Mathematics, UBC

Mon 30 Mar 2015, 9:00am
SPECIAL
One Time Event
Room 203, Graduate Student Centre (6371 Crescent Rd), UBC

Doctoral Exam: Twisted Extensions of Fermat's Last Theorem

Room 203, Graduate Student Centre (6371 Crescent Rd), UBC
Mon 30 Mar 2015, 9:00am11:00am
Details
In 2011, Michael Bennett, Florian Luca and Jamie Mulholland showed that the equation involving a twisted sum of cubes has no pairwise coprime nonzero integer solutions for primes excluded from the set S where S is the set of primes q for which there exists an elliptic curve of conductor 18q, 36q, or 72q with at least one nontrivial rational 2torsion point. In this dissertation, I present a solution that extends the result to include a subset of the primes in S; those primes q in S for which all curves with conductor 18q, 36q, or 72q with nontrivial rational 2torsion have discriminants not of the form an integer squared or 3 times an integer squared. Using a similar approach, I will classify certain integer solutions to the equation of a twisted sum of fifth powers which in part generalizes work done from Billerey and Dieulefait in 2009.
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Mon 30 Mar 2015, 1:00pm
Math Education Research Reading
MATX1118

Finnish school system and its implementation in North America

MATX1118
Mon 30 Mar 2015, 1:00pm2:00pm
Abstract
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UBC

Mon 30 Mar 2015, 3:00pm
Harmonic Analysis Seminar
Math 225

On Some Functional Analytic Properties Of Some Algebras Related to the Fourier Algebra

Math 225
Mon 30 Mar 2015, 3:00pm4:00pm
Abstract
Some functional analytic properties related to optimisation, such as the KreinMilman Property and the RadonNikodym Property, for some Banach Algebras related to the Fourier Algebra are investigated.
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Mathematics Manchester

Mon 30 Mar 2015, 3:00pm
SPECIAL
Institute of Applied Mathematics
LSK 460

IAMPIMS Distinguished Colloquium: Modelling plant cell and tissue growth

LSK 460
Mon 30 Mar 2015, 3:00pm4:00pm
Abstract
Plant growth typically occurs through the coordinated anisotropic expansion of plant cells. Growth is regulated by hormones and is driven by high intracellular pressures generated by osmosis. This machinery allows a plant primary root, for example, to penetrate soil in a direction guided by gravity, while seeking out nutrients and avoiding obstacles. I will describe the biomechanical aspects of a computational multiscale model for root gravitropism that incorporates descriptions of cell walls as fibrereinforced viscoelastic polymer networks and adopts upscaling approaches to efficiently describe the growth of multicellular tissues.
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Harvard University

Mon 30 Mar 2015, 3:00pm
CRG Geometry and Physics Seminar
ESB4127

Period integrals and their differential systems

ESB4127
Mon 30 Mar 2015, 3:00pm4:00pm
Abstract
Period integrals are geometrical objects which can be realized as special functions, or sections of certain bundles. Their origin goes back to Euler, Gauss and Legendre in the study of complex algebraic curves. In their modern version, period integrals naturally arise in Hodge theory, and more recently in mathematical physics, and the theory of hypergeometric functions. I will give an overview of a recent program to use differential equations and Dmodule theory to study period integrals. Connections to hypergeometric functions of Gel'fandKapranovZelevinsky (GKZ) will also be considered. We will see that the theory is intimately related to a particular infinite dimensional representation of a reductive Lie algebra, and the topology of certain affine varieties. I will describe how the theory could help calculate period integrals, and offers new insights into the GKZ theory, and mirror symmetry for toric and flag varieties. This talk is based on joint works with S. Bloch, B. Lian, V. Srinivas, ST. Yau, and X. Zhu.
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Mathematics, Bath

Tue 31 Mar 2015, 12:00pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133

Optimal mesh generation for PDEs with applications to meteorology

ESB 4133
Tue 31 Mar 2015, 12:00pm2:00pm
Abstract
When numerically solving a PDE in three dimensions, it is often necessary to generate a mesh on which to discretize the solution. Often this can be expensive to do. However, by using ideas from optimal transport it is possible both to construct a mesh quickly and cheaply, and also to prove that it has the necessary regularity properties to allow an accurate approximation of the solution of the PDE. In this talk I will describe these methods, prove results about their regularity and then apply them to some problems in meteorology.
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Felipe Garcia Ramos Aguilar
Mathematics, UBC

Tue 31 Mar 2015, 12:30pm
SPECIAL
One Time Event
Room 203 of the Graduate Student Centre (6371 Crescent Road), UBC

Doctoral Exam: Randomness and Structure in Dynamical Systems: Different Forms of Sensitivity and Equicontinuity

Room 203 of the Graduate Student Centre (6371 Crescent Road), UBC
Tue 31 Mar 2015, 12:30pm2:30pm
Details
In this thesis we study topological (continuous map on a compact metric space) and measure theoretical (measure preserving map on a probability space) dynamical systems.
Dynamical systems range from chaotic (random) to predictable (high structure). Structure and randomness can be represented with different forms of equicontinuity and sensitivity to initial conditions (sensitivity).
Inspired by the classical dichotomy between sensitivity and equicontinuity we define weak forms of topological and measure theoretical equicontinuity and strong forms of sensitivity for dynamical systems, and we study their relationships with spectral properties and sequence entropy. We also prove results of how measure theoretically equicontinuous cellular automata (a particular class of topological systems with close connections to computer science) behave in the long term.
The work of this thesis answers questions from  B. Scarpellini. Stability properties of flows with pure point spectrum. Journal of the London Mathematical Society, 2(3):451–464, 1982.  F. Blanchard and P. Tisseur. Some properties of cellular automata with equicontinuity points. Annales de l’Institut Henri Poincare (B) Probability and Statistics, 36(5):569 – 582, 2000.
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Williams College

Thu 2 Apr 2015, 3:30pm
Number Theory Seminar
room MATH 126

Characters and their nonresidues

room MATH 126
Thu 2 Apr 2015, 3:30pm4:30pm
Abstract
Understanding the least quadratic nonresidue (mod p) is a classical problem, with a history stretching back to Gauss. The approach which has led to the strongest results uses character sums, objects which are ubiquitous in analytic number theory. I will discuss character sums, their connection to the least nonresidue, and some recent work of myself and Jonathan Bober (University of Bristol) on a promising new approach to the problem.
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Thu 2 Apr 2015, 4:30pm
Symmetries and Differential Equations Seminar
Math 125

Cohomology of nonlocally related potential systems and subsystems

Math 125
Thu 2 Apr 2015, 4:30pm5:30pm
Abstract
In this talk I will discuss the tree construction from cohomological perspective. This is a work in progress and feedback is very much appreciated.
I assume familiarity with potential system and subsystems.
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