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 Events
University of Michigan
Thu 3 Jan 2013, 3:30pm SPECIAL
Algebraic Geometry Seminar
ESB 4133
Semiample Bertini Theorems over Finite Fields
ESB 4133
Thu 3 Jan 2013, 3:30pm-4:30pm

Abstract

For a smooth projective variety over a finite field, Poonen’s Bertini Theorem computes the probability that a high degree hypersurface section of that variety will be smooth.  We prove a semiample generalization of Poonen's result, where the probability of smoothness is computed as a product of local probabilities taken over the fibers of a corresponding morphism.  This is joint with Melanie Matchett Wood.

Note for Attendees

ESB 4133 is the library room attached to the PIMS lounge.
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U. Michigan
Fri 4 Jan 2013, 3:00pm
Department Colloquium
MATX 1100
Equations, syzygies, and vector bundles
MATX 1100
Fri 4 Jan 2013, 3:00pm-4:00pm

Abstract

For a system of polynomial equations, it has long been known that the relations (or syzygies) among the polynomials provide geometric information about the corresponding projective variety.  I will describe a collection of new ideas about how to study syzygies,and how these lead to classification results and a duality between syzygies and vector bundles.
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Sat 5 Jan 2013, 9:00am SPECIAL
One Time Event
Math 100
Qualifying Exams (Analysis)
Math 100
Sat 5 Jan 2013, 9:00am-12:00pm

Details

http://www.math.ubc.ca/Grad/QualifyingExams/Analysis_syllabus.pdf
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Sat 5 Jan 2013, 1:00pm SPECIAL
One Time Event
Math 100
Qualifying Exams (Differential Equations)
Math 100
Sat 5 Jan 2013, 1:00pm-4:00pm

Details

http://www.math.ubc.ca/Grad/QualifyingExams/Differential_Equations_syllabus.pdf
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Sat 5 Jan 2013, 1:00pm SPECIAL
One Time Event
Math 100
Qualifying Exams (Algebra)
Math 100
Sat 5 Jan 2013, 1:00pm-4:00pm

Details

http://www.math.ubc.ca/Grad/QualifyingExams/Algebra_syllabus.pdf
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MIT
Mon 7 Jan 2013, 4:00pm SPECIAL
Department Colloquium
MATX 1100
Quantum invariants of plane curve singularities
MATX 1100
Mon 7 Jan 2013, 4:00pm-5:00pm

Abstract

Consider a critical point of a function f(x,y) in two complex variables.  Milnor showed that the number of non-degenerate critical points into which it splits under a general perturbation is encoded by the Alexander polynomial of the link of the singular fibre of f:C^2 --> C passing through the critical point.  

Analogously, one can consider a (k-1)-parameter family of such functions f, and ask: into how many k-nodal curves does the fiber containing a critical point split under a general perturbation?  As we will explain, they are counted by the coefficients of the HOMFLY polynomial of the link. The relation goes through the Hilbert schemes of points, which parameterize subschemes of the singular curve.  

These latter spaces and their generalizations in fact contain contain enough information to recover all the coefficients of the HOMFLY polynomial, and, conjecturally, their cohomologies are the Khovanov-Rozansky homology of the link.
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MIT
Tue 8 Jan 2013, 3:30pm SPECIAL
Algebraic Geometry Seminar
ESB 4133
Special divisors on hyperelliptic curves
ESB 4133
Tue 8 Jan 2013, 3:30pm-4:30pm

Abstract

A divisor on a curve is called "special'' if its linear equivalence class is larger than expected.  On a hyperelliptic curve, all such come from pullbacks of points from the line.  But one can ask subtler questions.  Fix a degree zero divisor Z; consider the space parameterizing divisors D where D and D+Z are both special.  In other words, we wish to study the intersection of the theta divisor with a translate; the main goal is to understand its singularities and its cohomology.

The real motivation comes from number theory.  Consider, in products of the moduli space of elliptic curves, points whose coordinates all correspond to curves with complex multiplication.  The Andre-Oort conjecture controls the Zariski closure of sequences of such points (and in this case is a theorem of Pila) and a rather stronger equidistribution statement was conjectured by Zhang.  The locus introduced above arises naturally in the consideration of a function field analogue of this conjecture.  This talk presents joint work with Jacob Tsimerman.

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UBC
Tue 8 Jan 2013, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012 (in the new PIMS building)
m-Liouville theorems for elliptic PDEs
ESB 2012 (in the new PIMS building)
Tue 8 Jan 2013, 3:30pm-4:30pm

Abstract

De Giorgi in 1978 conjectured that bounded and monotone solutions of the Allen-Cahn equation must be one-dimensional up to dimension eight. This conjecture is known to be true for N=<3 and with extra (natural) assumptions for 4=<N=<8. We state a counterpart of the above conjecture for gradient systems introducing the concept of monotonicity for systems. Then, we prove this conjecture for dimensions up to three and applying a geometric Poincare inequality for stable solutions we show that the gradients of various components of the solutions are parallel. 


On the other hand, we ask under what conditions we can prove solutions of a PDE are m-dimensional for 0=<m=<N-1. This leads us to define the concept of “m-Liouville theorem” for PDEs. The motivation to this definition is the Liouville theorem (or 0-Liouville theorem) that we have seen in elementary analysis stating that bounded harmonic functions on the whole space must be constant (0-dimensional).


This is the main part of my dissertation under the supervision of Nassif Ghoussoub.

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UBC
Wed 9 Jan 2013, 3:10pm
Topology and related seminars
ESB 4127
Holomorphic maps between moduli spaces
ESB 4127
Wed 9 Jan 2013, 3:10pm-4:10pm

Abstract

Consider the moduli space M_{g,s} of Riemann surfaces of genus g with s marked points as an orbifold. In this talk I will determine all (non-constant) holomorphic maps M_{g,s}\to M_{g',s'} if g\ge 6 and g'\le 2g-2. This is joint work with Javier Aramayona.
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Stanford University
Mon 14 Jan 2013, 3:00pm
PIMS Seminars and PDF Colloquiums
LSK Bldg. Room 460 (6356 Agricultural Road, UBC)
How Does Google Google? The Math Behind the Internet
LSK Bldg. Room 460 (6356 Agricultural Road, UBC)
Mon 14 Jan 2013, 3:00pm-4:00pm

Abstract

We all "Google". You may even have found this talk by Googling. What you may not know is that behind Google and others' search engines is beautiful and elegant mathematics.

Margot Gerritsen will explain the workings of page ranking and search engines using only rusty calculus.

Dr. Margot Gerritsen is an Associate Professor and Director, Institute for Computational and Mathematical Engineering at Stanford University. Her research focuses on the design of highly accurate and efficient parallel computational methods to predict the performance of enhanced oil recovery methods with a particular interest in gas injection and in-situ combusion processes. Outside petroleum engineering, she is active in coastal ocean simulation, yacht research and pterosaur flight mechanics, and the design of search algorithms in collaboration witth the Library of Congress and colleagues from the Institute of Computational and Mathematical Engineering.

This is a joint CMS/PIMS/IAM public lecture, part of the Cross Canada Series of Lectures on Math of Planet Earth.
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Patrick LaVictoire
University of Wisconsin, Madison
Mon 14 Jan 2013, 3:00pm
Harmonic Analysis Seminar
Math 126
Convolution Powers as a Fourier Transform Alternative
Math 126
Mon 14 Jan 2013, 3:00pm-4:00pm

Abstract

When studying sequences of convolution operators, the curvature or pseudorandomness of measures are reflected in the Fourier transform. But in cases where the Fourier transform is inconvenient or unavailable, it can be gleaned instead from convolution powers of the measure with itself. I will show how this tactic, pioneered by Fefferman and by Christ, helps to prove some endpoint results for nonstandard ergodic theorems and singular variants of the Lebesgue Differentiation Theorem.

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ETH Zürich
Mon 14 Jan 2013, 3:10pm
Algebraic Geometry Seminar
ESB 2012
Behrend's function is constant on Hilb^n(C^3)
ESB 2012
Mon 14 Jan 2013, 3:10pm-4:10pm

Abstract

By a theorem of Behrend Donaldson-Thomas invariants can be defined interns of a certain constructible function. We will compute this function at all points in the Hilbert scheme of points in three dimensions and see that it is constant. As a corollary we see that this Hilbert scheme of points is generically reduced and its components have the same dimension mod 2. This gives an application of the techniques of BPS state counting to a problem in Algebraic Geometry.
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Stanford University
Tue 15 Jan 2013, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133
A computational mathematician combusts - simulation of in-situ combustion for heavy oil recovery
ESB 4133
Tue 15 Jan 2013, 12:30pm-1:30pm

Abstract

Large-scale production of very heavy oil is gaining momentum. Unfortunately, production of such reservoirs typically leads to large environmental impacts. One promising technique that may mitigate these impacts is in-situ combustion (ISC). In this process, (enriched) air is injected into the reservoir. After ignition a combustion front develops in situ that burns a small percentage of the oil in place and slowly moves through the reservoir producing steam along the way. The steam moves ahead of the front, heats up the oil, makes it runnier and hence easier to produce. A side benefit of this process is that the heat thus generated often cracks the oil into heavy, undesirable components that stay behind in the reservoir and lighter, more valuable components that can be brought up to the surface. In the last few years, my colleagues and I plunged into heavy oil recovery to see if computational mathematics could make a difference in pushing this process over less environmentally friendly processes in the industry. ISC processes are notoriously hard to predict. We developed a workflow involving laboratory experiments, various simulation tools and upscaling methods that increases the confidence of the oil reservoir engineer in ISC. We hope that this will lead to a wider acceptance and use of this technique.

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UBC
Tue 15 Jan 2013, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012 (in the new PIMS building)
A Bernstein theorem for the Willmore equation
ESB 2012 (in the new PIMS building)
Tue 15 Jan 2013, 3:30pm-4:30pm

Abstract

A classical theorem in minimal surface theory says that any entire minimal graph in R^3 is a plane. We ask the same question for the Willmore equation which is of 4th order. We prove that an entire Willmore graph is a plane if its Willmore functional is finite (i.e. if the mean curvature of the graph is square integrable). This is joint work with Tobias Lamm.
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Enrique Torres
Universidad de Guanajuato
Wed 16 Jan 2013, 3:00pm
Topology and related seminars
ESB 4127
Topological Complexity
ESB 4127
Wed 16 Jan 2013, 3:00pm-4:00pm

Abstract

Topological Complexity (TC) of a space is a concept motivated by the motion planning problem in Robotics. This turns out to be a homotopy invariant, closely related to Lusternik-Schnirelmann category (LS-cat). In fact, TC has proved more delicate than LS-cat given its relationship with some difficult problems in Algebraic Topology such as the Immersion Problem for Projective Spaces. 
In this talk we will discuss basic properties and examples of TC. We will also discuss some recent progress on the computation of TC of some homogeneous spaces, and talk about some new techniques to compute TC based on Hopf-like invariants. 
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Josh Zahl
UCLA
Wed 16 Jan 2013, 3:00pm SPECIAL
Harmonic Analysis Seminar
Math 126 (Note unusual date of event)
On the Wolff circular maximal function
Math 126 (Note unusual date of event)
Wed 16 Jan 2013, 3:00pm-4:00pm

Abstract

I will discuss a new proof of the boundedness of the Wolff circular maximal function. This maximal function helps us understand BRK sets---compact subsets of the plane that contain a circle of every radius, and it is also a stepping stone towards understanding the Kakeya problem in three dimensions. This new proof uses some modern ideas from combinatorial geometry, namely the "discrete polynomial partitioning" method developed by Guth and Katz to solve the Erdos distinct distances problem in the plane.
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University of Southern California
Wed 16 Jan 2013, 4:00pm SPECIAL
Department Colloquium
MATH 104
The interplay between algebraic geometry and higher representation theory
MATH 104
Wed 16 Jan 2013, 4:00pm-5:00pm

Abstract

We begin by rediscovering the Lie algebra sl(2) in a very elementary way via counting points on Grassmannians. Natural generalizations of this construction lead to quantum groups and then "higher" representation theory. We illustrate how this theory can be used to understand the original geometry and then discuss various applications such as new constructions of derived equivalences and homological knot invariants.

Note for Attendees

Refreshments will be served in MATH 125 at 3:45 p.m.
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USC
Thu 17 Jan 2013, 3:00pm SPECIAL
Algebraic Geometry Seminar
MATH 126 (previously announced as ESB 4127)
Categorical actions on Hilbert schemes of points of C^2
MATH 126 (previously announced as ESB 4127)
Thu 17 Jan 2013, 3:00pm-4:00pm

Abstract

We define an action of a Heisenberg algebra on categories of coherent sheaves on Hilbert schemes of points of C^2. This lifts the constructions of Nakajima and Grojnowski from cohomology to derived categories. Vertex operator techniques are then used to extend this to an action of sl_infty. We end with applications to knot homology and a discussion of future research directions.
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Columbia University
Thu 17 Jan 2013, 4:00pm
Number Theory Seminar
room MATH 126
Compatibility between Satake and Bernstein-type isomorphisms in characteristic p
room MATH 126
Thu 17 Jan 2013, 4:00pm-5:00pm

Abstract

Let F be a locally compact non archimedean field with residue characteristic p and G the group of F-points of a split connected reductive group. Let k be an algebraically closed field of characteristic p.
 
We are interested in the link between the k-representations of the spherical and affine Hecke algebras associated to G and the smooth k-representations of G.  In particular, the so-called supersingular representations of G (and the corresponding supersingular Hecke modules) are still poorly understood. However, these are the representations which are expected to play a prominent role in a potential mod p local Langlands correspondence for G.
 
In the pro-p Iwahori-Hecke k-algebra H, we define a family of commutative subalgebras, each containing the center of H. We use these subalgebras to do the following: 1. Construct an inverse Satake isomorphism (one can subsequently show that this is the inverse of the Satake isomorphism defined by Herzig). 2. Prove that the center of H contains an affine semigroup algebra which is naturally isomorphic to the spherical Hecke algebra attached to an irreducible smooth k-representation of a given hyperspecial maximal compact subgroup of G. 3. Apply this to study the "supersingular block" of the category of finite length H-modules and relate it to supersingular representations of G.
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Columbia U.
Fri 18 Jan 2013, 3:00pm
Department Colloquium
MATX 1100
Modular representation theory and the mod p Langlands program
MATX 1100
Fri 18 Jan 2013, 3:00pm-4:00pm

Abstract

The representation theory of finite groups is significantly more complicated and deeper if, instead of looking at representations with complex coefficients, we consider modular representations such as, for example, mod p representations of GL_n(F_p).
 
Likewise, the (smooth) mod p representation theory of the p-adic group GL_n(Q_p) is more complicated than its complex representation counterpart. Various subtleties can be illustrated by observing the simpler but still curious behavior of mod p representations of GL_n(F_p).
 
Using GL_n(F_p) a guideline, we will explain what can be said about GL_n(Q_p). More precisely, while trying to avoid number theoretic technicalities, we will describe a few results pointing towards a mod p local Langlands correspondence. While hopeful, we will also sketch some strange phenomena which add to the many mysteries in this field.
 
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UBC
Tue 22 Jan 2013, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012 (in the new PIMS building)
Decoupling DeGiorgi's systems via multi-marginal mass transport
ESB 2012 (in the new PIMS building)
Tue 22 Jan 2013, 3:30pm-4:30pm

Abstract

 We expose and exploit a surprising relationship between elliptic gradient systems of PDEs and a multi-marginal Monge-Kantorovich optimal transport problem.  We show that the notion of an "orientable" elliptic system (Fazly-Ghoussoub) conjectured to imply that stable solutions are essentially 1-dimensional, is equivalent to the definition of a "compatible" cost function (Carlier-Pass), known to imply uniqueness and structural results for optimal measures to certain Monge-Kantorovich problems.  We use this equivalence to show that solutions to these elliptic PDEs, with appropriate monotonicity properties, are related to optimal measures in the Monge-Kantorovich problem.  We also prove a decoupling result for solutions to elliptic PDEs and show that under the orientability condition, the decoupling has additional properties, due to the connection to optimal transport.
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Brendon Rhoades
UCSD
Tue 22 Jan 2013, 4:00pm
Discrete Math Seminar
MATH 126
Parking spaces
MATH 126
Tue 22 Jan 2013, 4:00pm-5:00pm

Abstract

A sequence (a_1, \dots, a_n) of positive integers is a {\it parking function} if its nondecreasing rearrangement (b_1 \leq \dots \leq b_n) satisfies b_i < i+1 for all i. Parking functions were introduced by Konheim and Weiss to study a hashing problem in computer science, but have since received a great deal of attention in algebraic combinatorics. We will define two new objects attached to any (finite, real, irreducible) reflection group which generalize parking functions and deserve to be called parking spaces. We present a conjecture (proved in some cases) which asserts a deep relationship between these constructions. This is joint work with Drew Armstrong at the University of Miami and Vic Reiner at the University of Minnesota.
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ENS Lyon
Wed 23 Jan 2013, 3:00pm
Probability Seminar
ESB 2012
The critical behavior of the two-dimensional random-cluster model
ESB 2012
Wed 23 Jan 2013, 3:00pm-4:00pm

Abstract

The random-cluster model, introduced by Fortuin and Kasteleyn as a way to unify the study of percolation and the Ising and Potts models, provides a tool to extend geometric intuition to the derivation of properties of spin systems. Interest in its two-dimensionalversions has been revived with Smirnov's introduction of the parafermionic observable.

I will present our recent results with Duminil-Copin and Smirnov, focusing more specifically on two of them: the derivation of its critical point, and the study of the asymptotic behavior of its two-point function away from criticality.
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UBC
Wed 23 Jan 2013, 3:00pm
Undergraduate Colloquium
MATH 104
Introduction to Similarity Methods for Partial Differential Equations
MATH 104
Wed 23 Jan 2013, 3:00pm-4:00pm

Abstract

UBC/UMC is the Undergraduate Mathematics Colloquium at UBC.

These talks are for undergraduates interested in mathematics and mathematical research. They are put on by professors, senior graduate students and visitors to the department. Graduate students are also invited to attend.

The first talk will be given by one of our most popular speakers, Professor George Bluman.

Title: Introduction to Similarity Methods for Partial Differential Equations

Abstract:

It will be shown how to find systematically solutions and the conservation laws for PDEs. Most systematic methods are symmetry-based (directly or through extensions). A PDE is a compact way of describing a family of surfaces. The surfaces are the solutions of the PDE. It turns out that one can find symmetries as well as conserved quantities of such a family of surfaces systematically without knowing specific surfaces.  In turn, this allows one to find specific surfaces.

In general, a symmetry of a PDE is any transformation that maps its solutions to other solutions, i.e. a symmetry leaves invariant the family of surfaces that are the solutions of the PDE.  Hence, in principle, any PDE has symmetries.  Problems: How to use symmetries systematically, how to find symmetries systematically, and how to calculate symmetries efficiently for a given PDE, especially a nonlinear PDE.



Related to this talk, the following references are available online through the UBC library.

Bluman and Anco, Symmetry and Integration Methods for Differential Equations, Springer 2002.
Bluman, Cheviakov and Anco, Applications of Symmetry Methods to Partial Differential Equations, Springer 2010.
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University of Geneva
Wed 23 Jan 2013, 4:00pm
Probability Seminar
ESB 2012
On the Gibbs states of the non-critical Potts model on Z^2
ESB 2012
Wed 23 Jan 2013, 4:00pm-5:00pm

Abstract

All Gibbs states of the supercritical q-state Potts model on Z^2 are convex combinations of the q pure phases; in particular, they are all translation invariant. We recently proved this theorem with Hugo Duminil-Copin (Geneva), Dima Ioffe (Haifa) and Yvan Velenik (Geneva). I will explain the basic concepts
underlying this result and present the heuristics of the proof, which consists of considering the model in large finite boxes with arbitrary boundary condition, and proving that the center of the box lies deeply inside a pure phase with high probability. Our estimate of the finite-volume error term is of essentially optimal order, which stems from the Brownian scaling of fluctuating interfaces. The results hold at any supercritical
value of the inverse temperature beta > beta_c(q)=log(1+sqrt(q)).

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Daniel Valesin
UBC
Thu 24 Jan 2013, 2:30pm
Symbolic Dynamics and Ergodic Theory Seminar
Math Annex 1102
A brief introduction to Statistical Mechanics (Part 1)
Math Annex 1102
Thu 24 Jan 2013, 2:30pm-4:00pm

Abstract



We will discuss roughly the first half of Chapter 2 of Mézard-Montanari, which contains an elementary overview of Statistical Mechanics in the context of finite state spaces. We will introduce Boltzmann distributions, partition functions and thermodynamic potentials such as free energy, internal energy and entropy. Some properties of these potentials will be explored, including the fluctuation-dissipation relations. Next, we will have a somewhat heuristic discussion of thermodynamic limits and phase transitions. Finally, we will start studying the Ising model on finite graphs. 
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UBC
Thu 24 Jan 2013, 3:30pm
Number Theory Seminar
room MATH 126
Iwasawa theory for Artin representations
room MATH 126
Thu 24 Jan 2013, 3:30pm-4:30pm

Abstract

I'll give a report on joint work with Greenberg on the Iwasawa theory for modular forms of weight 1.
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ENS Lyon
Fri 25 Jan 2013, 3:00pm
Department Colloquium
MATX 1100
Recent progress in two-dimensional statistical physics
MATX 1100
Fri 25 Jan 2013, 3:00pm-4:00pm

Abstract

 Two-dimensional models of statistical physics have long been studied by physicists, using tools such as quantum and conformal field theories and renormalization groups as well as through explicit computations in integrable cases. On the mathematics front, two objects were introduced over the last decade, shedding new light on their geometry: first, stochastic Loewner evolutions, proved by Schramm to be the unique possible scaling limits of models exhibiting conformal invariance; second, (para)fermionic observables, used by Smirnov to actually prove conformal invariance of several of them. I will present a panorama of these recent advances and some of the most puzzling open questions remaining to be solved.

Note for Attendees

 Refreshments will be served at around 2:30 in the Math lounge. 
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Mathematics, UBC
Tue 29 Jan 2013, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133
A general framework for high accuracy solutions to energy gradient flows from material science models
ESB 4133
Tue 29 Jan 2013, 12:30pm-2:00pm

Abstract

A computational framework is presented for materials science models that come from energy gradient flows that lead to the evolution of structure involving two or more phases. The models are considered in periodic cells and standard Fourier spectral discretization in space is used. Implicit time stepping is used, and the resulting implicit systems are solved iteratively with the preconditioned conjugate gradient method. The dependence of the condition number of the preconditioned system on the size of the time step and the order parameter in the model (that represents the scaled width of transition layers between phases) is investigated. The framework is easily extended to higher order derivative models, higher dimensional settings, and vector problems. Several examples of its application are demonstrated, including a sixth order problem in three dimensions. Higher order time stepping and a GPU implementation is described briefly. A comparison to time-stepping with operator splitting (into convex and concave parts) is done. 
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Annalisa Panati
University du Sud Toulon Var, visiting McGill
Tue 29 Jan 2013, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012 (in the new PIMS building)
Infrared (and ultraviolet) aspects of a model of QFT on a static space time
ESB 2012 (in the new PIMS building)
Tue 29 Jan 2013, 3:30pm-4:30pm

Abstract

We consider the Nelson model with variable coeffcients, which can be seen as a model describing a particle interacting with a scalar field on a static space time. We consider the problem of the existence of the ground state, showing that it depends on the decay rate of the coeffcients at infinity. We also show that it is possible to remove the ultraviolet cutoff, as it is in the flat case. We'll explain some open conjecture. (joint work with C.Gérard, F.Hiroshima, A.Suzuki)
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UBC
Wed 30 Jan 2013, 3:00pm
Probability Seminar
ESB 2012
On chemical distances and shape theorems in percolation models with long-range correlations
ESB 2012
Wed 30 Jan 2013, 3:00pm-4:00pm

Abstract

We provide general conditions on a one parameter family of random infinite subsets of Z^d to contain a unique infinite connected component for which the chemical distances are comparable to the
Euclidean distances, focusing primarily on models with long-range correlations. We also prove a shape theorem for balls in the chemical
distance under such conditions. Our general statements give novel results about the structure of the infinite connected component of the
vacant set of random interlacements and the level sets of the Gaussian free field. As a corollary, we obtain new results about the (chemical)
diameter of the largest connected component in the complement of the trace of the random walk on the torus. Joint work with Alexander Drewitz and Artem Sapozhnikov.
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UBC
Wed 30 Jan 2013, 3:00pm
Topology and related seminars
ESB 4127
Retractions of representation varieties of nilpotent groups
ESB 4127
Wed 30 Jan 2013, 3:00pm-4:00pm

Abstract

Consider the variety \Hom(\Gamma,G) where \Gamma is a finitely generated nilpotent group, and G a semisimple Lie group. I will discuss joint work with Juan Souto on homotopy retractions from this variety to the representation variety in K, a maximal compact subgroup of G.
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Daniel Valesin
UBC
Thu 31 Jan 2013, 2:30pm
Symbolic Dynamics and Ergodic Theory Seminar
Math Annex 1102
A brief introduction to Statistical Mechanics (Part 2)
Math Annex 1102
Thu 31 Jan 2013, 2:30pm-4:00pm

Abstract

We will continue our discussion of Chapter 2 of Mézard-Montanari. We will show the solution of the Ising model on the complete graph (also called the Curie-Weiss model) and discuss the finite-temperature phase transition. Time permitting, we will also briefly discuss spin glasses, by defining the Edwards-Anderson model and presenting some of the difficulties that arise in its study. 

This is a continuation of part 1, the talk given on January 24. 

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UBC
Thu 31 Jan 2013, 3:30pm
Number Theory Seminar
room MATH 126
Norm form equations
room MATH 126
Thu 31 Jan 2013, 3:30pm-4:30pm

Abstract

In this talk, we'll survey the state-of-the-art on this and related topics, including recent techniques for solving such equations in more than two variables.
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