UBC

Wed 8 May 2013, 9:30am
SPECIAL
Math 126

Mock Calculus Lecture

Math 126
Wed 8 May 2013, 9:30am10:30am
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UBC

Wed 8 May 2013, 3:00pm
SPECIAL
Math 126

Contributions to Pedagogy

Math 126
Wed 8 May 2013, 3:00pm4:00pm
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University of Victoria

Thu 9 May 2013, 9:00am
SPECIAL
MATH 126

Mock Calculus Lecture

MATH 126
Thu 9 May 2013, 9:00am10:00am
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University of Victoria

Thu 9 May 2013, 1:00pm
MATH 126

Contributions to Pedagogy

MATH 126
Thu 9 May 2013, 1:00pm2:00pm
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SFU Physics

Thu 9 May 2013, 2:00pm
Mathematical Biology Seminar
ESB 2012

Linking the DNA strand asymmetry to the spatiotemporal replication program

ESB 2012
Thu 9 May 2013, 2:00pm3:00pm
Abstract
The replication process is known to be strand asymmetric: it requires the opening of the DNA double helix and acts differently on the two DNA strands, which generates different mutational patterns and in turn different nucleotide compositions on the two DNA strands (compositional asymmetry). During my PhD thesis, we modeled the spatiotemporal program of DNA replication and its impact on the DNA sequence evolution. I will show how this model helps understand the relationship between compositional asymmetry and replication in eukaryotes and explains the patterns of compositional asymmetry observed in the human genome. During the last part of my talk, I will present our ongoing project: inferring the spatiotemporal replication program from experimental replication kinetics data.
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University of Washington Bothell

Fri 10 May 2013, 11:00am
SPECIAL
Math 126

Mock Calculus Lecture

Math 126
Fri 10 May 2013, 11:00am12:00pm
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University of Washington Bothell

Fri 10 May 2013, 3:00pm
SPECIAL
Math 126

Contributions to Pedagogy

Math 126
Fri 10 May 2013, 3:00pm4:00pm
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Thomas Erneux, Fonds National de la Recherche Scientifique (Belgium)
International Visiting Research Scholar, Peter Wall Institute, UBC

Fri 10 May 2013, 3:00pm
SPECIAL
Math Annex Room 1102

Public Talk: Singular perturbation methods for delay differential equations exhibiting a large delay

Math Annex Room 1102
Fri 10 May 2013, 3:00pm4:00pm
Details
Delay differential equation problems appear in all areas of science and engineering and are mostly investigated numerically. Analytical studies using asymptotic techniques are rare but are needed because some of the
dynamical phenomena caused by the delay have never been seen before. We review the method of multiple time scales for an oscillator described by a delay differential equation and admitting a Hopf bifurcation. We show that if the delay is large, the slow time amplitude equation is itself a delay differential equation. A specific example of a delayed optoelectronic oscillator is examined and a secondary bifurcation to quasiperiodic oscillations is predicted. Analytical and experimental bifurcation diagrams are compared quantitatively. Periodic squarewave oscillations of scalar delay differential equations exhibiting a large delay have been rigorously studied in the 1980’s. They result from a Hopf bifurcation and the plateau lengths are nearly equal to one delay. The total period is close to two delays. Recent experimental observations of delayed optoelectronic oscillators and lasers
subject to delayed feedbacks show more complex forms of squarewave oscillations. The squarewaves may become asymmetric with two plateaus of different lengths and a total period of one delay or they may exhibit bursting oscillations on one of the two plateaus. Two specific examples motivated by experiments are investigated.
Dr. Thomas Erneux is currently a Research Director by the Fonds National de la Recherche Scientifique (Belgium) and he teaches asymptotic methods for nonlinear problems in physics and chemistry. In 2009, he received the Prix de La Recherche mention Sciences de la Communication – parrainage CNRS for his work on the applications of delay differential equations. He received his PhD in Chemistry in 1979 in the group of Ilya Prigogine (Nobel Prize 1977) at the Université Libre de Bruxelles (ULB). He then went to the U.S. to study applied mathematical techniques (197980 Caltech, 1980 Northwestern University). After his military duty at the Royal Military School in Brussels (1981), he came back to Northwestern University now as a professor (19821993). He worked on bifurcation problems mostly motivated by chemical instabilities and by laser stability problems. In 1993, he joined the newly formed Nonlinear Optics group at ULB. His current interests concentrate on nonlinear dynamical problems, and, in particular, on delay differential equation problems in all areas of science and engineering.
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Okanagan College

Mon 13 May 2013, 10:45am
MATH 126

Mock Calculus Lecture

MATH 126
Mon 13 May 2013, 10:45am11:30am
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Okanagan College

Mon 13 May 2013, 2:30pm
MATH 126

Contributions to Pedagogy Lecture

MATH 126
Mon 13 May 2013, 2:30pm3:30pm
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IMPA

Wed 15 May 2013, 3:00pm
Probability Seminar
ESB 2012

Soft local times and decoupling of random interlacements

ESB 2012
Wed 15 May 2013, 3:00pm4:00pm
Abstract
During this talk we will introduce a method, called 'soft local times', to couple the trace of two Markov chains running on the same state space. This method is general and can give nontrivial bounds for several models of interest. We then give a particularly useful example of application involving the model of random interlacements on Z^d. For that, we will first introduce this process in detail and show
how the method of soft local times can help decoupling the random interlacements in two separated sets. An interesting consequence of such result is the exponential decay of the connectivity function for d > 3.
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Tue 21 May 2013, 12:30pm
SPECIAL
Graduate Student Center, Room 203

Doctoral Exam

Graduate Student Center, Room 203
Tue 21 May 2013, 12:30pm3:00pm
Details
ABSTRACT
We investigate some problems on the uniqueness of mean curvature flow and the
existence of minimal surfaces, by geometric and analytic methods. A summary of the
main results is as follows.
(1) The special Lagrangian submanifolds form a very important class of minimal
submanifolds, which can be constructed via the method of mean curvature flow. In
the graphical setting, the potential function for the Lagrangian mean curvature flow
satisfies a fully nonlinear parabolic equation.
We prove a uniqueness result for unbounded solutions for this equation without any
growth condition, via the method of viscosity solutions: for any continuous initial
function in , there exists a unique continuous viscosity solution in ×[o,∞). We
also study the CauchyDirichlet problem for this equation.
(2) We prove an existence result for free boundary minimal surfaces of general
topological type. Let N be a complete, homogeneously regular Riemannian manifold
of dim(N) not less than 3 and let M be a compact submanifold of N. Let Σ be a
compact Riemann surface with boundary. A branched immersion u: (Σ, ∂Σ) →(N,M) is
a minimal surface with free boundary in M if u(Σ) has zero mean curvature and u(Σ) is
orthogonal to M along u(∂Σ). We prove that
• if Σ is not a disk, then there exists a minimal immersion of Σ with free boundary in M
that minimizes area in any given conjugacy class of a map in Cº(Σ,∂Σ;N,M) that is
incompressible;
• the kernel of the induced map of the inclusion M → N admits a generating set such
that each member is freely homotopic to the boundary of an area minimizing disk that
solves the free boundary problem.
(3) Under certain nonnegativity assumptions on the curvature of a 3manifold N and
convexity assumptions on the boundary M=∂N, we investigate controlling topology for
index1 or stable free boundary minimal surfaces:
• We derive bounds on the genus, number of boundary components;
• We prove a rigidity result;
• We give area estimates in term of the scalar curvature of N.
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Thomas Erneux, Fonds National de la Recherche Scientifique (Belgium)
International Visiting Research Scholar, Peter Wall Institute, UBC

Tue 21 May 2013, 3:00pm
Mathematical Biology Seminar
Henry Angus Bldg. Room 241

Delay: Friend or Enemy?

Henry Angus Bldg. Room 241
Tue 21 May 2013, 3:00pm4:00pm
Abstract
Delay problems appear in all scientific disciplines from biology to physics. As soon as there is a mechanical, physiological, or human control, there is a delay because time is needed to observe and react. If the delay is too important, oscillatory responses appear. But a properly used delayed feedback may also stabilize an unstable system. Our understanding of the positive and negative effects of a delay has progressed to the point that oscillatory outputs are used in applications. The presentation will review a series of problems and illustrate the different expectations of the researcher depending on his background.
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University of Alberta

Thu 23 May 2013, 3:00pm
SPECIAL
Algebraic Geometry Seminar
4127 ESB (PIMS Video conference room)

An Archimedean Height Pairing on the Equivalence Relation Defining Bloch's Higher Algebraic Cycle Groups

4127 ESB (PIMS Video conference room)
Thu 23 May 2013, 3:00pm4:00pm
Abstract
The existence of a height pairing on the equivalence relation defining Bloch's higher cycle groups is a surprising consequence of some recent joint work by myself and Xi Chen on a nontrivial K_1class on a selfproduct of a general K3 surface. I will explain how this pairing comes about.
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University of Arkansas (Fayetteville), NSF

Fri 24 May 2013, 11:00am
SPECIAL
Harmonic Analysis Seminar
MATX 1118

Higherorder analogues of exterior derivative

MATX 1118
Fri 24 May 2013, 11:00am12:00pm
Abstract
I will discuss some earlier joint work with E. M. Stein concerning divcurl type inequalities
for the exterior derivative operator and its adjoint in Euclidean space.?I will then present various
higherorder generalizations of the notion of exterior derivative, and discuss some recent divcurl
type estimates ?for such operators (part of this work is joint with A. Raich).
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Ecole Polytechnique

Mon 27 May 2013, 11:30am
SPECIAL
Department Colloquium
Math Annex Bldg, (MATX) Room 1100

Niven Lecture: Fluids and optimal transport: from Euler to Kantorovich

Math Annex Bldg, (MATX) Room 1100
Mon 27 May 2013, 11:30am12:30pm
Abstract
In 1757, Euler presented to the Berlin Academy of Sciences the basic equations of fluid mechanics. As pointed out by V.I. Arnold in 1966, the Euler equations for incompressible fluids have a very simple geometric interpretation that combines the concept of geodesics and the concept of volume preserving maps. The later concept is very simple and nothing but a continuous version of the discrete and more elementary concept of permutation. Conversely, the Euler equations have a natural discrete counterpart in terms of permutation and combinatorial optimization, which establishes a direct link with the mathematical theory of "optimal transport". This theory, that goes back to Monge 1781 and has been renewed by Kantorovich since 1942, is nowadays a flourishing field with many applications, in natural sciences, economics, differential geometry and analysis.
About the Niven Lectures: Ivan Niven was a famous number theorist and expositor; his textbooks won numerous awards, have been translated into many languages and are widely used to this day. Niven was born in Vancouver in 1915, earned his Bachelor's and Master's degrees at UBC in 1934 and 1936 and his Ph.D. at the University of Chicago in 1938. He was a faculty member at the University of Oregon from 1947 until his retirement in 1982. The annual Niven Lecture Series, held at UBC since 2005, is funded in part through a generous bequest from Ivan and Betty Niven to the UBC Mathematics Department.
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Mon 27 May 2013, 12:30pm
SPECIAL
MATH 125

Math Graduation Reception

MATH 125
Mon 27 May 2013, 12:30pm2:00pm
Details
The Niven Lecture (11:30a.m.12:30p.m.) precedes the Graduation Reception.
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Ecole Polytechnique, France

Tue 28 May 2013, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
Earth Sciences Bldg ESB, Room 2012 (PIMS building)

Diffusion of knots and magnetic relaxation

Earth Sciences Bldg ESB, Room 2012 (PIMS building)
Tue 28 May 2013, 3:30pm4:30pm
Abstract
Motivated by seeking stationary solutions to the Euler equations with prescribed vortex topology, H.K. Moffatt has described in the 80s a diffusion process, called "magnetic relaxation", for 3D divergencefree vector fields that (formally) preserves the knot structure of their integral lines. (See also the book by V.I. Arnold and B. Khesin.)
The magnetic relaxation equation is a highly degenerate parabolic PDE which admits as equilibrium points all stationary solutions of the Euler equations. Combining ideas from P.L. Lions for the Euler equations and AmbrosioGigliSavar\'e for the scalar heat equation, we provide a concept of "dissipative solutions" that enforces first the "weakstrong" uniqueness principle in any space dimensions and, second, the existence of global solutions at least in two space dimensions.
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Note for Attendees
The Seminar will be preceded by refreshments at PIMS, ESB 4th floor.