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 Events
Miles Lubin
Sloan School of Management, MIT
Tue 1 Nov 2016, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Mixed-integer convex optimization
ESB 4133 (PIMS Lounge)
Tue 1 Nov 2016, 12:30pm-1:30pm

Abstract


Mixed-integer convex optimization problems are convex problems with the additional (non-convex) constraints that some variables may take only integer values. Despite the past decades' advances in algorithms and technology for both mixed-integer *linear* and *continuous, convex* optimization, mixed-integer convex optimization problems have remained relatively more challenging and less widely used in practice. In this talk, we describe our recent algorithmic work on mixed-integer convex optimization which has yielded advances over the state of the art, including the globally optimal solution of open benchmark problems. Based on our developments, we have released Pajarito, an open-source solver written in Julia and accessible from popular optimization modeling frameworks. Pajarito is immediately useful for solving challenging mixed combinatorial continuous problems arising from engineering and statistical applications.
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University of Oregon
Tue 1 Nov 2016, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Minimal hypersurfaces with free boundary and positive scalar curvature
ESB 2012
Tue 1 Nov 2016, 3:30pm-4:30pm

Abstract

There is a well-known technique due to Schoen-Yau from the late 70s which uses (stable) minimal hypersurfaces to find topological implications of a (closed) manifold's ability to support positive scalar curvature metrics. In this talk, we describe a version of this technique for manifolds with boundary and discuss how it can be used to study bordisms of positive scalar curvature metrics.
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University of California, San Diego
Wed 2 Nov 2016, 3:00pm
Probability Seminar
ESB 2012
Joint behavior of volume growth and entropy of random walks on groups
ESB 2012
Wed 2 Nov 2016, 3:00pm-4:00pm

Abstract

In the last few years there has been significant advancement in understanding the possible range of behaviors of the volume growth and of the entropy and rate of escape of random walks on groups. Bartholdi and Erschler constructed the first family of intermediate growth groups whose volume growth function follows any prescribed nice enough function in the exponent range [\alpha_0,1] for some explicit \alpha_0 \approx 0.7674. We discuss a variant of a construction of Kassabov and Pak which provides an alternative proof of the Bartholdi-Erschler result. Different behaviors of entropy of random walks on these two families of groups allow us to deduce a result concerning possible joint behavior of intermediate volume growth and entropy of random walks within a certain range of parameters. Joint with Gidi Amir.
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Princeton University
Fri 4 Nov 2016, 3:00pm SPECIAL
Department Colloquium
ESB 2012
PIMS-UBC Distinguished Colloquium-- Statistical and Ergodic Properties of the Moebius Function.
ESB 2012
Fri 4 Nov 2016, 3:00pm-4:00pm

Abstract

In this talk I shall discuss the results which were obtained by several people: M.Avdeeva, F.Cellarosi, Dong Li and myself. Moebius function is one of the most important functions in number theory also connected with Riemann hypothesis. Its simplest part leads to the well-known in probability theory Dickman-de Bruijn distribution. The so-called Mirsky formulas allow to construct the dynamical system with pure point spectrum corresponding to the square of the Moebius function.  In the last part of the talk the famous Hall theorem about the variance  of the number of square-free numbers will be discussed.

Note for Attendees

Refreshments are served in ESB 4133 from 2:30pm-3:00pm before the colloquium.
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Waterloo
Mon 7 Nov 2016, 3:00pm
Algebraic Geometry Seminar
MATX 1102
An Introduction to Toric Stacks, and Conjectures in Cycle Theory
MATX 1102
Mon 7 Nov 2016, 3:00pm-4:00pm

Abstract

We will not assume any prior knowledge of stacks for this talk. Toric stacks, like toric varieties, form a concrete class of examples which are particularly amenable to computation. We give an introduction to the subject and explain how we have used toric stacks to obtain an unexpected result in cycle theory. We end the talk by discussing some conjectures recently introduced by myself and Dan Edidin.
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Stanford University
Tue 8 Nov 2016, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
The moduli space of 2-convex embedded spheres
ESB 2012
Tue 8 Nov 2016, 3:30pm-4:30pm

Abstract

The space of smoothly embedded n-spheres in Rn+1 is the quotient space Mn:=Emb(Sn,Rn+1)/Diff(Sn). In 1959 Smale proved that M1 is contractible and conjectured that M2 is contractible as well, a fact that was proved by Hatcher in 1983.

While it is known that not all Mn are contractible, for n\get 3 no single homotopy group of Mn is known. Even knowing whether the Mn are path connected or not would be extremely interesting. For instance, if M3 is not path connected, the 4-d smooth Poincare conjecture can not hold true. 

In this talk, I will first explain how mean curvature flow  can assist in studying the topology of geometric relatives of Mn.
I will first illustrate how the theory of 1-d mean curvature flow (aka curve shortening flow) yields a very simple proof of Smale's theorem about the contractibility of M1.
I will then describe a recent joint work with Reto Buzzno and Robert Haslhofer, utilizing mean curvature flow with surgery to prove that the space of 2-convex embedded spheres is path connected.  
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University of Bath
Wed 9 Nov 2016, 3:00pm
Probability Seminar
ESB 2012
Phase transition in a sequential assignment problem on graphs
ESB 2012
Wed 9 Nov 2016, 3:00pm-4:00pm

Abstract

We study the following game on a finite graph G = (V, E). At the start, each edge is assigned an integer n_e \ge 0, n = \sum_{e \in E} n_e. In round t, 1 \le t \le n, a uniformly random vertex v \in V is chosen and one of the edges f incident with v is selected by the player. The value assigned to f is then decreased by 1. The player wins, if the configuration (0, \dots, 0) is reached; in other words, the edge values never go negative. Our main result is that there is a phase transition: as n \to \infty , the probability that the player wins approaches a constant c_G > 0 when (n_e/n : e \in E) converges to a point in the interior of a certain convex set \mathcal{R}_G, and goes to 0 exponentially when (n_e/n : e \in E) is bounded away from \mathcal{R}_G. We also obtain upper bounds in the near-critical region, that is when (n_e/n : e \in E) lies close to \partial\mathcal{R}_G. We supply quantitative error bounds in our arguments.
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University of Washington
Wed 9 Nov 2016, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
Iterated Thom Spectra with Examples
ESB 4133 (PIMS Lounge)
Wed 9 Nov 2016, 3:15pm-4:15pm

Abstract

Given a fiber sequence of n-fold loop spaces X-->Y-->Z, and morphism of n-fold loop spaces Y-->Pic(R) for R an E_{n+1}-ring spectrum, we describe a method of producing a new morphism of (n-1)-fold loop spaces Z-->Pic(MX), where MX is the Thom spectrum associated to the composition X-->Y-->Pic(R). This new morphism has associated Thom spectrum MY, but constructed directly as an MX-module. In particular this induces a relative Thom isomorphism for MY over MX: MY⊗_{MX} MY = MY⊗Z. We will see a rough description of this construction as well as many examples allowing us to find equivalent forms of relative smash products of spectra like MString, MSpin, HZ/2, X(n) and many others. We also describe a way to use this construction to identify certain obstructions to giving a complex orientation on an associative ring spectrum.
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Reed College
Thu 10 Nov 2016, 3:15pm SPECIAL
Topology and related seminars
ESB 4127
The transfer map of free loop spaces
ESB 4127
Thu 10 Nov 2016, 3:15pm-4:15pm

Abstract

Associated to a fibration E --> B with homotopy finite fiber is a stable wrong way map LB --> LE of free loop spaces coming from the transfer map in THH.  This transfer is defined under the same hypotheses as the Becker-Gottlieb transfer, but on different objects. I will use duality in bicategories to explain why the THH transfer contains the Becker-Gottlieb transfer as a direct summand.  The corresponding result for the A-theory transfer may then be deduced as a corollary.  When the fibration is a smooth fiber bundle, the same methods give a three step description of the THH transfer in terms of explicit geometry over the free loop space.  (Joint work with C. Malkiewich)
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UBC
Thu 10 Nov 2016, 3:30pm
Number Theory Seminar
MATH 126
Counting irreducible divisors and irreducibles in progressions
MATH 126
Thu 10 Nov 2016, 3:30pm-5:15pm

Abstract

Let  K/\mathbb{Q}  be a number field with ring of integers \mathbb{Z}_K. If K has class number one, the set of irreducible elements of \mathbb{Z}_K coincides with the set of prime elements; in general, this need not be the case. One is led to wonder: Do statements about primes in \mathbb{Z} have analogues for irreducibles in \mathbb{Z}_K, for a general choice of K? This talk concerns two instances where the answer is yes. We will discuss the maximal order of the number of irreducible divisors of an element of \mathbb{Z}_K, and we will provide an asymptotic formula for the number of irreducible elements of norm up to x belonging to a given arithmetic progression.
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TU Darmstadt, Department of Mechanical Engineering
Mon 14 Nov 2016, 3:00pm
Institute of Applied Mathematics
ESB 2012
New conservation laws of Euler and Navier-Stokes equations. Subtitle: Generic and dimensionally reduced cases for plane, axisymmetric and helically symmetric flows
ESB 2012
Mon 14 Nov 2016, 3:00pm-4:00pm

Abstract

It has long been known that 3D time-dependent Navier-Stokes equations for incompressible fluids admit the classical conservation laws (CL) of mass, momentum, angular momentum and centre-of-mass theorem. For inviscid flows, i.e. Eulers equation, this is extended by the conservation of helicity and energy. Employing the “direct method” (DM) by Anco, Bluman (1997) it has been shown that this set of conservation laws is complete for primitive variables. The DM is a substantial generalization of Noethers theorem and does not rely on a variational principle, and, further, is directly applicable to any type of differential equation, even dissipative ones.  With this an additional infinite set of CL for Navier-Stokes equations in vorticity formulation are derived. Various examples are shown.
Interesting enough, even more CLs exist for Euler and Navier-Stokes equations in spatially reduced coordinate systems such as for plane, axisymmetric and helically symmetric flows. E.g. an infinite set of CLs for the generalization of helicity has been derived, and, surprisingly, even new CL for plane flows haven been identified.

Note for Attendees

Tea served beforehand in ESB 4133 (PIMS lounge) 
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Avner Segal
UBC
Mon 14 Nov 2016, 3:00pm
Number Theory Seminar
ESB 4127
New-Way Integrals
ESB 4127
Mon 14 Nov 2016, 3:00pm-5:00pm

Abstract

In the theory of automorphic representations the study of L-functions plays a key role. A common method to study the analytic behavior of such functions (and, in fact, proving that they are meromorphic functions) is the Rankin-Selberg method. In this method an integral representation, with good analytic properties, is attached to the L-function. Many examples of Rankin-Selberg integrals were studied along the years. However most examples rely on the uniqueness of certain models of the representation (most popular in use is the Whittaker model but many other, such as the  Peterson bilinear form and Bessel model, are used). In a pioneering paper ("A new-way to get Euler products", Krelle, 1988) I. Piatetski-Shapiro and S. Rallis suggested a remarkable mechanism that makes it possible to use integrals containing a "non-unique model" by a slight strengthening of the unramified computations.

In the first part of my talk we will have a crash-course on cuspidal automorphic representations and the new-way mechanism via the classical example of Hecke's integral representation for L-functions of cuspidal representations of GL_2.

In the second part of my talk I will present a joint work with N. Gurevich in which we proved that a family of Rankin-Selberg integrals representing the standard twisted L-function of a cuspidal representation of the exceptional group of type G_2. In its unfolded form (a term which will be explained in the talk), the integrals contain a non-unique model and we apply the new-way mechanism. The unramified computation gives rise to two interesting objects: the generating function of the L-function and its approximations. If time permits, I will discuss the possible poles of this L-function and some applications to the theory of cuspidal representations of G_2.
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Chair of Fluid Dynamics, TU Darmstadt
Tue 15 Nov 2016, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
An Extended Discontinuous Galerkin (XDG) scheme for high-order multi-phase simulations using non-smooth basis functions at the phase interface
ESB 4133 (PIMS Lounge)
Tue 15 Nov 2016, 12:30pm-1:30pm

Abstract


The development of the new discontinuous Galerkin (DG) framework BoSSS (bounded support spectral solver) starting in 2007. Solvers for incompressible as well as compressible single and multi-phase flows were implemented. 

The code features a modern object-oriented design and is of course MPI-parallel. Within the development cycle, we use unit-testing to ensure software quality: this covers a wide range of tests, form very simple ones that test e.g. accuracy of implemented quadrature rules or the derivatives of a scalar field to complex MPI-parallel Navier-Stokes simulations and convergence tests. All these checks and tests are automatically executed by a dedicated server, whenever a developer commits changes to the GIT-repository. 

BoSSS supports arbitrary partitioning of the grid, on an arbitrary number of compute-nodes at start-up time, which is an important perquisite for the adaptive meshing which is addressed by this proposal. Quite recently, support for mixed meshes (combining e.g. triangles and quads) and hanging nodes has been added. 

The most outstanding feature of the code is the support for multiphase-flows and immersed boundary methods. For both of these applications, the interface is described by a level-set-method. The novelty is that we can demonstrate arbitrarily high spectral convergence in the presence of curved interfaces. This becomes possible due to a novel numerical integration technique for implicitly defined surfaces, the so-called hierarchical moment fitting (HMF) technique. 
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Massachusetts Institute of Technology
Wed 16 Nov 2016, 3:00pm
Probability Seminar
ESB 2012
Liouville quantum gravity and peanosphere
ESB 2012
Wed 16 Nov 2016, 3:00pm-4:00pm

Abstract

We will discuss Liouville quantum gravity as a scaling limit theory for random planar maps. In particular, we will focus on a recent approach called peanosphere or mating of trees and provide several applications of this framework.

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UIC
Fri 18 Nov 2016, 1:00pm
Discrete Math Seminar
MATX1102
New developments in hypergraph Ramsey theory
MATX1102
Fri 18 Nov 2016, 1:00pm-2:00pm

Abstract

 I will describe lower bounds (i.e. constructions) for several hypergraph Ramsey problems. These constructions settle old conjectures of Erdos-Hajnal on classical Ramsey numbers as well as more recent questions due to Conlon-Fox-Lee-Sudakov and others on generalized Ramsey numbers and the Erdos-Rogers problem. Most of this is joint work with Andrew Suk.
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Penn State
Fri 18 Nov 2016, 3:00pm
Department Colloquium
Math Annex 1100
Reduction theory for Fuchsian groups and coding of geodesics.
Math Annex 1100
Fri 18 Nov 2016, 3:00pm-4:00pm

Abstract

I will discuss a method of coding of geodesics on quotients of the hyperbolic plane by Fuchsian groups using boundary maps and “reduction theory”. These maps are piecewise fractional-linear given by generators of the Fuchsian group, and the orbit of a point under the boundary map defines its boundary expansion. For compact surfaces they are generalizations of the Bowen-Series map, and for the modular surface are related to a family of (a,b)-continued fractions. For the natural extensions of the boundary maps Zagier’s Reduction Theory Conjecture (RTC) holds: for the appropriate open sets of parameters they have attractors with finite rectangular structure to which (almost) every point is mapped after finitely many iterations. I will also explain how the RTC is used for representing the geodesic flow as a special flow over a cross-section of “reduced” geodesics parametrized by the attractor.  This was proved for the modular group and generalizes for Fuchsian groups that satisfy the RTC. The talk is based on joint works with Ilie Ugarcovici.

Note for Attendees

Refreshments will be served at 2:45pm in MATH 126.
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Purdue University
Mon 21 Nov 2016, 1:45pm
Harmonic Analysis Seminar
MATH 202
Extremizers for the 2D Kakeya problem
MATH 202
Mon 21 Nov 2016, 1:45pm-2:45pm

Abstract

Our talk investigates the subtle relationship between the size of the level sets of the (bilinear) Kakeya function and the corresponding geometric distribution of the points within these level sets. Under suitable conditions, our goal is to characterize the situation in which the size of these level sets is maximal and thus to provide qualitative and quantitative information about the extremizers associated with the (bilinear) Kakeya function.
 
Our analysis will involve additive combinatorics (e.g. Plünnecke sum-set estimate) and incidence geometry (e.g. Szemeredi-Trotter) techniques and relates with a class of problems including Bourgain's sum-product theorem and Katz-Tao ring conjecture.
 
This is a joint work with Michael Bateman.
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Johns Hopkins University
Mon 21 Nov 2016, 3:00pm SPECIAL
Department Colloquium
MATH ANNEX 1100
Quests for Golden numbers, old and new
MATH ANNEX 1100
Mon 21 Nov 2016, 3:00pm-4:00pm

Abstract

1. Let A be a 2x2 matrix over any universal field with any characteristic and An be any power of A. Our main proposition describes each component of An, the n‐th power, in terms of eigenvalues of A and values of well known cyclotomic rational function F(n,X,Y) at those eigenvalues. When A={0,1;1,1}, the case of Fibonacci, X is the golden number 1.61803... and Y=‐0.61803..., and F(n) is the well known sequence.

2. We apply algebraic results in Part 1 to the case of real quadratic fields and study the action of the group of units on the ring of integers of the quadratic fields. We will introduce a family of infinitely many real quadratic fields parametrised by odd integers q. In the classical case q=1.

Biography:
Professor Takashi Ono is a world‐renowned and highly accomplished mathematician, specializing in number theory and algebraic groups. He has made major contributions to the field of number theory, and his work is considered a cornerstone of arithmetic algebraic geometry. Having received his PhD from Nagoya University in 1958 under the supervision of Shokichi Iyanaga, Takashi Ono moved to the Institute of Advanced Study in Princeton, New Jersey, where he held a fellowship from 1959‐1961 at the invitation of J. Robert Oppenheimer. He then spent three years working as a mathematics professor at the University of British Columbia, followed by five years at the University of Pennsylvania. He then moved to Johns Hopkins University in 1969 and remained there until his retirement in 2011. Professor Ono has received a number of honours, including an invitation to speak at the International Congress of Mathematicians in Moscow 1966 and election as a Fellow of the American Mathematical Society in 2012. His mathematical contributions are complemented by the talent and hard work of his family: his eldest son is the musician Momoro Ono, his youngest son is the mathematician Ken Ono and his middle son is Santa Ono, President and Vice‐Chancellor of the University of British Columbia.

Note for Attendees

Pre‐lecture reception at 2.30 PM in MATH 126.
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MIT
Mon 21 Nov 2016, 4:15pm
Algebraic Geometry Seminar
MATX 1102
Elliptic Calabi-Yau threefolds and Jacobi forms via derived categories
MATX 1102
Mon 21 Nov 2016, 4:15pm-5:15pm

Abstract

By physical considerations Huang, Katz and Klemm conjecture that the generating series of Donaldson-Thomas invariants of an elliptic Calabi-Yau threefold is a Jacobi form. In this talk I will explain a mathematical approach to proving part of their conjecture. The method uses an autoequivalence of the derived category, and wallcrossing techniques developed by Toda. This leads to strong structure results for curve counting invariants. As a leading example we will discuss the elliptic fibration over P2 in degree 1. 

This is joint work with Junliang Shen.
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UC Berkeley
Tue 22 Nov 2016, 4:00pm
Discrete Math Seminar
ESB 4127
On Percolation and NP-Hardness
ESB 4127
Tue 22 Nov 2016, 4:00pm-5:00pm

Abstract

We study the computational hardness of problems whose inputs are obtained by applying random noise to worst-case instances. For an appropriate notion of noise we show that a number of classical NP-hard problems on graphs remain essentially as hard on the noisy instances as they are in the worst-case.
 
Focusing on the Graph Coloring problem, we establish the following result: Given any graph G, let H be a random subgraph of G obtained by deleting the edges of G independently with probability 0.5. We show that if \chi(G) is large, then \chi(H) is also large with high probability. This means that the chromatic number of any graph is ``robust'' to random edge deletions.
 
Joint work with Huck Bennett and Daniel Reichman.
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Qingsan Zhu
UBC Math
Wed 23 Nov 2016, 3:00pm
Probability Seminar
ESB 2012
On the critical branching random walk in supercritical and critical dimensions.
ESB 2012
Wed 23 Nov 2016, 3:00pm-4:00pm

Abstract

We extend several results in the potential theory of random walk to critical branching random walk. In the supercritical dimensions (d\geq 5), we introduce branching capacity for any finite subset of \Z^d and establish its connections with the hitting probability by branching random walk and branching recurrence. In the critical dimension (d=4), we also establish the asymptotics of the hitting probability and some related results.
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UBC
Wed 23 Nov 2016, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
A functorial version of Vinogradov’s theorem on free products of orderable groups.
ESB 4133 (PIMS Lounge)
Wed 23 Nov 2016, 3:15pm-4:15pm

Abstract

An ordered group (G,<) is a group G together with a strict total ordering < of its elements which is invariant under left- and right-multiplication.  If such an ordering exists for a group, the group is said to be orderable. It is easy to see that if G and H are orderable, then so is their direct product.  In 1949, A. A. Vinogradov proved that if G and H are orderable groups, then the free product G*H is also orderable.  I’ll show that such an ordering can be constructed in a functorial manner, in the category of ordered groups and order-preserving homomorphisms, using an algebraic trick due to G. Bergman.  This was motivated by a certain question in the theory of the braid groups B_n and the Artin representation of B_n in the automorphism group Aut(F_n) of a free group.
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University of Oregon
Thu 24 Nov 2016, 2:00pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
ESB 4127
The Calabi flow with rough initial data (note special time & room)
ESB 4127
Thu 24 Nov 2016, 2:00pm-3:00pm

Abstract

The Calabi flow is a fourth order nonlinear parabolic flow, introduced by Calabi in 1980s, and it aims to find Kahler metrics with constant scalar curvature (or more generally extremal Kahler metrics). We prove that the Calabi flow can have a unique smooth short time solution with continuous initial metric. As a byproduct, we prove some elementary but new Schauder type estimates for biharmonic heat equation on compact manifolds. This is a joint work with Yu Zeng (University of Rochester). Our result partially answers a problem proposed by Xiuxiong Chen.
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David Gleich
Department of Computer Science, Purdue University
Fri 25 Nov 2016, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Higher-order methods for clustering data
ESB 4133 (PIMS Lounge)
Fri 25 Nov 2016, 12:30pm-1:30pm

Abstract

Higher-order methods that use multiway and multilinear correlations are necessary to identify important structures in complex data from biology,
neuroscience, ecology, systems engineering, and sociology. We will study our recent generalization of spectral clustering to higher-order structures in depth. This will include a generalization of the Cheeger inequality (a concise statement about the approximation quality) to higher-order structures in networks including network motifs. This is easy to implement and seamlessly enables spectral clustering-style methods for directed, signed, and many other types of complex networks. If there is time, we will see software demonstrations in the Julia language for reproducibility. I will also briefly highlight recent methods we have developed that use new types of stochastic processes and random walks to study these data involving tensor eigenvectors. These topics motivate a number of exciting open questions at the intersection of numerical linear algebra, optimization, and data analysis. 
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Emory University
Fri 25 Nov 2016, 3:00pm SPECIAL
Department Colloquium
ESB 2012
PIMS-UBC Distinguished Colloquium - New theorems at the interface of number theory and representation theory
ESB 2012
Fri 25 Nov 2016, 3:00pm-4:00pm

Abstract

The Rogers-Ramanujan identities and Monstrous moonshine are among the deepest results which occur at the interface of number theory and representation theory. In this lecture the speaker will discuss these identities, and describe recent work with Duncan, Griffin on Warnaar on their recent generalizations. This will include a framework of Rogers-Ramanujan identities and singular moduli, and the theory of umbral Moonshine.

Note for Attendees

Refreshments (A light reception) will be served in ESB 4133 from 2:30pm-3:00pm before the colloquium.
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Imperial College
Mon 28 Nov 2016, 3:00pm SPECIAL
Institute of Applied Mathematics
ESB 2012
The "Hole Story" of a forgotten function, and how to use it
ESB 2012
Mon 28 Nov 2016, 3:00pm-4:00pm

Abstract

Motivated by problems arising in the applied sciences, I will tell the story of what might reasonably be called a "forgotten function". It was discovered in the late 1800s, but has hardly ever been used in the physical sciences even though, as I will show, its applications in science and engineering turn out to be many and varied.
 
In particular, I will survey a new theoretical approach to solving problems in what mathematicians call "multiply connected" domains. These are ubiquitous in applications; whenever two or more objects or entities (airfoils, bacteria, vortices, inhomogeneities in an elastic medium, black holes!...) interact in some ambient medium the analysis may call for the methods I will discuss.
 
Some illustrative example problems from applications, especially in fluid dynamics, will be described and their solutions explicitly constructed. I will also describe freely available numerical codes that we have developed for the computation of this "forgotten function" in order to promote its use.
 
We hope to demonstrate that the new methods are sufficiently general that they provide broad scope for tackling a variety of problems.

Note for Attendees

Tea beforehand in the PIMS lounge (ESB 4133) 
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Caltech
Mon 28 Nov 2016, 3:00pm
Algebraic Geometry Seminar
MATX 1102
Compactifications and Gauged Gromov-Witten Theory
MATX 1102
Mon 28 Nov 2016, 3:00pm-4:00pm

Abstract

I will give an introduction to gauged Gromov-Witten theory. The theory naturally leads to studying compactifications of the moduli space of G bundles on nodal curves, which I'll discuss briefly.  Then I'll focus on a version of gauged Gromov-Witten theory developed by Woodward and Gonzalez and I'll present a theorem which is joint work with Woodward and Gonzalez on the properness of the moduli of scaled gauged maps satisfying a stability condition introduced by Mundet and Schmitt.
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UBC
Mon 28 Nov 2016, 3:00pm
Number Theory Seminar
ESB 4127
The modular method and Fermat's Last Theorem
ESB 4127
Mon 28 Nov 2016, 3:00pm-5:00pm

Abstract

Fermat's Last Theorem states that the equation x^n + y^n = z^n for n > 2 has no integer solutions such that xyz \neq 0. It's proof was completed in 1995 by the groundbreaking work of Andrew Wiles on the modularity of semistable elliptic curves over Q. From its proof a new revolutionary method to attack Diophantine equations was born. This method, now known as the modular method, builds on the work of Frey, Serre, Ribet, Mazur and makes use of the Galois representations attached to modular forms and elliptic curves.
 
In the first part of this talk, guided by the proof of FLT, we will introduce the tools and sketch the basic strategy behind the modular method. In the second part, we will discuss the main obstacles that arise when we try to apply the method to other type of equations or over number fields.
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Fok-Shuen Leung
Department of Mathematics, UBC
Tue 29 Nov 2016, 12:30pm
Lunch Series on Teaching & Learning
MATH 126
Half-flip: the recitation model in first-year Math classes
MATH 126
Tue 29 Nov 2016, 12:30pm-1:30pm

Abstract

For the past two years I have been using a "recitation model" to teach the MATH 100/MATH 101 sequence at Vantage College. Instead of three lectures a week, students have one large lecture (run by me) and two small problem-based recitations (run by graduate and undergraduate instructors). I will be testing this model in a mainstream section of MATH 101 next term.

I will discuss the strengths and weaknesses of the model, and whether or not it should be used for our large first-year Math classes.
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Universidade Federal de Juiz de Fora
Tue 29 Nov 2016, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Hénon Problem in Hyperbolic Space
ESB 2012
Tue 29 Nov 2016, 3:30pm-4:30pm

Abstract

We deal with a class of the semilinear elliptic equations of the Hénon-type in hyperbolic space. The problem involves a logarithm weight in the Poincaré ball model, bringing singularities on the boundary. Considering radial functions, a compact Sobolev embedding result is proved, which extends a former Ni result made for a unit ball in R^N. Combining this compactness embedding with the Mountain Pass Theorem, an existence result is established.
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Natalie Hobson
U. Georgia
Tue 29 Nov 2016, 4:00pm
Discrete Math Seminar
ESB 4127
Quantum Kostka and the rank on problem for sl_2m
ESB 4127
Tue 29 Nov 2016, 4:00pm-5:00pm

Abstract

In this talk we will define and explore an infinite family of vector bundles, known as vector bundles of conformal blocks, on the moduli space M0,n of marked curves. These bundles arise from data associated to a simple Lie algebra. We will show a correspondence (in certain cases) of the rank of these bundles with coefficients in the cohomology of the Grassmannian. This correspondence allows us to use a formula for computing "quantum Kostka" numbers and explicitly characterize families of bundles of rank one by enumerating Young tableaux. We will show these results and illuminate the methods involved.
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University of Victoria
Wed 30 Nov 2016, 1:45pm
Mathematical Biology Seminar
PIMS
The coexistence or replacement of two subtypes of influenza
UBC Math
Wed 30 Nov 2016, 3:00pm
Probability Seminar
ESB 2012
Update Tolerance in Uniform Spanning Forests
ESB 2012
Wed 30 Nov 2016, 3:00pm-4:00pm

Abstract

The uniform spanning forests (USFs) of an infinite graph G are defined to be infinite volume limits of uniformly chosen spanning trees of finite subgraphs of G. These limits can be taken with respect to two extremal boundary conditions, yielding the free uniform spanning forest (FUSF) and wired uniform spanning forest (WUSF). While the wired uniform spanning forest has been quite well understood since the seminal paper of Benjamini, Lyons, Peres and Schramm (’01), the FUSF is less understood, and some very basic questions about it remain open. In this talk I will introduce a new tool in the study of USFs, called update tolerance, and describe how update tolerance can be used to prove, among other things, that the FUSF has either one or infinitely many connected components on any infinite Cayley graph, and that components of either the FUSF and WUSF are indistinguishable from each other by invariantly defined properties on any infinite Cayley graph. Another crucial component of these proofs is the Mass-Transport Principle, which I will also give an introduction to.
 
Based in part on joint work with Asaf Nachmias.
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