Montpellier / PIMSUBC

Tue 1 Oct 2013, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

Asymptotically harmonic manifolds of nonpositive curvature

ESB 2012
Tue 1 Oct 2013, 3:30pm4:30pm
Abstract
Harmonic manifolds are those Riemannian manifolds whose harmonic functions satisfy the meanvalue property, or equivalently, whose spheres have constant mean curvature. F. Ledrappier introduced an asymptotic version of harmonicity which was mainly studied in the cocompact and homogeneous cases. In this talk, I will review some classical facts on harmonic manifolds and prove some new results on asymptotically harmonic manifolds, including a characterization in term of the volume form . This is a joint work with Andrea Sambusetti.
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UBC

Tue 1 Oct 2013, 4:00pm
Discrete Math Seminar
ESB 4133

Maximal supports and Schurpositivity among connected skew shapes

ESB 4133
Tue 1 Oct 2013, 4:00pm5:00pm
Abstract
The Schurpositivity order on skew shapes is denoted by B < A if the difference of their respective Schur functions is a positive linear combination of Schur functions. It is an open problem to determine those connected skew shapes that are maximal with respect to this ordering. In this talk we see that to determine the maximal connected skew shapes in the Schurpositivity order it is enough to consider a special class of ribbon shapes. We also explicitly determine the support for these ribbon shapes.
This is joint work with Peter McNamara and assumes no prior knowledge.
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UBC

Wed 2 Oct 2013, 3:00pm
Probability Seminar
ESB 2012

Selfavoiding walk in four dimensions (I)

ESB 2012
Wed 2 Oct 2013, 3:00pm4:00pm
Abstract
I will review connections, including the Dynkin isomorphism, between the Gaussian free field on a lattice and local time of random walk. These connections give useful representations for walks with selfinteractions.
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IPMU

Wed 2 Oct 2013, 3:10pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UAlberta)

On the extended Walgebra of type sl_2 at positive rational level

ESB 4127 (host: UAlberta)
Wed 2 Oct 2013, 3:10pm4:10pm
Abstract
The extended Walgebra of type sl_2 at positive rational level is a vertex operator algebra that is of great interest in logarithmic conformal field theory. In this talk I will give an overview of how it is constructed as a subvertex operator algebra of a lattice vertex operator algebra by means of so called screening operators. I will also explain how the screening operator formalism allows one to prove c_2 cofiniteness, compute relations in Zhu's algebra and classify all simple modules of the extended Walgebra of type sl_2 at positive rational level.
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Complex Fluids Lab, UBC

Wed 2 Oct 2013, 4:00pm
Fluids Lab Meeting
LSK 203

GuardHeated Wall Shear Stress Sensors for Turbulent Flows

LSK 203
Wed 2 Oct 2013, 4:00pm5:00pm
Abstract
This talk presents analysis of the performance of multielement guardheated hotfilm wall shear stress microsensors for turbulent flows. Previous studies of conventional, singleelement sensors show that a significant portion of heat generated in the hotfilm travels through the substrate before reaching the fluid, causing spectral and phase errors in the wall shear stress signal and drastically reducing the spatial resolution of the sensor. Earlier attempts to reduce these errors have focused on reducing the effective thermal conductivity of the substrate. New guardheated microsensor designs proposed to overcome the severe deficiencies of the conventional design are investigated. Guardheaters remove the errors associated with substrate heat conduction, by forcing zero temperature gradient at the edges and bottom face of the hotfilm, and hence, block the indirect heat transfer to the flow. Air and water flow over the sensors are studied numerically to investigate design, performance and signal strength of the guardheated sensors. Our results show, particularly for measurements in lowconductivity fluids such as air, that edge guardheating needs to be supplemented by a subsurface guardheater, to make substrate conduction errors negligible. With this twoplane guardheating, a strong nonlinearity in the standard singleelement designs can be corrected, and spectral and phase errors arising from substrate conduction can be eliminated.
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Laurent Charette and Tom Hutchcroft
UBC

Thu 3 Oct 2013, 12:30pm
Graduate Student Seminar
Math 204

Lattice Symmetry Breaking Perturbation for Spiral Waves // On the Circle Packing Theorem

Math 204
Thu 3 Oct 2013, 12:30pm2:00pm
Abstract
Laurent:
The spiral wave is a pattern on a surface occurring in several natural
phenomena, such as in chemical reactions an on the cardiac tissue. It is
usually a byproduct in several pathologies such as stated in Mathematical
Physiology by Keener and Sneyd: "spirals on the heart are fatal, spirals on
the cerebral cortex may lead to epileptic seizures, and spirals on the
retina may cause hallucinations". In this talk, we will briefly go over the
background research on spiral waves and will present results of a perturbed
simple system, describing rigidly rotating waves and linearly travelling
waves in the unperturbed case. The perturbation used must have lattice
symmetry, that is symmetry on quarter rotations and unit translations in
two orthogonal directions. We will first look at the derivation of the
general form of the perturbation. Then, we will state findings obtained in
both rotating and travelling waves, supported by numerical simulations.
Tom:
A \emph{circle packing} $P$ is a collection $\{C_v : v \in V\}$ of discs of disjoint interior in the (extended) complex plane. Given a circle packing $P$, we may define its \emph{tangency graph} as $(V,E)$ where $\{u,v\} \in E$ if and only if $C_v$ and $C_u$ are tangent.
The Circle Packing Theorem states that any finite planar\footnote{A graph is said to be \emph{planar} if we can draw it in the plane such that no two distinct edges cross.} graph arises as the tangency graph of some circle packing. In fact, when the graph is a triangulation of the sphere, the circle packing is unique up to reflections and Mobius transformations of the sphere.
In this talk, we aim to provide an elementary, detailsfree introduction to the Circle Packing Theorem, its extensions and corollaries.
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UBC

Thu 3 Oct 2013, 3:00pm
Topology and related seminars
ESB 4133

The integral cohomology of configuration spaces of pairs of points in real projective spaces

ESB 4133
Thu 3 Oct 2013, 3:00pm4:00pm
Abstract
We compute the integral cohomology ring of configuration spaces of two distinct points on a given real projective space. As an application, we obtain the symmetric topological complexity of real projective spaces of dimensions 5 and 6.
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Columbia University

Thu 3 Oct 2013, 3:30pm
Number Theory Seminar
Room MATH 126

Towards a Langlands correspondence for Hecke modules of type A_n in characteristic p

Room MATH 126
Thu 3 Oct 2013, 3:30pm4:30pm
Abstract
We show how to realize the propIwahoriHecke algebra of SL_{n} as a subalgebra of the propIwahoriHecke algebra of GL_{n}. Using the interplay between these two algebras, we deduce a correspondence between "packets" of Hecke modules and modp projective Galois representations.
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UBC

Fri 4 Oct 2013, 3:00pm
Department Colloquium
MATX 1100

Quantization of random frame expansions

MATX 1100
Fri 4 Oct 2013, 3:00pm4:00pm
Abstract
In this talk, we will review the literature on frame quantization and present a number of recent results. Motivated by compressed sensing we will focus on "subGaussian random frames" and explain why classical quantization methods are bound to be substantially suboptimal. We will then show that by using the socalled sigmadelta quantizers along with reconstruction via ”Sobolev duals”, we can improve the quantization error substantially when we quantize subGaussian frame expansions. Specifically, we prove that using an rth order sigmadelta scheme, we get an accuracy of order (r)th power of the aspect ratio of the frame. Furthermore, if we optimize the order of the scheme depending on the aspect ratio, this yields rootexponential accuracy. Finally, we will discuss how these results can be used for constructing effective quantization methods for compressed sensing.
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UBC

Mon 7 Oct 2013, 2:00pm
Math Education Research Reading
Math 126

Math Education Reading and Discussion Group

Math 126
Mon 7 Oct 2013, 2:00pm3:00pm
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CS, UBC

Mon 7 Oct 2013, 3:00pm
Institute of Applied Mathematics
LSK 460

Formal Identification of DC Operating Points in Integrated Circuits and some Lessons in (Ir)Reproducible Research in Computational Math

LSK 460
Mon 7 Oct 2013, 3:00pm4:00pm
Abstract
A DC operating point is an equilibrium toward which a circuit will be drawn for sufficiently nearby initial conditions when any inputs are held fixed. DC operating points may or may not be desirable features in a circuit  in an oscillator they represent lockup, but in a memory element they are the mechanism whereby discrete state is stored. Consequently, it is useful to identify a circuit's DC operating points. Because the circuit is naturally drawn towards them, the most common technique to identifying such equilibria is through simulation; however, it is quite possible for the domain of attraction of an equilibrium to be small enough that simulation is unlikely to find it, yet large enough to cause occasional problems.
In this joint work with Mohamed Zaki & Mark Greenstreet, we strung together a collection of public software from the formal verification and numerical analysis communities to rigourously identify and classify all potential DC operating points for surprisingly complex circuit models. Unfortunately, the resulting workflow has proved fragile, and significant effort would be required for reproduction and/or extension. In the second half of the talk I will discuss some tools and techniques that would have significantly improved the reproducibility of the results had they been adopted.
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U. Lorraine /PIMSUBC

Tue 8 Oct 2013, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

Compactness and stability of some nonlinear elliptic equations: glueing of a peak on a static profile

ESB 2012
Tue 8 Oct 2013, 3:30pm4:30pm
Abstract
In this talk, I will review a few issues and results on compactness of equations of scalar curvature type. In particular, I will focus on the difficulty of the degeneracy of the kernel of the solutions to such equations. This is joint work with Jérôme Vétois (Nice).
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UBC

Wed 9 Oct 2013, 3:15pm
SPECIAL
Topology and related seminars
ESB 4133

Groups of PL homeomorphisms

ESB 4133
Wed 9 Oct 2013, 3:15pm4:15pm
Abstract
Let M be a connected, orientable, piecewise linear manifold of dimension n and let B be a closed submanifold of M. Let PL(M, B) be the group of orientation preserving PL homeomorphisms of M which are pointwise fixed on B. The group operation is composition of functions.
In joint work with Danny Calegari we show that if B has codimension zero or one, the group PL(M,B) is locally indicable. This means that every finitelygenerated subgroup has the integers as a quotient. It follows that PL(M,B) is leftorderable and therefore has no elements of finite order.
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UBC

Thu 10 Oct 2013, 3:30pm
Number Theory Seminar
room MATH 126

Eventual stability for rational functions

room MATH 126
Thu 10 Oct 2013, 3:30pm4:30pm
Abstract
Let f be an irreducible polynomial over a number field. Under what conditions is it true that all iterates of f are also irreducible? We call polynomials with this property stable. Eventual stability is the weaker property that the number of factors of the nth iterate of f is bounded uniformly in n. We can extend this definition to rational functions. We conjecture that all rational functions are eventually stable when 0 is not periodic, and show that this is a case for a large class of functions using Newton polygon techniques. (joint with R. Jones)
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George Washington U.

Tue 15 Oct 2013, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

Double bubble and coreshell solutions in an inhibitory ternary system

ESB 2012
Tue 15 Oct 2013, 3:30pm4:30pm
Abstract
We consider a inhibitory ternary system of three constituents, a model motivated by the triblock copolymer theory. The free energy of the system consists of two parts: the interfacial energy coming from the boundaries separating the three constituents, and the longer range interaction energy that functions as an inhibitor to limit micro domain growth. One solution of this system, found by Lu Xie in her PhD thesis, is a coreshell pattern where the first constituent forms the core, the second forms the shell, and the third fills the back ground. Another solution is shown in a joint work with Juncheng Wei: there is a perturbed double bubble that exists as a stable solution of the system. Each bubble is occupied by one constituent. The third constituent fills the complement of the double bubble. This solution has two triple junction points.
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UBC

Tue 15 Oct 2013, 4:00pm
Discrete Math Seminar
ESB 4133

Induction: the gift that keeps on giving

ESB 4133
Tue 15 Oct 2013, 4:00pm5:00pm
Abstract
I would like to report some advances made while on sabbatical in South Carolina working with Lincoln Lu. These are problems of extremal combinatorics in the area of Forbidden Configurations. We first crack an `old chestnut' that had been around since 1990. We use a new inductive approach. We then apply this new induction to a result of Balogh and Bollobas which is a kind of Ramsey Theorem for Forbidden Configurations. Not surprisingly Ramsey Theory shows up.
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UBC

Wed 16 Oct 2013, 3:00pm
Probability Seminar
ESB 2012

SelfInteracting Walk and the Gaussian field (II)

ESB 2012
Wed 16 Oct 2013, 3:00pm4:00pm
Abstract
In the first lecture of this series the square of a Gaussian field was related to the local time of random walk and a Poisson process of random loops. In this lecture I will show how to "get rid" of the loops and end up with a representation for selfinteracting walk as an almost Gaussian integral. This lecture will use the algebra of differential forms, but I will make it selfcontained by reviewing what we need to know about differential forms.
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UBC

Thu 17 Oct 2013, 12:30pm
Graduate Student Seminar
Math 204

Well Approximable Numbers

Math 204
Thu 17 Oct 2013, 12:30pm1:30am
Abstract
I will discuss the size of the set of real numbers x that can be well approximated by rational numbers (in the sense that xp/q < 1/q^s for infinitely many rational numbers p/q) using tools from number theory, harmonic analysis, and probability theory. The talk should be accessible to all math graduate students.
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UBC

Thu 17 Oct 2013, 3:00pm
Topology and related seminars
ESB 4133

The topology of nilpotent representations in reductive groups and their maximal compact subgroups

ESB 4133
Thu 17 Oct 2013, 3:00pm4:00pm
Abstract
I will discuss the topology of the space Hom(N,G) of homomorphisms from a finitely generated group N into a reductive complex linear algebraic group G (e.g. a special linear group). When K is a maximal compact subgroup of G (e.g. the subgroup of special unitary matrices), Hom(N,K) is a subspace of Hom(N,G). Although in general these topological spaces are quite different, I will show that when N is nilpotent there is a strong deformation retraction of Hom(N,G) onto Hom(N,K).
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UBC

Thu 17 Oct 2013, 3:30pm
Number Theory Seminar
room MATH 126

Unlikely intersections for varieties defined over function fields

room MATH 126
Thu 17 Oct 2013, 3:30pm4:30pm
Abstract
We present analogues of the classical conjectures of ManinMumford, Bogomolov and PinkZilber for function fields (of arbitrary characteristic). We also present a function field analogue of the Bounded Height Conjecture (which appears in the study of the PinkZilber Conjecture).
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UBC

Mon 21 Oct 2013, 2:00pm
Mathematical Education
Math 126

The Calculus Concept Inventory

Math 126
Mon 21 Oct 2013, 2:00pm3:00pm
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George Washington University

Mon 21 Oct 2013, 3:00pm
Institute of Applied Mathematics
LSK 460

Growth, inhibition, and geometric structures in selforganizing physical and biological systems

LSK 460
Mon 21 Oct 2013, 3:00pm4:00pm
Abstract
Exquisitely structured patterns arise in many physical and biological systems as orderly outcomes of selforganization principles. Common in these patternforming systems is that a deviation from homogeneity has a strong positive feedback on its further increase. To prevent unlimited increase and spreading, pattern formation requires in addition a longer ranging confinement of the locally selfenhancing process. I will use the OhtaKawasaki diblock copolymer model and the GiererMeinhardt system as examples to demonstrate the roles played by the growth and inhibition properties, and show how they lead to a nonlocal geometric problem for which structures like discs, rings, balls, ovals, tori, etc, arise as solutions.
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UBC

Wed 23 Oct 2013, 3:00pm
Probability Seminar
ESB 2012

A Phase Transition for Measurevalued SIR Epidemics

ESB 2012
Wed 23 Oct 2013, 3:00pm4:00pm
Abstract
We study a scaling limit of the long range SIR epidemic model in which infected individuals cannot be reinfected. The limit, which exists in up to 3 dimensions, has been studied by Lalley and Zheng and is reminiscent of a onedimensional model proposed by Durrett and studied by Mueller and Tribe. It is a measurevalued process similar to superBrownian motion with drift \theta but with an additional killing term proportional to its local time. We show there is a nontrivial phase transition in \theta for dimension 2 and 3, above which the process survives and below which it goes extinct, and prove that in one dimension there is always extinction. Moreover we show that in any dimension there is always extinction on compact sets. The results suggest some conjectures for long range bond percolation. This is joint work with Steve Lalley and Xinghua Zheng.
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Wed 23 Oct 2013, 3:00pm
Mathematical Education
Math 126

Applying Bloom's Taxonomy to the Calculus Classroom

Math 126
Wed 23 Oct 2013, 3:00pm10:00am
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Applied Mathematics Department, University of Washington

Thu 24 Oct 2013, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133

Finite Volume Methods for Hyperbolic PDEs and the Clawpack Software

ESB 4133
Thu 24 Oct 2013, 12:30pm2:00pm
Abstract
I will give a brief introduction to highresolution (shockcapturing) finite volume methods for hyperbolic PDEs that model wave propagation. These methods are based on solving Riemann problems at cell interfaces and using wave limiters to develop secondorder accurate methods that avoid nonphysical oscillations around discontinuities in the solution. Riemann solver methods are also well adapted to problems of wave propagation in heterogeneous media with discontinuities in the material parameters.
The Clawpack (Conservation Laws Package) software package implements these algorithms along with adaptive mesh refinement. I will give an overview of some of the recent developments in this project, including extensions to higherorder methods and to supercomputers through the PyClaw project. More about this open source software can be found at www.clawpack.org.
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Indiana University

Thu 24 Oct 2013, 3:00pm
Topology and related seminars
ESB 4133

Any finite group acts freely and homologically trivially on a product of spheres

ESB 4133
Thu 24 Oct 2013, 3:00pm4:00pm
Abstract
Theorem: If a finite group G acts freely and homologically trivially on a finite complex K which has the homotopy type of a product of kspheres, then G acts freely and homologically trivially on a product of (k+1)spheres.
Corollary: Any group acts freely and homologically trivially on a product of spheres.
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SFU

Thu 24 Oct 2013, 3:30pm
Number Theory Seminar
room ASB 10908 (IRMACS  SFU)*

Counting dihedral function fields

room ASB 10908 (IRMACS  SFU)*
Thu 24 Oct 2013, 3:30pm4:30pm
Abstract
In the early 70's Davenport and Heilbronn derived the leading term in the asymptotic formula for the number of cubic number fields with bounded discriminant. However, as algorithmic data became available, a large "gap" became evident between the actual number of cubic number fields of small discriminant and the asymptotic prediction. We will discuss this and the analogous situation in the function field setting. We will present methods for constructing and tabulating dihedral function fields (which includes nonGalois cubics) and prove the existence of a similar "gap" for cubic function fields of small discriminant and the leading term of the corresponding asymptotic.
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Indiana University Bloomington

Fri 25 Oct 2013, 3:00pm
Department Colloquium
MATX 1100

Rigidity

MATX 1100
Fri 25 Oct 2013, 3:00pm4:00pm
Abstract
An object is rigid with respect to two properties if whenever it satisfies one property it automatically satisfies a stronger property. Many examples of rigidity will be given, focusing on examples involving group theory, topology, and geometry. The best example of topological rigidity is the Borel Conjecture, which states that two closed aspherical manifolds with isomorphic fundamental groups are homeomorphic. The talk will conclude with a discussion of the equivariant rigidity problem and recent joint work with Connolly and Khan.
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UBC

Mon 28 Oct 2013, 2:00pm
Mathematical Education
Math 126

Applying Bloom's Taxonomy to the Calculus Classroom

Math 126
Mon 28 Oct 2013, 2:00pm3:00pm
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Department of Electrical Engineering, Stanford University

Mon 28 Oct 2013, 3:00pm
SPECIAL
Institute of Applied Mathematics
LSK 460

Two Tales of Information and Estimation (IAMPIMS Distinguished Colloquium)

LSK 460
Mon 28 Oct 2013, 3:00pm4:00pm
Abstract
The first part will consist of a tour through a sparse sample of the information theory literature  both classical and recent  on relations between information and estimation. Beyond aesthetic value, these relations underlie some of the main tools in Shannon theory. They also give considerable insight into and a quantitative understanding of several estimation theoretic objects, such as the costs of causality and of mismatch, as well as the performance and structure of minimax estimators. Further, they enable the transfer of analytic tools and algorithmic knowhow from one domain to another. Examples will be given to illustrate these points. The second will begin by introducing Directed Information and making the case for caring about how to estimate it. I will then describe some approaches to this estimation problem which are based on universal sequential probability assignments. The estimators inherit much of the algorithmic simplicity and convergence properties of the latter. I will conclude by showcasing some experimental results illustrating the efficacy of directed information estimation as a tool for detecting and measuring causality.
Much of the talk is based on collaborations with Rami Atar, Jiantao Jiao, YoungHan Kim, Albert No, Haim Permuter, Kartik Venkat, and Lei Zhao.
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Maryland

Mon 28 Oct 2013, 3:10pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)

Stable pair theory of K3 fibrations

ESB 4127 (host: UBC)
Mon 28 Oct 2013, 3:10pm4:10pm
Abstract
I will talk about my joint work with A. Sheshmani and Y. Toda. We study the stable pair theory of K3 fibrations over curves with possibly nodal fibers. We express the stable pair invariants of the fiberwise irreducible classes in terms of the famous KawaiYoshioka formula for the Euler characteristics of moduli space of stable pairs on K3 surfaces and NoetherLefschetz numbers of the fibration. In the case that the K3 fibration is a projective CalabiYau threefold, by means of wallcrossing techniques, we write the stable pair invariants of the fiberwise curve classes in terms of the generalized DonaldsonThomas invariants of 2dimensional Gieseker semistable sheaves supported on the fibers.
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UBC

Tue 29 Oct 2013, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

On Fractional Minimal Surfaces

ESB 2012
Tue 29 Oct 2013, 3:30pm4:30pm
Abstract
We consider fractional minimal surfaces introduced by Caffarelli, Roquejoffre and Savin (2009). Up to now the only examples of fractional minimal surfaces are hyperplanes. In this talk, we first prove the existence of the analog of fractional Lawson's minimal cones and establish their stability/instability in low dimensions. In particular we find that there are stable fractional minimal cones in dimension 7, in contrast with the case of classical minimal surfaces. Then we prove the existence of fractional catenoids and fractional CostaHoffmanMeeks surfaces. Interestingly the interaction of planes in fractional minimal surfaces is governed by an nonlinear elliptic equation with negative power which arises in the study of MEMS. (Joint work with J. Davila and M. del Pino.)
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ENS

Wed 30 Oct 2013, 3:10pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UAlberta)

Integrable PDEs on semisimple Lie algebras

ESB 4127 (host: UAlberta)
Wed 30 Oct 2013, 3:10pm4:10pm
Abstract
Motivated partly by previous work on the zero curvature representation (ZCR) of completely integrable chiral models and partly by the underlying Hamiltonian structures of ideal complex fluids, we derive systems of partial differential equations, called Gstrands, that admit a quadratic zero curvature representation for an arbitrary real semisimple Lie algebra. Using the root space decomposition, the Gstrand equations can be formulated explicitly for the compact real form and the normal real form of
any semisimple Lie algebra. We present several particular examples, including the exceptional group G_2. We also determine the general form of Hamilton's principles and Hamiltonians for these systems, and analyze the linear stability of their equilibrium solutions.
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Emory University

Thu 31 Oct 2013, 3:30pm
Number Theory Seminar
room MATH 126

Quadratic forms and Galois cohomology

room MATH 126
Thu 31 Oct 2013, 3:30pm4:20pm
Abstract
The discriminant and the Clifford invariant are classical invariants for quadratic forms. Milnor conjecture proposes successive higher invariants for quadratic forms and asserts that these invariants determine the isomorphism class of a quadratic form up to planes. Milnor conjecture is a theorem due to Voevodsky, Orlov and Vishik. We explain how the Galois cohomology invariants can be used to study the question whether a quadratic form in sufficiently many variables represents zero nontrivially over function fields of curves over number fields and local fields.
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Note for Attendees
Pizza and pop will be provided during the break between the talks.