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 Events
Philippe Castillon
Montpellier / PIMS-UBC
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, 3:30pm-4:30pm

Abstract

Harmonic manifolds are those Riemannian manifolds whose harmonic functions satisfy the mean-value 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 Schur-positivity among connected skew shapes
ESB 4133
Tue 1 Oct 2013, 4:00pm-5:00pm

Abstract

The Schur-positivity 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 Schur-positivity 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
Self-avoiding walk in four dimensions (I)
ESB 2012
Wed 2 Oct 2013, 3:00pm-4:00pm

Abstract

I will review connections, including the Dynkin isomorphism, between the Gaussian free fi eld on a lattice and local time of random walk. These connections give useful representations for walks with self-interactions.
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IPMU
Wed 2 Oct 2013, 3:10pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UAlberta)
On the extended W-algebra of type sl_2 at positive rational level
ESB 4127 (host: UAlberta)
Wed 2 Oct 2013, 3:10pm-4:10pm

Abstract

The extended W-algebra 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 W-algebra of type sl_2 at positive rational level.
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Ali Etrati, PhD Student
Complex Fluids Lab, UBC
Wed 2 Oct 2013, 4:00pm
Fluids Lab Meeting
LSK 203
Guard-Heated Wall Shear Stress Sensors for Turbulent Flows
LSK 203
Wed 2 Oct 2013, 4:00pm-5:00pm

Abstract

This talk presents analysis of the performance of multi-element guard-heated hot-film wall shear stress microsensors for turbulent flows. Previous studies of conventional, single-element sensors show that a significant portion of heat generated in the hot-film 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 guard-heated microsensor designs proposed to overcome the severe deficiencies of the conventional design are investigated. Guard-heaters remove the errors associated with substrate heat conduction, by forcing zero temperature gradient at the edges and bottom face of the hot-film, 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 guard-heated sensors. Our results show, particularly for measurements in low-conductivity fluids such as air, that edge guard-heating needs to be supplemented by a sub-surface guard-heater, to make substrate conduction errors negligible. With this two-plane guard-heating, a strong non-linearity in the standard single-element 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, 12:30pm-2:00pm

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 by-product 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, details-free introduction to the Circle Packing Theorem, its extensions and corollaries.



Note for Attendees

Pizza and pop will be provided during the break between the talks.
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Carlos Dominguez
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, 3:00pm-4:00pm

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, 3:30pm-4:30pm

Abstract

We show how to realize the pro-p-Iwahori-Hecke algebra of SLn as a subalgebra of the pro-p-Iwahori-Hecke algebra of GLn. Using the interplay between these two algebras, we deduce a correspondence between "packets" of Hecke modules and mod-p 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, 3:00pm-4:00pm

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 "sub-Gaussian random frames" and explain why classical quantization methods are bound to be substantially suboptimal. We will then show that by using the so-called sigma-delta quantizers along with reconstruction via ”Sobolev duals”, we can improve the quantization error substantially when we quantize sub-Gaussian frame expansions. Specifically, we prove that using an r-th order sigma-delta 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 root-exponential accuracy.  Finally, we will discuss how these results can be used for constructing effective quantization methods for compressed sensing.

Note for Attendees

Refreshments will be served at 2:45 p.m. in the Math Lounge area, MATH 125.
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Wes Maciejewski
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, 2:00pm-3:00pm

Abstract

 This week we'll discuss Michele Artigue's The Teaching and Learning of Mathematics at the University Level which can be found here: http://homepage.math.uiowa.edu/~wseaman/IMAP%5E2/June2009-EquationSolving/fea-artigueNoticesAMS1999.pdf
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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, 3:00pm-4:00pm

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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Frédéric Robert
U. Lorraine /PIMS-UBC
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, 3:30pm-4:30pm

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, 3:15pm-4:15pm

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 finitely-generated subgroup has the integers as a quotient. It follows that PL(M,B) is left-orderable and therefore has no elements of finite order.
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Alon Levy
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, 3:30pm-4:30pm

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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Xiaofeng Ren
George Washington U.
Tue 15 Oct 2013, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Double bubble and core-shell solutions in an inhibitory ternary system
ESB 2012
Tue 15 Oct 2013, 3:30pm-4:30pm

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 core-shell 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, 4:00pm-5:00pm

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
Self-Interacting Walk and the Gaussian field (II)
ESB 2012
Wed 16 Oct 2013, 3:00pm-4:00pm

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 self-interacting walk as an almost Gaussian integral. This lecture will use the algebra of  differential forms, but I will make it self-contained by reviewing what we need to know about differential forms.
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Kyle Hambrook
UBC
Thu 17 Oct 2013, 12:30pm
Graduate Student Seminar
Math 204
Well Approximable Numbers
Math 204
Thu 17 Oct 2013, 12:30pm-1:30am

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 |x-p/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.

Note for Attendees

Pizza and pop will be provided
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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, 3:00pm-4:00pm

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, 3:30pm-4:30pm

Abstract

We present analogues of the classical conjectures of Manin-Mumford, Bogomolov and Pink-Zilber 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 Pink-Zilber Conjecture).
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Sandra Merchant
UBC
Mon 21 Oct 2013, 2:00pm
Mathematical Education
Math 126
The Calculus Concept Inventory
Math 126
Mon 21 Oct 2013, 2:00pm-3:00pm

Abstract

The article may be found here: http://www.ams.org/notices/201308/rnoti-p1018.pdf
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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 self-organizing physical and biological systems
LSK 460
Mon 21 Oct 2013, 3:00pm-4:00pm

Abstract

Exquisitely structured patterns arise in many physical and biological systems as orderly outcomes of self-organization principles. Common in these pattern-forming 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 self-enhancing process. I will use the Ohta-Kawasaki diblock copolymer model and the Gierer-Meinhardt 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 Measure-valued SIR Epidemics
ESB 2012
Wed 23 Oct 2013, 3:00pm-4:00pm

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 one-dimensional model proposed by Durrett and studied by Mueller and Tribe.  It is a measure-valued process similar to super-Brownian motion with drift \theta but with an additional killing term proportional to its local time. We show there is a non-trivial 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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Chia Ying Lee
Wed 23 Oct 2013, 3:00pm
Mathematical Education
Math 126
Applying Bloom's Taxonomy to the Calculus Classroom
Math 126
Wed 23 Oct 2013, 3:00pm-10:00am

Abstract

Chia will lead a discussion on this paper: http://www.math.ubc.ca/~wes/bloomstaxonomy.pdf
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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, 12:30pm-2:00pm

Abstract

I will give a brief introduction to high-resolution (shock-capturing) 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 second-order accurate methods that avoid non-physical 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 higher-order 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, 3:00pm-4:00pm

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 k-spheres, 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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Colin Weir
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, 3:30pm-4:30pm

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 non-Galois cubics) and prove the existence of a similar "gap" for cubic function fields of small discriminant and the leading term of the corresponding asymptotic. 

Note for Attendees

* People can attend the talk via videoconferencing in room MATH 126 at UBC.
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Indiana University Bloomington
Fri 25 Oct 2013, 3:00pm
Department Colloquium
MATX 1100
Rigidity
MATX 1100
Fri 25 Oct 2013, 3:00pm-4:00pm

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.

Note for Attendees

Refreshments will be served at 2:45 p.m. in MATH 125 lounge prior to the colloquium.
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Chia Ying Lee
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, 2:00pm-3:00pm

Abstract

Chia will lead a discussion on "An Evaluative Calculus Project: Applying Bloom's Taxonomy to the Calculus Classroom", an article that can be found here: http://www.math.ubc.ca/~wes/bloomstaxonomy.pdf
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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 (IAM-PIMS Distinguished Colloquium)
LSK 460
Mon 28 Oct 2013, 3:00pm-4:00pm

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 know-how 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, Young-Han Kim, Albert No, Haim Permuter, Kartik Venkat, and Lei Zhao.

Note for Attendees

Refreshments start 15 minutes before the talk in the IAM Lounge, Room 306 of the LSK building.
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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, 3:10pm-4:10pm

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 Kawai-Yoshioka formula for the Euler characteristics of moduli space of stable pairs on K3 surfaces and Noether-Lefschetz numbers of the fibration. In the case that the K3 fibration is a projective Calabi-Yau threefold, by means of wall-crossing techniques, we write the stable pair invariants of the fiberwise curve classes in terms of the generalized Donaldson-Thomas invariants of 2-dimensional Gieseker semistable sheaves supported on the fibers.
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Jun-Cheng Wei
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, 3:30pm-4:30pm

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 Costa-Hoffman-Meeks 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, 3:10pm-4:10pm

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 G-strands, that admit a quadratic zero curvature representation for an arbitrary real semisimple Lie algebra. Using the root space decomposition, the G-strand 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, 3:30pm-4:20pm

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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