matrices for which we have recently been able to rigorously prove descriptive convergence bounds, namely real Toeplitz (constant diagonal) matrices. Our results apply regardless of non-normality or any 'degree' of nonsymmetry.

Gil Strang proposed the use of circulant matrices (and the FFT) for preconditioning symmetric Toeplitz matrix systems in 1986 and there is now a well-developed theory which guarantees rapid convergence of the conjugate gradient method for such preconditioned positive definite symmetric systems.

In this talk we describe our recent approach which provides a preconditioned MINRES method with the same guarantees for real nonsymmetric Toeplitz systems regardless of the non-normality, and demonstrate the application of the approach for time-dependent PDE problems.

This is joint work with Jennifer Pestana (Strathclyde University) and Elle McDonald (Oxford University).
hide
Vitali Vougalter
University of Toronto Mississauga
Tue 6 Sep 2016, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Solvability of some integro-differential equations with anomalous diffusion
ESB 2012
Tue 6 Sep 2016, 3:30pm-4:30pm

#### Abstract

The work deals with the existence of solutions of an integro-differential equation in the case of the anomalous diffusion with the Laplace operator in a fractional power. The proof of existence of solutions relies on a fixed point technique. Solvability conditions for elliptic operators without Fredholm property in unbounded domains are used.
hide
University of California, San Diego
Wed 7 Sep 2016, 3:00pm
Probability Seminar
ESB 2012
Bulk Fluctuations and the Hard Edge of Unitary Brownian Motion
ESB 2012
Wed 7 Sep 2016, 3:00pm-4:00pm

#### Abstract

The Brownian motion on the Unitary group \mathrm{U}(N) has a large-N (spectral) limit: for each fixed time, the histogram of eigenvalues converges almost surely to a deterministic law with a (mostly) smooth density on the circle.  This was proved by Philippe Biane in the late 1990s.
One can think of this as a companion to Wigner's semicircle law for Hermitian Gaussian random matrices: the latter is really about the Brownian motion on the Unitary Lie algebra, and so it is compelling that some of the same behavior carries over to the Lie group.

In this lecture, I will talk about two finer properties of the large-N limit of Unitary Brownian motion.
•  In joint work with Guillaume Cébron, following related work of Thierry Lévy and Mylène Maïda, we showed that the bulk fluctuations (a.k.a. linear statistics) of the eigenvalues are Gaussian, with an explicit covariance that generalizes the Haar unitary case studied by Evans and Diaconis.
• In joint work with Benoît Collins and Antoine Dahlqvist, we showed that the largest (angle) eigenvalue of the Brownian motion has an explicit almost sure limit.
In both cases, we proved multi-dimensional versions of the theorems, which I will also describe if time permits.

hide
UCLA
Fri 9 Sep 2016, 3:00pm
Department Colloquium
ESB 2012
Paths of minimal lengths on the set of exact differential k–forms
ESB 2012
Fri 9 Sep 2016, 3:00pm-4:00pm

#### Abstract

We initiate the study of optimal transportation of exact differential k–forms and introduce various distances as minimal actions. Our study involves dual maximization problems with constraints on the codifferential of k–forms. When k < n, only some directional derivatives of a vector field are controlled. This is in contrast with prior studies of optimal transportation of volume forms (k = n), where the full gradient of a scalar function is controlled. Furthermore, our study involves paths of bounded variations on the set of k–currents. This talk is based a joint work with B. Dacorogna and O. Kneuss.

#### Note for Attendees

Refreshments will be served in ESB 4133 (the PIMS Lounge).
hide
UBC
Mon 12 Sep 2016, 3:00pm
Algebraic Geometry Seminar
MATX 1101
Hilbert scheme of points on simple singularities
MATX 1101
Mon 12 Sep 2016, 3:00pm-4:00pm

#### Abstract

Given a smooth surface, the generating series of Euler characteristics of its Hilbert schemes of points can be given in closed form by (a specialisation of) Goettsche's formula. I will discuss a generalisation of this formula to surfaces with rational double points. A certain representation of the affine Lie algebra corresponding to the surface singularity (via the McKay correspondence), and its crystal basis theory, play an important role in our approach. Joint work with András Némethi and Balázs Szendrői.
hide
UBC
Tue 13 Sep 2016, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
EBS 2012
On some functional and geometric inequalities
EBS 2012
Tue 13 Sep 2016, 3:30pm-4:30pm

#### Abstract

In this talk, we will discuss the Trudinger-Moser and Caffarelli-Kohn-Nirenberg inequalities in the settings where the classical Schwarz rearrangement cannot be used. We will then talk about some approaches to study the maximizers for these problems. This is joint work with Guozhen Lu.

hide
UCLA
Wed 14 Sep 2016, 3:00pm
Probability Seminar
ESB 2012
Convolution powers of complex-valued functions on \mathbb{Z}^d.
ESB 2012
Wed 14 Sep 2016, 3:00pm-4:00pm

#### Abstract

The study of convolution powers of a finitely supported probability distribution \phi on the d-dimensional square lattice is central to random walk theory. For instance, the nth convolution power \phi^{(n)} is the distribution
of the nth step of the associated random walk and is described by the classical local limit theorem. When such distributions take on complex values, their convolution powers exhibit surprising and disparate behaviors not seen in the probabilistic setting.  In this talk, I will discuss new results concerning the asymptotic behavior of convolution powers of complex-valued functions on \mathbb{Z}^d, specifically generalized local limit theorems and sup-norm estimates. This joint work with Laurent Saloff-Coste extends previous results by I. J. Shoenberg, T. N. E. Greville, P. Diaconis and L. Saloff-Coste.
hide
Reed College
Wed 14 Sep 2016, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
ESB 4133 (PIMS Lounge)
Wed 14 Sep 2016, 3:15pm-4:15pm

#### Abstract

The classifying functor from categories to topological spaces provides a way of constructing spaces with certain properties or structure from categories with similar properties of structure. An important example of this is the construction of infinite loop spaces from symmetric monoidal categories. The particular kinds of extra structure can typically be encoded by monads on the category of small categories. In order to provide more flexibility in the kinds of morphisms allowed, one can work with the associated 2-monad in the 2-category of categories, functors, and natural transformations. In this talk I will give the categorical setup required, and I will give examples of interest to homotopy theorists. I will also outline how this method of working can give general statements about strictifications and comparisons of homotopy theories. This is partially based on work with two different sets of collaborators: Nick Gurski, Niles Johnson, and Marc Stephan; Bert Guillou, Peter May, and Mona Merling.
hide
UBC
Mon 19 Sep 2016, 3:00pm
Algebraic Geometry Seminar
MATX 1101
The Picard group of the universal abelian variety and the Franchetta conjecture for abelian varieties (joint work with R.Fringuelli)
MATX 1101
Mon 19 Sep 2016, 3:00pm-4:00pm

#### Abstract

Let g>2 be a positive integer, and let M_g be the moduli space of smooth curves of genus g over \mathbb{C}. The classical Franchetta conjecture asserts that the Picard group of the generic curve C_{\mu} over Mg is freely generated by its cotangent bundle. It was proved by Arbarello and Cornalba in 1980, Then Mestrano ('87) and Kouvidakis ('91) deducted the Strong Franchetta conjecture, which asserts that the rational points of the relative picard scheme Pic_{C_{\mu} / \mu} are precisely the multiples of the cotangent bundle.

We will show that a suitably modified version of the Franchetta conjecture holds for a different moduli problem over \mathbb{C}, that of principally polarised abelian varieties (p.p.a.v.) of genus g\geq 3 with n-level structure. The abelian Franchetta conjecture states that the generic p.p.a.v. of genus g with n-level structure X_{g,n} has Picard group isomorphic to \mathbb{Z} \oplus (\mathbb{Z}/n\mathbb{Z})^{2g}, where the free part is generated by the bundle inducing the polarization, and the torsion part comes from the level structure.

In the abelian case, the weak" statement immediately implies the corresponding strong" statement regarding the rational points of the relative Picard scheme. Using duality, we will use this to compute the Picard group of the universal abelian variety \mathscr{X}_{g,n} over the moduli stack \mathscr{C}_{g,n} of genus g p.p.a.v. with n-level structure.
hide
Ben Krause
UBC
Mon 19 Sep 2016, 3:00pm
Harmonic Analysis Seminar
MATH 126
Weak (1,1) Bounds for Maximally Truncated Oscillatory Singular Integrals
MATH 126
Mon 19 Sep 2016, 3:00pm-4:00pm

#### Abstract

For any polynomial P(y), and any Calder\'{o}n-Zygmund kernel, K, the operator below maps L^1 to weak  L^1.

\sup _{\epsilon >0} |\int_{|y| > \epsilon} f (x-y) e ^{2 \pi i P (y) } K(y) dy |.

The bound is only a function of the degree of the polynomial P, the dimension, and on the kernel K. The same bound, without maximal truncations, is a special case of a result due to Chanillo and Christ (1987).

hide
Statistics UC Berkeley
Mon 19 Sep 2016, 3:00pm
PIMS Seminars and PDF Colloquiums
ESB 2012
UoI Lasso: Union of Intersection Method for Lasso
ESB 2012
Mon 19 Sep 2016, 3:00pm-4:00pm

#### Abstract

For many modern scientific and machine learning applications, it is often desired to use statistical learning methods that are scalable, highly predictive, highly interpretable, and robust.  However, generally speaking, current methods do not simultaneously enjoy all of these properties. We introduce the Union of Intersections (UoI) framework for designing such “all-in-one” methods. In particular, within the context of Lasso, we introduce UoI Lasso and describe its superior theoretical properties under less restrictive conditions. We further demonstrate the performance of UoI Lasso on a variety of benchmark biomedical data: extraction of meaningful functional networks from human electrophysiology recordings and dramatically more parsimonious prediction of behavioral and physiological phenotypes from genetic data.

#### Note for Attendees

Tea served before the talk in ESB 4133 (PIMS lounge)
hide
Stilianos Louca
Mathematics, UBC
Tue 20 Sep 2016, 12:30pm SPECIAL
Doctoral Exam: The ecology of microbial metabolic pathways
Tue 20 Sep 2016, 12:30pm-2:30pm

#### Details

Abstract:
Microbial metabolic activity drives biogeochemical cycling in virtually every ecosystem. Yet, microbial ecology and its role in ecosystem biochemistry remain poorly understood, partly because the enormous diversity found in microbial communities hinders their modeling. Despite this diversity, the bulk of global biogeochemical fluxes is driven by a few metabolic pathways encoded by a small set of genes, which through time have spread across microbial clades that can replace each other within metabolic niches. Hence, the question arises whether the dynamics of these pathways can be modeled regardless of the hosting organisms, for example based on environmental conditions. Such a pathway-centric paradigm would greatly simplify the modeling of microbial processes at ecosystem scales.
Here I investigate the applicability of a pathway-centric paradigm for microbial ecology. By examining microbial communities in replicate "miniature" aquatic environments, I show that similar ecosystems can exhibit similar metabolic functional community structure, despite highly variable taxonomic composition within individual functional groups. Further, using data from a recent ocean survey I show that environmental conditions strongly explain the distribution of microbial metabolic functional groups across the world's oceans, but only poorly explain the taxonomic composition within individual functional groups. Using statistical tools and mathematical models I conclude that biotic interactions, such as competition and predation, likely underlie much of the taxonomic variation within functional groups observed in the aforementioned studies. The above findings strongly support a pathway-centric paradigm, in which the distribution and activity of microbial metabolic pathways is strongly determined by energetic and stoichiometric constraints, whereas additional mechanisms shape the taxonomic composition within metabolic guilds.

These findings motivated me to explore concrete pathway-centric mathematical models for specific ecosystems. Notably, I constructed a biogeochemical model for Saanich Inlet, a seasonally anoxic fjord with biogeochemistry analogous to oxygen minimum zones. The model describes the dynamics of individual microbial metabolic pathways involved in carbon, nitrogen and sulfur cycling, and largely explains geochemical depth profiles as well as DNA, mRNA and protein sequence data. This work yields insight into ocean biogeochemistry and demonstrates the potential of pathway-centric models for microbial ecology.

#### Note for Attendees

hide
Department of Statistics, University of California, Berkeley
Tue 20 Sep 2016, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Sub-sampled Newton Methods: Uniform and Non-Uniform Sampling
ESB 4133 (PIMS Lounge)
Tue 20 Sep 2016, 12:30pm-1:30pm

#### Abstract

Many data analysis applications require the solution of optimization problems involving a sum of large number of functions. We consider the problem of minimizing a sum of n functions over a convex constraint set. Algorithms that carefully sub-sample to reduce n can improve the computational efficiency, while maintaining the original convergence properties. For second order methods, we first consider a general class of problems and give quantitative convergence results for variants of Newtons methods where the Hessian or the gradient is uniformly sub-sampled. We then show that, given certain assumptions, we can extend our analysis and apply non-uniform sampling which results in modified algorithms exhibiting more robustness and better dependence on problem specific quantities, such as the condition number.

hide
University of Minnesota
Tue 20 Sep 2016, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
On the Cauchy problem for vortex rings
ESB 2012
Tue 20 Sep 2016, 3:30pm-4:30pm

#### Abstract

We consider the initial-value problem for the 3d Navier-Stokes equation when the initial vorticity is supported on a circle. Such initial datum is in certain function spaces where perturbation theory works for small data, but not for large data, even for short times, and there are good reasons to believe that this is not just a technicality. We prove global existence and uniqueness for large data in the class of axi-symmetric solutions. The main tools are Nash-type estimates and certain monotone quantities. Uniqueness in the class of solutions which are not necessarily axi-symmetric remains a difficult open problem, which we plan to discuss briefly.  Joint work with Thierry Gallay.
hide
UBC
Tue 20 Sep 2016, 4:00pm
Discrete Math Seminar
ESB 4127
Pattern Avoidance in Restricted Growth Functions
ESB 4127
Tue 20 Sep 2016, 4:00pm-5:00pm

#### Abstract

hide
University of Washington and Tohoku univeristy
Wed 21 Sep 2016, 3:00pm
Probability Seminar
ESB 2012
Dimension of harmonic measures in hyperbolic spaces
ESB 2012
Wed 21 Sep 2016, 3:00pm-4:00pm

#### Abstract

We discuss random walks on groups acting on hyperbolic spaces (e.g. the Poincaré disk), and their limiting behaviour on the boundary. The limiting distribution of the random walk (the harmonic measure) is of particular interest for description of bounded harmonic functions on the group (the Poisson boundary). We consider the Hausdorff dimension of harmonic measure on the boundary and give a formula in terms of the entropy and the drift under a general moment condition. Related recent results are also discussed during the talk.
hide
Wed 21 Sep 2016, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
Multiplicative structures and the twisted Baum-Connes assembly map
ESB 4133 (PIMS Lounge)
Wed 21 Sep 2016, 3:15pm-4:15pm

#### Abstract

Using some ideas of Atiyah and Segal and a pushforward map defined using deformation groupoids we explain how to endow to the twisted geometric K-homology groups of a discrete group with an external product. Using the Baum-Connes assembly maps one can transfer this product to the twisted K-theory groups of the reduced group C*-algebra. This is a joint work with Noé Barcenas and Paulo Carrillo.
hide
University of Minnesota
Fri 23 Sep 2016, 3:00pm SPECIAL
Department Colloquium
ESB 2012
PIMS-UBC Distinguished Colloquium -- PDE aspects of fluid flows
ESB 2012
Fri 23 Sep 2016, 3:00pm-4:00pm

#### Abstract

We explain some of the recent results in concerning PDEs describing fluid flows, as well as some of the difficulties. Model equations will also be discussed.

hide
UBC
Mon 26 Sep 2016, 3:00pm
Algebraic Geometry Seminar
MATX 1102
Taking roots vs taking logarithms
MATX 1102
Mon 26 Sep 2016, 3:00pm-4:00pm

#### Abstract

I will report on joint work with D. Carchedi, S. Scherotzke and N. Sibilla, about a comparison between two objects obtained from a fs log scheme over the complex numbers: the "infinite root stack" and the "Kato-Nakayama space". I will also hint at more recent work that explains how parabolic sheaves (with real or rational weights) interact with the picture.

I will be as little technical as possible and focus on examples rather than on the general theory.
hide
Division of Chemistry & Chemical Engineering and Engineering & Applied Science Caltech
Mon 26 Sep 2016, 3:00pm
Institute of Applied Mathematics
ESB 2012
The Swim Pressure of Active Matter
ESB 2012
Mon 26 Sep 2016, 3:00pm-4:00pm

#### Abstract

One of the distinguishing features of many living systems is their ability to move, to self-propel, to be active. Through their motion, either voluntarily or involuntarily, living systems are able self-assemble: birds flock, fish school, bacteria swarm, etc. But such behavior is not limited to living systems. Recent advances in colloid chemistry have led to the development of synthetic, nonliving particles that are able to undergo autonomous motion by converting chemical energy into mechanical motion and work – chemical swimming. This swimming or intrinsic activity imparts new behaviors to active matter that distinguish it from equilibrium condensed matter systems. For example, active matter generates its own internal pressure (or stress), which can drive it far from equilibrium and free it from conventional thermodynamic constraints, and by so doing active matter can control and direct its own behavior and that of its surroundings. In this talk I will discuss our recent work on swimmers and on the origin of a new source for stress that is responsible for self-assembly and pattern formation in active matter.

#### Note for Attendees

Tea beforehand in the PIMS lounge (ESB 4133)
hide
UBC
Mon 26 Sep 2016, 3:00pm
Harmonic Analysis Seminar
MATH 126
MATH 126
Mon 26 Sep 2016, 3:00pm-4:00pm

#### Abstract

Let $m$ be a radial multiplier supported in a compact subset away from the origin. For dimensions $d\ge 2$, it is conjectured that the multiplier operator $T_m$ is bounded on $L^p(R^d)$ if and only if the kernel $K=\hat{m}$ is in $L^p(R^d)$, for the range $1<p<2d/(d+1)$. Note that there are no a priori assumptions on the regularity of the multiplier. This conjecture belongs near the top of the tree of a number of important related conjectures in harmonic analysis, including the Local Smoothing, Bochner-Riesz, Restriction, and Kakeya conjectures. We discuss new progress on this conjecture in dimensions $d=3$ and $d=4$. Our method of proof will rely on a geometric argument involving sizes of multiple intersections of three-dimensional annuli.
hide
Seckin Demirbas
UBC
Tue 27 Sep 2016, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Gibbs' measure and almost sure global well-posedness for one dimensional periodic fractional Schrodinger equation
ESB 2012
Tue 27 Sep 2016, 3:30pm-4:20pm

#### Abstract

In this talk we will present recent local and global well-posedness results on the one dimensional periodic fractional Schrodinger equation. We will also talk about construction of Gibbs' measures on certain Sobolev spaces and how we can prove almost sure global well-posedness using this construction.
hide
Foster Tom
UBC
Tue 27 Sep 2016, 4:00pm
Discrete Math Seminar
ESB 4127
Schur-Positivity of Equitable Ribbons
ESB 4127
Tue 27 Sep 2016, 4:00pm-5:00pm

#### Abstract

Schur functions form an important basis for the space of symmetric functions and show up in areas from representation theory to quantum mechanics. Given an appropriate diagram of boxes, we construct its corresponding Schur function by counting the numbers of tableaux: fillings of these boxes with positive integers that satisfy some simple conditions. We then form the Schur-positivity partially ordered set by comparing these numbers of tableaux. In this talk, we present some new results of how order relations in this partially ordered set can be derived from properties of the diagrams. We then present some progress toward long-standing conjectures.
hide
Oregon State University
Wed 28 Sep 2016, 3:00pm
Probability Seminar
ESB 2012
Some probability theory that arises from worrying about Navier-Stokes and other quasilinear equations
ESB 2012
Wed 28 Sep 2016, 3:00pm-4:00pm

#### Abstract

The success of probability theory in the analysis of linear, or even certain semi-linear,  parabolic and elliptic pde’s is well documented.  In spite of various attempts to find a stochastic foothold for the analysis of Navier-Stokes equations and related quasilinear equations, the problem remains a substantial challenge.  That said, the quest can lead to new stochastic structures and problems that relate to modern probability in fundamental ways.  In this talk I will try to indicate this with a few explicit examples largely stemming from the Lejan-Sznitman multiplicative cascade/branching random walk  framework for Navier-Stokes equations.

This talk is  primarily based on recent joint work with Radu Dascaliuc, Nicholas Michalowski, and Enrique Thomann with partial support from the National Science Foundation.

hide
University of Illinois, Urbana–Champaign
Wed 28 Sep 2016, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
An equivariant motivic slice filtration
ESB 4133 (PIMS Lounge)
Wed 28 Sep 2016, 3:15pm-4:15pm

#### Abstract

Mixing Voevodsky's filtration in motivic homotopy and Dugger's in C_2-equivariant homotopy theory leads to an interesting filtration on the C_2-equivariant motivic homotopy category. In this talk, I'll introduce these slice filtrations and talk about some joint work with P. A. Ostvaer, where we compute the resulting zero slice of the equivariant motivic sphere spectrum.

hide
UBC Math
Fri 30 Sep 2016, 3:00pm
Department Colloquium
ESB 2012
UBC Mathematics and PIMS Faculty Award Colloquium -- On the local Langlands conjectures
ESB 2012
Fri 30 Sep 2016, 3:00pm-4:00pm

#### Abstract

The Langlands program, initiated in the 1960s, is a set of conjectures predicting a unification of number theory and the representation theory of groups. More precisely, the Langlands correspondence provides a way to interpret results in number theory in terms of group theory, and vice versa.

In this talk we sketch a few aspects of the local Langlands correspondence using elementary examples. We then comment on some questions raised by the emerging "mod p" Langlands program.
hide