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 Events
Sunil Chhita
KTH
Wed 4 Jan 2012, 3:00pm
Probability Seminar
WMAX 110
Edge statistics of domino tilings on the Aztec Diamond.
WMAX 110
Wed 4 Jan 2012, 3:00pm-4:00pm

Abstract

Domino tilings on the Aztec Diamond have been extensively studied over the past twenty years.  Tilings of large Aztec diamonds exhibit four frozen regions and an elliptic liquid region.  In this talk, we focus on the interface between the liquid and frozen regions, explaining some of the new behavior we have observed.  This is ongoing work with Benjamin Young and Kurt Johansson.

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UC Berkeley
Fri 6 Jan 2012, 3:00pm
Department Colloquium
MATX 1100
A logician's view of diophantine geometry (PIMS Distinguished Guest Lecture)
MATX 1100
Fri 6 Jan 2012, 3:00pm-4:00pm

Abstract

To a logician diophantine geometry, the study of geometric relations on points of arithmetic origin, is almost a contradiction in terms since geometrical reasoning has long been known to be tame and decidable (from the 1929 work of Tarski on elementary geometry) while by Gödel's incompleteness theorems arithmetic is known to be infected by inherent undecidability.  However, this tension has not prevented geometers and number theorists from investigating a subject they know to be hard but one in which ideas from geometry explain the apparent regularity of the solutions in rational numbers, roots of unity, or other arithmetically interesting to certain geometrically constrained systems of equations.   In many important cases, model theorists can explain or prove such theorems by showing that the structure on the arithmetic points simply reflects the tameness of the class of definable sets in some structure intermediate between algebraic geometry and arithmetic.

With this lecture I will broadly survey the project of applying the model theory of enriched, though still tractable, geometries such as those coming from differential or difference algebra, to number theoretic problems such as those around the conjectures of Mordell-Lang and André-Oort or arising from arithmetic dynamics.
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University of Utah
Mon 9 Jan 2012, 4:00pm SPECIAL
Department Colloquium
MATX 1100
How fast does a polynomial vanish?
MATX 1100
Mon 9 Jan 2012, 4:00pm-5:00pm

Abstract

A way of quantifying is to impose integrability conditions on powers of the polynomial. This leads to the definition of the complex singularity exponent, an analytic invariant of the singularity that appears naturally in several branches of mathematics and has become known in algebraic geometry with the name of log canonical threshold. In this talk I will overview general properties of this invariant and present some applications to the study of algebraic varieties.
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University of Utah
Tue 10 Jan 2012, 3:30pm
Algebraic Groups and Related Structures
MATX 1102
The volume of an isolated singularity.
MATX 1102
Tue 10 Jan 2012, 3:30pm-4:30pm

Abstract

Wahl’s characteristic number is a topological invariant of the link of a normal surface singularity: its behavior under finite morphisms captures information about surface singularities that carry finite non-invertible endomorphisms. In this talk I will discuss how this is in fact a completely general invariant of an isolated normal singularity of any dimension. This fact has implications for instance regarding polarized endomorphisms of projective manifolds. The talk is based on joint work with S. Boucksom and C. Favre.
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UBC
Wed 11 Jan 2012, 3:00pm
Topology and related seminars
WMAX 216 (PIMS)
Ordering knot groups
WMAX 216 (PIMS)
Wed 11 Jan 2012, 3:00pm-4:00pm

Abstract

The "group" a knot in 3-space is by definition the fundamental group of its complement; it is one of the oldest algebraic tools used to study knots. Only recently was it discovered that all knot groups can be endowed with a left-invariant ordering. Some even have two-sided invariant orderings, while others do not. This talk will discuss the current state of the art on this subject, and why it is interesting. It will be accessible to grad students.
 
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ENS Lyon
Wed 11 Jan 2012, 3:00pm
Probability Seminar
WMAX 110
The random pinning model: Harris criterion and disorder relevance
WMAX 110
Wed 11 Jan 2012, 3:00pm-4:00pm

Abstract

The so-called Harris criterion (A. B. Harris '74), is a non-rigorous argument, frequently used in theoretical physics literature to predict whether the critical properties of a statistical mechanics system will be qualitatively modified by a small concentration of impurities ("relevance of disorder"). Giving mathematical bases to this argument is an old challenge in the theory of disordered systems and rigorous results are very scarce. In recent years, the so-called polymer pinning model has proved to be the ideal context to attack this problem. In particular, we have given a rigorous justification of the Harris criterion for this class of models and we have solved a long controversy about the "relevance" of disorder for the pinning model in (1+1) dimensions. I will give a non-technical overview of related results.

Based on joint works with: B. Derrida, G. Giacomin, H. Lacoin.
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Wed 11 Jan 2012, 3:30pm
One Time Event
Matx1102
Matx1102
Wed 11 Jan 2012, 3:30pm-4:30pm

Details

 
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George Bluman
UBC Math
Thu 12 Jan 2012, 2:30pm
Symmetries and Differential Equations Seminar
Math Annex 1118
Some recent developments in symmetries and conservation laws for PDEs: Part IX: Nonlocally related systems
Math Annex 1118
Thu 12 Jan 2012, 2:30pm-3:30pm

Abstract

     Given a PDE system, it will be shown how to construct systematically a tree of nonlocally related systems with the properties that
*a solution of any PDE system within the tree yields, through a specific formula, a solution of any other system in the tree.
*there is not a one-to-one correspondence between two systems in the tree.
     It will be shown that such systems within a tree can arise constructively as follows:
*through conservation laws.
*through symmetries.
*through subsystems.
     As a consequence, one is able to seek systematically nonlocal symmetries and nonlocal conservation laws for a given PDE system.  Many examples will be given including nonlinear wave equations, nonlinear diffusion equations, and gas dynamics equations.  It will be shown that Eulerian and Lagrangian descriptions of continuum mechanics arise systematically as nonlocally related systems in a tree of nonlocally related systems
     The situation is especially interesting in multidimensions where gauge constraints can play a central role.
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University of California - Berkeley
Thu 12 Jan 2012, 3:00pm
Number Theory Seminar
Room WMAX 216 (PIMS - UBC Campus)
p-independent bounds in the positive characteristic Mordell-Lang problem (part 1)
Room WMAX 216 (PIMS - UBC Campus)
Thu 12 Jan 2012, 3:00pm-3:50pm

Abstract

The usual Mordell-Lang conjecture, a theorem of Faltings, asserts that if A is an abelian variety over C, \Gamma < A(C) is a finitely generated subgroup, and X \subseteq A is a closed subvariety, then X(C) \cap \Gamma is a finite union of cosets of subgroups of \Gamma.  If one were to ask instead that A be defined over a field K of positive characteristic, then such a conclusion cannot hold in general as if A were defined over a finite field, F: A \to A were the associate Frobenius morphism, \subseteq A were defined over the same finite field, and P \in Y(K) \cap \Gamma, then { Fn(P): n \in N } \subseteqY(K) \cap \Gamma.  Other anomalous intersections may arise as sums of such orbits. Some years ago, in joint work with Moosa, I showed that these are essentially the only counterexamples to a na&iuml;ve translation of the Mordell-Lang conjecture to semiabelian varieties defined over a finite field.   Our proof which was long but elementary yields bounds which explicitly depend on the characteristic.  In these lectures, I shall explain how to deduce characteristic independent bounds from a differential algebraic argument.

Note for Attendees

Refreshments will be served between the two talks.
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University of California - Berkeley
Thu 12 Jan 2012, 4:10pm
Number Theory Seminar
Room WMAX 216 (PIMS - UBC Campus)
p-independent bounds in the positive characteristic Mordell-Lang problem (part 2)
Room WMAX 216 (PIMS - UBC Campus)
Thu 12 Jan 2012, 4:10pm-5:00pm

Abstract

 
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CNRS and Ecole Normale Supérieure de Lyon
Fri 13 Jan 2012, 3:00pm SPECIAL
Department Colloquium
MATX 1100
Stochastic dynamics of discrete interfaces
MATX 1100
Fri 13 Jan 2012, 3:00pm-4:00pm

Abstract

I will begin from two different motivations: 1) (the mathematical physics motivation) trying to derive a macroscopic, deterministic "mean-curvature-type" evolution for the boundary between two coexisting phases, starting from a microscopic stochastic dynamics and 2) (the computer science motivation) analyzing the running time of Monte Carlo Markov Chain (MCMC) algorithms that sample uniformly among lozenge tilings of a large region of the plane. I will discuss the link between these two problems and try to emphasize their connections with dimer covering problems and with interacting particle systems. Our results include: a) bounds on the disappearence time of droplets for the three-dimensional Ising model at zero temperature b) derivation of mean-curvature evolution for the two-dimensional Ising model at zero temperature and c) (in some situations) "almost-optimal" bounds on the running time of the lozenge tiling MCMC.

Based on joint works with: P. Caputo, H. Lacoin, E. Lubetzky, F. Martinelli, F. Simenhaus, A. Sly.
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Qualifying Exams
Sat 14 Jan 2012, 9:00am SPECIAL
One Time Event
MATH 100
Qualifying Exams
MATH 100
Sat 14 Jan 2012, 9:00am-4:00pm

Details


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Lucien Brush
University of Washington
Mon 16 Jan 2012, 3:00pm
Complex Fluids Seminar / Institute of Applied Mathematics
LSK 301
Dynamics of Metal Foam Films
LSK 301
Mon 16 Jan 2012, 3:00pm-4:00pm

Abstract

Metallic gas-liquid foams are precursors to porous solid materials that are lightweight and useful in transportation, energy, medical and other applications. The crowded gas bubbles in a gas-liquid metal foam are highly unstable, because there is capillary-suction flow of liquid from the thin lamellar regions into the Plateau borders. The liquid drainage leads to lamellar rupture, gas bubble coalescence and rapid foam coarsening, so that successful solidification of a metal foam is not possible without liquid additives such as particles. Our research focuses on the microscale flow and interface evolution of pure liquid foam films, in order to glean knowledge that can be used to improve the processing of bulk metal foam. In this talk, our calculations of the thinning and the onset of instability of foam lamella and of the evolving unstable foam films with Plateau borders in a pure gas-liquid metallic foam will be presented. The linear stability results show that a draining lamella with Plateau borders is more stable than a lamellar film without flow and without Plateau borders. Numerical calculations track film evolution to a time just prior to rupture. The effects of variations in the Plateau border radii of curvature and of different initial conditions on rupture phenomena will be shown.
In practice, gas-liquid metal foams are stabilized against coarsening by the addition of particles. One effect of the addition of particles to thin draining films is the development of an oscillatory structural component of the disjoining pressure. Our research involving the analysis of a model of a particle-laden free film that includes the oscillatory structural component of the disjoining pressure will also be presented. By studying the effect of this component of the disjoining pressure on film dynamics we hope to gain insight into its role as a possible mechanism for foam stabilization by particles, to explain unique behaviors observed in particle-laden films such as stepwise thinning, and to identify potential novel film or foam structures. To date, the results of our analysis show that for certain ranges of film thickness to particle diameter ratios, a uniform film can spontaneously evolve into a multilayered film as a result of the structural oscillatory effect. The results reveal an analogy between the layering behavior of a particle-laden free film and classical first-order phase transformation kinetics observed in multicomponent solutions. A "phase" diagram delineating regions of stable layered and uniform films, constructed on a plot of the ratio of structural oscillatory to van der Waals components of the disjoining pressure versus the ratio of film thickness to particle diameter, will also be discussed.
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UCLA
Mon 16 Jan 2012, 4:00pm SPECIAL
Department Colloquium
MATX 1100
Probabilistic Techniques in Mathematical Phylogenetics
MATX 1100
Mon 16 Jan 2012, 4:00pm-5:00pm

Abstract

Abstract: Recent advances in DNA sequencing technology have led to new
mathematical challenges in the analysis of the massive datasets
produced in current evolutionary studies. In particular, much progress
has been made in the design and analysis of computationally efficient
algorithms for assembling the Tree of Life from present-day molecular
sequences. In the first half of the talk, I will briefly review some
of the mathematical techniques that have led to our current
understanding of large-scale tree-building algorithms. Prior rigorous
results, however, have typically relied on models of molecular
evolution that are too simplistic. In the second half, I will discuss
recent work on the probabilistic modeling and analysis of more complex
settings, including mutation-rate variation across sites,
insertion-deletion events and lateral genetic transfer. No biology
background will be assumed.
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Ricardo Oyarzua
Mathematics Department, UBC
Tue 17 Jan 2012, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
WMAX 110
Mixed finite element methods for the coupling of fluid flow with porous media flow
WMAX 110
Tue 17 Jan 2012, 12:30pm-1:30pm

Abstract

In this talk we a introduce mixed finite element method for the coupling of fluid flow with porous media flow. Flows are governed by the Stokes and Darcy equations, respectively, and the corresponding transmission conditions are given by mass conservation, balance  of normal forces, and the Beavers-Joseph-Saffman law. We consider mixed formulations in both the Stokes domain and the Darcy region, which yields the introduction of the traces of the porous media pressure and the fluid velocity as suitable Lagrange multipliers. Then, considering generic  finite element spaces with some technical conditions, we apply the Babuska-Brezzi theory together with  a classical result on projection methods for Fredholm operators of index zero to show stability, convergence, and a priori error estimates for the associated Galerkin scheme. Finally, we generalize the previous results and introduce a mixed finite element method for the coupling of fluid flow with nonlinear porous media flow.
This is joint work with G.N. Gatica (University of Concepcion) and F.-J. Sayas (University of Delaware).
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UCLA
Tue 17 Jan 2012, 2:30pm SPECIAL
Probability Seminar
WMAX 110
Relating Combinatorial and Variational Distances Between Trees
WMAX 110
Tue 17 Jan 2012, 2:30pm-3:30pm

Abstract

I will describe recent results on a connection between the so-called reconstruction problem on Markov random fields on trees and two important problems in computational evolutionary biology: the inference of ancestral states and the estimation of phylogenies using maximum likelihood. This is joint work with Allan Sly. No biology background will be assumed.
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Sogang University and UBC
Tue 17 Jan 2012, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
WMAX 110
Mathematical analysis of the stationary motion of an incompressible viscous fluid
WMAX 110
Tue 17 Jan 2012, 3:30pm-4:30pm

Abstract


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Columbia University
Wed 18 Jan 2012, 3:00pm SPECIAL
Algebraic Geometry Seminar / Topology and related seminars
WMAX 110 (PIMS)
Flops and about
WMAX 110 (PIMS)
Wed 18 Jan 2012, 3:00pm-4:00pm

Abstract

Stratified flops show up in the birational geometry of symplectic varieties such as moduli spaces of sheaves. Varieties related by such flops are often derived equivalent (meaning that there is an equivalence between their derived categories of coherent sheaves). After recalling a bit about the geometry of flops I will discuss a general method for constructing such equivalences and illustrate with some examples and applications.
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George Bluman
Math UBC
Thu 19 Jan 2012, 2:30pm
Symmetries and Differential Equations Seminar
Math Annex 1118
Some recent developments in symmetries and conservation laws for PDEs. Part X. Nonlocally related systems.
Math Annex 1118
Thu 19 Jan 2012, 2:30pm-3:30pm
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Columbia University
Fri 20 Jan 2012, 3:00pm
Department Colloquium
MATX 1100
The role of sl(2) in algebraic geometry
MATX 1100
Fri 20 Jan 2012, 3:00pm-4:00pm

Abstract

After recalling a few properties of sl(2), we will discover that it acts in a very elementary way via counting points. I will then sketch how this simple example is the starting point of many constructions in algebraic geometry with applications to representation theory and even low dimensional topology.
 
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UBC
Tue 24 Jan 2012, 3:30pm
Algebraic Groups and Related Structures
MATX 1102
A few words on cohomological invariants
MATX 1102
Tue 24 Jan 2012, 3:30pm-4:30pm

Abstract

We introduce the basic ideas in Cohomological invariant theory, with a particular focus on unramified cohomology and on invariants of coxeter groups.
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Stanford
Wed 25 Jan 2012, 3:00pm
Probability Seminar
WMAX 110
Asymptotics of cover times via Gaussian free fields: bounded-degree graphs and general trees
WMAX 110
Wed 25 Jan 2012, 3:00pm-4:00pm

Abstract

We show that on bounded degree graphs and general trees the cover time of the simple random walk is asymptotically equal to the product of the number of edges and the square of the supremum of the Gaussian free field on the graph, assuming that the maximal hitting time is significantly smaller than the cover time. Furthermore, for general trees, we derive exponential concentration for the cover time, which implies that the standard deviation of the cover time is bounded by the geometric mean of the cover time and the maximal hitting time.

In the talk, I will try to explain main steps for the proof of bounded degree graphs, including an application of sprinkling method, a detection argument for Gaussian free field, as well as a reconstruction of the embedded walk from local times which uses a connection with enumeration of Eulerian circuits.

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George Bluman
UBC Math
Thu 26 Jan 2012, 2:30pm
Symmetries and Differential Equations Seminar
Math Annex 1118
Some recent developments in symmetries and conservation laws for PDEs. Part XI. Nonlocally related systems continued.
Math Annex 1118
Thu 26 Jan 2012, 2:30pm-3:20pm

Abstract

More examples of nonlocally related systems and their use to obtain nonlocal symmetries.  Focus on equations of gas dynamics--Eulerian, Lagrangian and other nonlocally related systems and their use to obtain nonlocal symmetries for both Eulerian and Lagrangian descriptions.
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SFU
Thu 26 Jan 2012, 3:00pm
Number Theory Seminar
Room ASB 10900 (IRMACS - SFU Campus)
On small fractional parts
Room ASB 10900 (IRMACS - SFU Campus)
Thu 26 Jan 2012, 3:00pm-3:50pm

Abstract

This is joint work in progress with Alan Haynes and Jeffrey Vaaler. Let A be a finite, nonempty set of positive integers. For x in R/Z, we study Delta(A,x) := min { ||ax|| : a \in A }, where || y || = \min { |y-n| : n \in Z } is the distance from y to the nearest integer. If each element of A is odd, then it is obvious that  Delta(A,1/2)=1/2. However, in this talk, we will show that for most points x in R/Z the value of Delta(A,x) is not much bigger than |A|-1/2.

Note for Attendees

Refreshments will be served between the two talks.
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UBC
Thu 26 Jan 2012, 4:00pm
Mathematical Education
MATH 126
Teaching Seminar
MATH 126
Thu 26 Jan 2012, 4:00pm-5:00pm

Abstract

For this first session, we will have a short overview of the compilation of survey papers "Making the connection: Research and Teaching in Undergraduate Mathematics Education". Following from this, we will decide in which order to discuss the survey papers.

To give you a teaser, the topics covered by these surveys is organized by themes, each of which is then detailed in three to four survey papers. The themes are:
- Foundations for beginning calculus
- Infinity, limits and divisibility
- Proving theorems
- Interacting with students
- Using definitions, examples and technology
- Knowledge, assumptions and problem solving behaviours for teaching
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SFU
Thu 26 Jan 2012, 4:10pm
Number Theory Seminar
Room ASB 10900 (IRMACS - SFU Campus)
On the equation a^3 + b^{3n} = c^2
Room ASB 10900 (IRMACS - SFU Campus)
Thu 26 Jan 2012, 4:10pm-5:00pm

Abstract

I will explain how to apply the modular method to resolve cases of this family of generalized Fermat equations. (joint with M. Bennett, S. Dahmen, S. Yazdani)
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Stanford University
Fri 27 Jan 2012, 3:00pm
Department Colloquium
MATX 1100
Extreme values for random processes of tree structures
MATX 1100
Fri 27 Jan 2012, 3:00pm-4:00pm

Abstract

The main theme of this talk is that studying implicit tree structures of random processes is of significance in understanding their extreme values. I will illustrate this by several examples including cover times for random walks, maxima for two-dimensional discrete Gaussian free fields, and stochastic distance models. Our main results include:
 
(1) An approximation of the cover time on any graph up to a multiplicative constant by the maximum of the Gaussian free field, which yields a deterministic polynomial-time approximation algorithm for the cover time (D.-Lee-Peres 2010); the asymptotics for the cover time on a bounded-degree graph by the maximum of the GFF (D. 2011); a bound on the cover time fluctuations on the 2D lattice (D. 2011).

(2) Exponential and doubly exponential tails for the maximum of the 2DGFF (D. 2011); some results on the extreme process of the 2D GFF (D.-Zeitouni, in preparation).
 
(3) Critical and near-critical behavior for the mean-field stochastic distance model (D. 2011).
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Nike Sun
Stanford
Mon 30 Jan 2012, 3:00pm
Probability Seminar
MATH 126
Potts and independent set models on d-regular graphs
MATH 126
Mon 30 Jan 2012, 3:00pm-4:00pm

Abstract

We consider the ferromagnetic Potts on typical d-regular graphs, and the independent set model on typical bipartite d-regular graphs, with graph size tending to infinity. We show that the replica symmetric (Bethe) prediction applies for all parameter values in these two models. In this talk I will describe some of the proof techniques, which will give an indication of the contrast with the anti-ferromagnetic Potts model and the independent set model at high fugacity on non-bipartite graphs, where the Bethe prediction is known to fail.
This is joint work with Amir Dembo, Andrea Montanari, and Allan Sly.
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University of Illinois at Chicago
Mon 30 Jan 2012, 4:00pm SPECIAL
Department Colloquium
MATX 1100
Pictures and homogeneous spaces
MATX 1100
Mon 30 Jan 2012, 4:00pm-5:00pm

Abstract

Many important problems in representation theory have analogues in geometry. For example, decomposing tensor products of representations of GL(n) into irreducible representations is very  closely tied to the geometry of Grassmannians. Similarly, studying the restriction of a representation of GL(n) to subgroups such as SO(n) or SP(n) has geometric analogues in terms of the geometry of flag varieties. In this talk, I will show you how drawing pictures can help elucidate these problems. I will specifically concentrate on Littlewood-Richardson rules and geometric branching rules. I intend to make the talk accessible to anyone who is willing to be seduced by pictures.
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Christoph Schwarzbach
EOS, UBC
Tue 31 Jan 2012, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
WMAX 110
Finite element based inversion for geo-electromagnetics
WMAX 110
Tue 31 Jan 2012, 12:30pm-1:30pm

Abstract

High contrast in electrical conductivity motivates the investigation of electromagnetic methods in geophysics, for instance, for hydrocarbon and mineral exploration. A straightforward approach to modelling the spatial distribution of this parameter within the earth is the assumption of piecewise constant values, defined on a moderately fine tessellation of the volume under investigation by hexahedra or tetrahedra. We study here the solution of the 3-D forward problem for time-harmonic electromagnetic fields using finite elements, based on the above mentioned tessellation. Furthermore, we seek to reconstruct the spatial distribution of conductivity of an overparameterized model by a regularised output least squares approach. Our model assumption, a piecewise constant coefficient, allows for simplifications of the forward solver which eventually lead to an overall faster imaging algorithm. The model assumption also requires special care when the regularisation operator is derived for unstructured meshes within the finite element framework.
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Costanza Piccolo
UBC
Tue 31 Jan 2012, 12:30pm
Mathematical Education
MATH 126
Lunch series on Teaching and Learning: Effective strategies for integrating Matlab programming skills in a linear algebra course: The new computer labs in Math 152
MATH 126
Tue 31 Jan 2012, 12:30pm-1:30pm

Abstract

In 2009 and 2010 the Math 152 computer labs underwent major changes both in content and structure. In-depth assessments of the effectiveness of the new lab activities showed that learning of basic Matlab skills did occur in the labs and was not due to previous programming experience. More importantly, students who had attended the new labs performed better than the previous year's cohort when tested on basic Matlab programming concepts a few months after the end of the labs. We will discuss in what ways the new lab activities may have contributed to improving student learning and what challenges instructors face when they develop activities that support the learning of Matlab for novice programmers.
 
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University of Illinois at Chicago
Tue 31 Jan 2012, 2:00pm
Algebraic Groups and Related Structures
WMAX 110
The Birational Geometry of the Hilbert Scheme of Points in the Plane
WMAX 110
Tue 31 Jan 2012, 2:00pm-3:00pm

Abstract

The Hilbert scheme of n points in the plane P2[n] is a compactification of n unordered tuples of points in the plane. It is a smooth, irreducible variety of dimension 2n and plays a central role in algebraic geometry, combinatorics, representation theory and mathematical physics. In this talk, I will describe the birational geometry of P2[n]. I will explain how to run the minimal model program on P2[n] and how to interpret the resulting models as moduli spaces of Bridgeland semi-stable objects. This is joint work with Daniele Arcara, Aaron Bertram and Jack Huizenga.
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University of Chicago
Tue 31 Jan 2012, 2:00pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
MATX 1102 The time and location are changed!
Partial regularity for fully nonlinear elliptic PDE.
MATX 1102 The time and location are changed!
Tue 31 Jan 2012, 2:00pm-3:00pm

Abstract

We prove that solutions to a fully nonlinear elliptic equation F(D^2u)=0 are classical outside a set of dimension at most n-epsilon, where n is the dimension and epsilon is a small constant depending on the ellipticity bounds of F and dimension. We do not make any convexity assumption on the equation F, but we assume that it is differentiable. We will also discuss the relationship of the partial regularity result with the question of unique continuation of solutions. This is a joint work with Scott Armstrong and Charles Smart.
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Christina Koch
UBC
Tue 31 Jan 2012, 4:00pm
Discrete Math Seminar
Math 126
Obstacle Numbers of Graphs
Math 126
Tue 31 Jan 2012, 4:00pm-5:00pm

Abstract

This talk presents the concept of obstacle number--a recently defined characteristic of graphs, arising from how a graph can be drawn in the plane with 0, 1, or 2-dimensional "obstacles" blocking the non-edges of the graph.  We will define obstacle number and then present several results, including characterization of graphs with obstacle number 1 for 1 and 2 dimensional obstacles, as well as constructions of graphs with arbitrarily large obstacle number.
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