Mathematics Dept.
  Events
Department of Mathematics, Hong Kong Baptist University and South University of Science and Technology, China
Mon 1 Feb 2016, 3:00pm SPECIAL
Institute of Applied Mathematics
LSK 460
High order numerical methods for uncertainty quantification
LSK 460
Mon 1 Feb 2016, 3:00pm-4:00pm

Abstract

Uncertainty quantification (UQ) has been a hot research topic recently. UQ has a variety of applications, including hydrology, fluid mechanics, data assimilation, and weather forecasting. Among a large number of approaches, the high order numerical methods have become one of the important tools; and the relevant computational techniques and their mathematical theory have attracted great attention in recent years. This talk begins with a brief introduction to recent developments of high order numerical methods including Galerkin projection methods and stochastic collocation methods. The emphasis will be sample-based stochastic collocation methods, including random sampling, deterministic sampling and structured random sampling. We will also discuss approximating multivariate functions in unbounded domains by using discrete least squares projection with random point evaluations. Particular attention is given to functions with random Gaussian or gamma parameters. 

Note for Attendees

This is an IAM/PIMS distinguished speaker. Tea will be served before the talk in the IAM lounge (LSK 306). 
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Mohammad Bardestani
University of Ottawa
Mon 1 Feb 2016, 3:00pm
Harmonic Analysis Seminar
MATX 1102
Oscillatory integrals and the Borel chromatic number of quadratic graphs
MATX 1102
Mon 1 Feb 2016, 3:00pm-4:00pm

Abstract

For a field F and a quadratic form Q defined on an n-dimensional vector space V over F, let G_Q, called the quadratic graph associated to Q, be the graph with the vertex set V where vertices u,w in V form an edge if and only if Q(v-w)=1. Quadratic graphs can be viewed as natural generalizations of the unit-distance graph featuring in the famous Hadwiger-Nelson problem. In the present talk, we will prove that for a local field F of characteristic zero, the Borel chromatic number of G_Q is infinite if and only if Q represents zero non-trivially over F. The proof employs a recent spectral bound for the Borel chromatic number of Cayley graphs, combined with an analysis of certain oscillatory integrals over local fields. As an application, we will also answer a variant of question 525 proposed in the 22nd British Combinatorics Conference 2009.
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Sam Molcho
University of Colorado Boulder
Mon 1 Feb 2016, 3:00pm
Algebraic Geometry Seminar
MATH 126
Moduli of Logarithmic Stable Toric Varieties
MATH 126
Mon 1 Feb 2016, 3:00pm-4:00pm

Abstract

I am going to discuss Alexeev's and Brion's moduli space parametrizing maps
from broken toric varieties into a fixed toric variety V. Following ideas
of Olsson, I will explain how one can obtain a modular description of the
main irreducible component of Alexeev's and Brion's space, using an
analogous moduli space K(V) parametrizing logarithmic maps from broken
toric varieties into V. The resulting space K(V) is in fact a toric stack
-- it is a stacky enrichment of an appropriate Chow quotient of V. I will
conclude by explaining why K(V) and the Chow quotient stack coincide, and
describe explicitly the combinatorial data that determine the latter.

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University of Oregon
Tue 2 Feb 2016, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Computing the Hodge Laplacian on 1-forms of a manifold using random samples
ESB 2012
Tue 2 Feb 2016, 3:30pm-4:30pm

Abstract

Let M be a submanifold of Euclidean space, and let X be a subset of N points, randomly sampled. Belkin and Niyogi showed that one can recover the Laplacian on functions on M as N gets large, by integrating the heat kernel. More recently, Singer and Wu use Principle Component Analysis to construct connection matrices between approximate tangent spaces for nearby points in X. This allows them to construct a rough Laplacian on 1-forms. Together with Ache, we show that by iterating the Laplace operator of Belkin and Niyogi, a la Bakry and Emery, and appealing to the Bochner formula, we can reconstruct the Ricci curvature on the approximate tangent spaces. Combining our work with the work of Singer and Wu, we are able to approximate the Hodge Laplacian on 1-forms.
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IMA, University of Minnesota
Tue 2 Feb 2016, 4:00pm
Discrete Math Seminar
MATH 126
Enumeration of lozenge tilings of a hexagon with three dents
MATH 126
Tue 2 Feb 2016, 4:00pm-5:00pm

Abstract

MacMahon's classical theorem on boxed plane partitions states that the generating function of the plane partitions fitting in an $a\times b\times c$ box is equal to

\[\frac{H_q(a)H_q(b)H_q(c)H_q(a+b+c)}{H_q(a+b)H_q(b+c)H_q(c+a)},\]

where $H_q(n):=[0]_q![1]_q!\dots[n-1]_q!$ and  $[n]_q!:=\prod_{i=1}^{n}(1+q+q^2+\dots+q^{i-1})$. By viewing a boxed plane partition as a lozenge tiling of a semi-regular hexagon, MacMahon's theorem yields a natural $q$-enumeration of lozenge tilings of the hexagon. However, such $q$-enumerations do not appear often in the domain of enumeration of lozenge tilings. In this talk, we consider a new $q$-enumeration of lozenge tilings of a hexagon with three bowtie-shaped regions removed from three non-consecutive sides. 

The unweighted version of the result generalizes a problem posed by James Propp on enumeration of lozenge tilings of a hexagon of side-lengths $2n,2n+3,2n,2n+3,2n,2n+3$ (in cyclic order) with the central unit triangles on the $(2n+3)$-sides removed. 

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Wed 3 Feb 2016, 10:00am
Math Education Research Reading
MATH 126
"Not a One-Way Street: Bidirectional Relations Between Procedural and Conceptual Knowledge of Mathematics"
MATH 126
Wed 3 Feb 2016, 10:00am-11:00am

Abstract

 
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IMA, University of Minnesota
Wed 3 Feb 2016, 3:00pm
Department Colloquium
MATH 104
Tiling expression of minors
MATH 104
Wed 3 Feb 2016, 3:00pm-4:00pm

Abstract

The field of enumeration of tilings dates back to the early 1900s when MacMahon proved his classical theorem on plane partitions fitting in a given box. The enumeration of tilings has become a subfield of combinatorics with applications and connections to diverse areas of mathematics. In this talk we will consider a connection between the enumeration of tilings and the theory of electrical networks. 
 
The theory of electrical networks was studied systematically by Colin de Verdiere and Curtis, Ingerman, Moores, and Morrow in the 1990s. Associated with an electrical network is a "response matrix" that measures the response of the network to potential applied at  the nodes. Kenyon and Wilson showed how to test the well-connectivity of  an electrical network with n nodes by checking the positivity of n(n-1)/2 minors of the response matrix. Their test was based on the fact that any "contiguous minor" of a matrix is the generating function of domino tilings of a weighted Aztec diamond.  They conjectured that a larger family of minors, "semicontiguous minors",  can also be expressed in terms of domino tilings of certain regions. We prove this conjecture by describing explicitly the ``tiling expression" of the semicontiguous minors.

Note for Attendees

Refreshments will be served in MATH 125 before the colloquium.
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Henrik Rüping
University of British Columbia
Wed 3 Feb 2016, 4:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
Controlled Algebra, Part II
ESB 4133 (PIMS Lounge)
Wed 3 Feb 2016, 4:15pm-5:15pm

Abstract

As explained last week, Controlled Algebra is a way of building new additive categories with better properties out of given ones.  This time we will use it to describe K-theoretic assembly maps as maps induced by additive functors.

Note for Attendees

This week the seminar is moved to 4:15pm, to allow people to attend the Colloquium.
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M.I.T.
Thu 4 Feb 2016, 3:30pm
Discrete Math Seminar
MATH 126
New bounds for point-curve incidences in the plane
MATH 126
Thu 4 Feb 2016, 3:30pm-4:30pm

Abstract

A classical problem in combinatorial geometry is to determine the maximum number of incidences between a set of m points and n curves in the plane. If the curves are lines, then Szemerédi and Trotter proved that there could be at most O(m^{2/3}n^{2/3} + m + n) incidences, and this bound is tight. For other classes of curves, very few tight bounds are known. Work in this area progressed in the 80s and 90s, culminating in an incidence bound by Pach and Sharir in 1998 that applies to a very general class of curves. Since then, there have only been improvements for a few specific types of curves. In this talk I will discuss some new developments that improve upon Pach and Sharir's bound for a broad class of curves. A key innovation is the use of higher-dimensional incidence geometry, coupled with a new way of cutting collections of curves into segments so that the corresponding set of segments is better behaved than the original collection of curves. This is joint work with Micha Sharir.
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Oliver Leigh
UBC
Fri 5 Feb 2016, 1:00pm
Graduate Student Seminar
Math 225
Stable reduction in the moduli space of curves: Dealing with problem children.
Math 225
Fri 5 Feb 2016, 1:00pm-2:00pm

Abstract

The moduli space of stable curves is a community where families coexist peacefully. Unfortunately, this peacefulness comes at the price of conformity; you have to be "stable", and there is a strict screening process for families wishing to live there. If a family has undesirable members then they are barred from entering :(

Luckily, there is a process that a family can undergo to make themselves more desirable and be allowed entry. We examine this process when a nice family contains a single problem child. It may seems rather extreme, but this involves blowing up the family(!!) and gluing a pig's tail onto the problem child! :O

Note for Attendees

 Pizza and pop will be provided.
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M.I.T.
Fri 5 Feb 2016, 3:00pm
Department Colloquium
Math Annex 1100
Incidence geometry and low dimensional structure
Math Annex 1100
Fri 5 Feb 2016, 3:00pm-4:00pm

Abstract

Given a collection of points and a collection of lines, circles, or other simple geometric objects, an incidence occurs when a point is contained in one of the objects. Incidence geometry is a branch of extremal combinatorics that studies the maximum number of incidences that can occur amongst all possible arrangements of the objects in question. It turns out that problems from diverse areas of mathematics can be phrased as incidence geometry questions, and often this is an effective way of tackling these problems.

There is a general phenomena in incidence geometry, which is the principle that higher dimensional incidence geometry problems often have fewer incidences than lower dimensional ones unless the objects arrange themselves into a low dimensional structure. For example, any collection of points and lines in three dimensions has relatively few incidences unless many of the points and lines cluster into a plane. I will discuss this phenomena, as well as some of its implications in discrete math and harmonic analysis.

Note for Attendees

Refreshments will be served in MATH 125 before the colloquium.
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Institute for Computational Engineering and Mathematics, Stanford University
Tue 9 Feb 2016, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Towards an efficient, distributed-memory library for (arbitrary-precision) linear algebra, conic optimization, and lattice reduction
ESB 4133 (PIMS Lounge)
Tue 9 Feb 2016, 12:30pm-1:30pm

Abstract

While large numbers of researchers have investigated efficient distributed-memory schemes for dense and sparse-direct linear algebra, relatively little work has been performed on extensions into the important fields of conic optimization and lattice reduction.  (Perhaps surprising) performance barriers for distributed sparse Second-order Cone Programs will be discussed, and a case will be made for defaulting to explicitly storing quasi-constant edge-degree plus low-rank decompositions of the sparse KKT systems and then solving said systems via applying the iteratively-refined inverse of an a priori regularized, Symmetric Quasi-Semidefinite factorization as a preconditioner for Flexible GMRES(k). Recent work towards high-performance variants of lattice reduction schemes (LLL and BKZ 2.0) will also be briefly discussed to help make the case for the importance of high-precision arithmetic. Some practical issues related to the implementation of these techniques within the open source library Elemental (https://github.com/elemental/Elemental) will also be discussed.

Note for Attendees

Sushi lunch will be served at 12:25 p.m.
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Wed 10 Feb 2016, 10:00am
Math Education Research Reading
Math 126
"Peer-Assisted Reflection: A Design-Based Intervention for Improving Success in Calculus"
Math 126
Wed 10 Feb 2016, 10:00am-11:00am

Abstract

 
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Bernardo Villarreal Herrera
University of British Columbia
Wed 10 Feb 2016, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
Cosimplicial groups and spaces of homomorphisms
ESB 4133 (PIMS Lounge)
Wed 10 Feb 2016, 3:15pm-4:15pm

Abstract

In this talk I will give some relations between spaces of homomorphisms when the target group G is a real linear algebraic group,  through homotopy stable decompositions of simplicial spaces. To obtain a simplicial space Hom(L,G) out of spaces of homomorphisms we think of L, a (suitable) family of finitely generated groups, as a cosimplicial group.

 

Also, if G=U, the colimit of the unitary groups U(m), I will show when the geometric realization of Hom(L,U) has an "E-infinity-ring-space" structure.

Note for Attendees

 The seminar is back to the regular time!
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Bob Hough
Institute for Advanced Study, Princeton
Thu 11 Feb 2016, 3:30pm
Discrete Math Seminar
MATH 126
Random walk on unipotent groups
MATH 126
Thu 11 Feb 2016, 3:30pm-4:30pm

Abstract

Random walk on a group is an established but still-growing field.  I discuss aspects of recent work, alone and joint with Persi Diaconis, on random walks on unipotent groups.  Among our results, we have a new local limit theorem for random walk on the Heisenberg group, which applies to arbitrary centered measures of compact support and obtains an optimal rate. There is also a mixing time bound of degree times diameter squared for the mixing time of random walk on some Cayley graphs of cyclic groups.
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Pierre Tarrago
Fri 12 Feb 2016, 1:00pm
Probability Seminar
MATH 126
Thermodynamic limit on the graph of Zigzag diagrams
MATH 126
Fri 12 Feb 2016, 1:00pm-2:00pm

Abstract

 In this talk, I will first introduce the notions of Gibbs measures and thermodynamic limit on graded graphs, as they were defined by the Russian school (Vershik, Kerov, Olshanski,...). Then, I will present some results related to the thermodynamic limit on the graph of Zigzag diagrams: the latter is a graded graph whose set of vertices of degree n consists of words of length n-1 in two letters, and such that the edge structure is given by a simple combinatorial relation between words of consecutive lengths. This graph is related to the Young graph, and I will explain this relation by mapping paths on the graph of Zigzag diagrams to paths on the Young graph. "
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Bob Hough
Institute for Advanced Study, Princeton
Fri 12 Feb 2016, 3:00pm
Department Colloquium
MATX 1100
Covering systems of congruences and the Lovasz Local Lemma
MATX 1100
Fri 12 Feb 2016, 3:00pm-4:00pm

Abstract

The Lov\'{a}sz Local Lemma is a powerful technique from probabilistic combinatorics for treating many rare events with localized dependence structure.  I discuss the local lemma and its application in my negative solution to the following problem of Erd\H{o}s.

A distinct covering system of congruences is a collection of arithmetic progressions
 
a_i \bmod m_i, \qquad 1 < m_1 < m_2 < ... < m_k

whose union is the integers. Can m_1 be arbitrarily large?

Note for Attendees

Refreshments will be served in MATH 125 before the colloquium.
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Brown
Mon 22 Feb 2016, 3:00pm
Algebraic Geometry Seminar
MATH 126
Factorization of birational maps, with a shot of good energy
MATH 126
Mon 22 Feb 2016, 3:00pm-4:00pm

Abstract

Joint work with Michael Temkin, we extend the old results with Karu, Matsuki and Wlodarczyk from varieties to qe schemes and use this to prove factorization for various other categories.
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Mathematics and Dept of Chemical & Biological Engineering, UBC
Tue 23 Feb 2016, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
High performance computing for the numerical simulation of particle-laden flows
ESB 4133 (PIMS Lounge)
Tue 23 Feb 2016, 12:30pm-1:30pm

Abstract

Particle-laden flows are ubiquitous in environmental, geophysical and engineering processes. The intricate dynamics of these two-phase flows is governed by the momentum, heat and mass transfer between the continuous fluid phase and the dispersed particulate phase. While some multi-phase processes may be successfully modelled at the continuum scale through closure approximations, an increasing number of applications require resolution across scales, e.g. dense suspensions, fluidized beds. Within a multi-scale micro/meso/macro-framework, we develop robust numerical models at the micro and meso-scales, that both account for hydrodynamic interactions and particle/particle collisions. We present the mathematical issues related to modelling this type of flows together with the main numerical and computational features of our own simulation methods. Serial computations are almost not an option anymore and highly scalable codes on the most recent supercomputer architectures have become mandatory. We illustrate what can be gained from massively parallel computations in terms of physical insight into both fundamental questions and applications (essentially from the chemical engineering and process industry). We shortly discuss the next steps in the development of advanced numerical methods for particle-laden flows. Finally, we explain how knowledge gained at the micro scale can cascade upwards and contribute to the development of enhanced meso and macro-scale models.
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Krisztina Vasarhelyi
IMPACT-HIV and SFU Health Sciences
Wed 24 Feb 2016, 12:00pm
PIMS Seminars and PDF Colloquiums
UBC Robson Square
PIMS Vancouver Lunchbox Lecture: Systems Modeling for HIV Health Service Delivery
UBC Robson Square
Wed 24 Feb 2016, 12:00pm-1:00pm

Abstract

Public health program managers and policy makers are regularly faced with complex decisions that affect the health and well-being of the public. Mathematical models and operations research tools can be used to consider diverse interacting factors, such as the epidemiology and clinical aspects of a condition, delivery methods of health services, and constraints on budget and resources. Creating reliable, data-driven models that are tractable and useful for informing policy decisions requires close collaboration of stakeholders and mathematicians.

This presentation will describe a health systems modeling project to inform the delivery of HIV health services in Vancouver, which illustrates the promise, challenges and rewards of cross-sector collaborations and offers possible avenues for the expanded use of modeling in public policy.

Registration is free and a light lunch will be provided. For more details and to register for this event, please visit http://www.pims.math.ca/industrial-event/160224-pllkv .


Note for Attendees

About the PIMS Lunchbox Series

The PIMS Lunch Box Series create a beneficial link between researchers in industry and academics in the mathematical sciences. Researchers with industrial and commercial concerns are invited to present their current work, demonstrating how the latest advances in the mathematical sciences apply to current, real-world issues in industrial processes such as seismic and medical imaging, financial mathematics and complex fluids. PIMS has been holding lunchbox lectures in Calgary for seven years and is now expanding to Vancouver. To learn more about PIMS, please visit  www.pims.math.ca<http://www.pims.math.ca> .


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UBC and PIMS
Wed 24 Feb 2016, 3:00pm
Probability Seminar
ESB 2012
Stable-like processes with indices greater than two
ESB 2012
Wed 24 Feb 2016, 3:00pm-4:00pm

Abstract

 In Euclidean space, symmetric stable process with index α ∈ (0,2) is obtained by a time change of Brownian motion using the subordinator of index α/2By a similar subordination, there exists stable-like random walks with indices greater than two on various fractals and fractal-like graphs. However, existing methods to obtain transition probability estimates fail in this setting. 
 
Davies' method is a technique introduced by E. B. Davies to obtain heat kernel upper bounds for uniformly elliptic operators in Euclidean space. This method was extended to general symmetric Markov semigroups by Carlen, Kusuoka and Stroock. In this talk, I will introduce some of the ideas involved in extending Davies method to obtain heat kernel bounds for stable-like processes with indices greater than two.
 
This talk is based on joint works with Laurent Saloff-Coste.
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Daniel Sheinbaum
University of British Columbia
Wed 24 Feb 2016, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
Topology of Fermi surfaces and Anomalies
ESB 4133 (PIMS Lounge)
Wed 24 Feb 2016, 3:15pm-4:15pm

Abstract

We will introduce basic notions of quantum mechanics, mostly employed in condensed matter physics, such as a separable Hilbert space, Bloch's theorem and Fermi surfaces. Then we will describe the problem of stability of Fermi surfaces and relate it to the mathematical concepts of Fredholm operators and homotopy classes. Equipped with these concepts we show that our proposed scheme yields a classification of topologically stable Fermi surfaces by K-1(X), where X is the Brillouin zone and K-1 is a well known functor in K-theory. We will show an explicit example when X = S1, known as the spectral flow and its relation to quantum anomalies. This is work in progress joint with Alejandro Adem and Gordon W. Semenoff.
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UBC
Thu 25 Feb 2016, 3:30pm
Number Theory Seminar
room MATH 126
The story of the Lebesgue-Nagell equation and mathematical dead-ends
room MATH 126
Thu 25 Feb 2016, 3:30pm-4:30pm

Abstract

The Lebesgue-Nagell equation is a Diophantine equation that arises in a variety of contexts, ranging from the classification of finite simple groups to Catalan’s problem. In this talk, we will discuss a variety of approaches to this equation that share the common thread of failing to solve it. This is joint work with Aaron Levin.
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Princeton University
Fri 26 Feb 2016, 3:00pm SPECIAL
Department Colloquium / PIMS Seminars and PDF Colloquiums
ESB 2012
Coloring some perfect graphs -PIMS/UBC Distinguished Colloquium
ESB 2012
Fri 26 Feb 2016, 3:00pm-4:00pm

Abstract

Perfect graphs are a class of graphs that behave particularly well with respect to coloring. In the 1960's Claude Berge made two conjectures about this class of graphs, that motivated a great deal of research, and by now they have both been solved.

The following remained open however: design a combinatorial algorithm that produces an optimal coloring of a perfect graph. Recently, we were able to make progress on this question, and we will discuss it in this talk. Last year, in joint work with Lo, Maffray, Trotignon and Vuskovic we were able to construct such an algorithm under the additional assumption that the input graph is square-free (contains no induced four-cycle). More recently, together with Lagoutte, Seymour and Spirkl, we solved another case of the problem, when the clique number of the input graph is fixed (and not part of the input).

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DAMTP, Cambridge University
Mon 29 Feb 2016, 3:00pm SPECIAL
Institute of Applied Mathematics
LSK 460
Explaining the flow of elastic liquids
LSK 460
Mon 29 Feb 2016, 3:00pm-4:00pm

Abstract

The behaviour of elastic liquids does not follow simply from our understanding of both elastic solids and viscous liquids. Four anomalous behaviours will be discussed :-- (i) long wakes at low Reynolds numbers, (ii) large vortices upstream of a constriction, (iii) long times for capillary forces to squeeze a filament, and (iv) different devices measuring wildly different values of `the' extensional viscosity for the international standard liquid M1. Many features can be explained and understood using the simplest constitutive equation, that of an Oldroyd-B fluid, which generates the important ideas of tension in streamlines and delays for the stress to respond. This model fluid has however an undesirable negative viscosity under certain conditions, which can be regularized  by requiring a finite extensibility of the underlying microstructure, in the FENE modification. This modification enables the remain anomalous behaviours to be understood, with a high extensional viscosity to increase drag and an anisotropy to create the long upstream vortices.

Note for Attendees

This is an IAM/PIMS distinguished speaker. Tea will be served before the talk in the IAM lounge (LSK 306). 
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MIT
Mon 29 Feb 2016, 3:00pm
Algebraic Geometry Seminar
MATH 126
Gromov-Witten theory of K3 x P1 and Quasi-Jacobi forms
MATH 126
Mon 29 Feb 2016, 3:00pm-4:00pm

Abstract

Let S be a K3 surface. Generating series of Gromov-Witten invariants of the product geometry SxP1 are conjectured to be quasi-Jacobi forms. We sketch a proof of this conjecture for classes of degree 1 or 2 over P1 using genus bounds on hyperelliptic curves in K3 surfaces by Ciliberto and Knutsen. This has applications to a GW/Hilb correspondence for K3 surfaces, and curve counting on SxE, where E is an elliptic curve.
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