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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Postdoctoral Fellow, Mechanical Engineering Department, UBC

Tue 7 Apr 2015, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)

Residualbased Discretization Error Estimation for Computational Fluid Dynamics

ESB 4133 (PIMS Lounge)
Tue 7 Apr 2015, 12:30pm2:00pm
Abstract
The largest and most difficult numerical approximation error to estimate is discretization error. Residualbased discretization error estimation methods are a category of error estimators that use an estimate of the source of discretization error and information about the specific application to estimate the discretization error using only one grid level. The higherorder terms are truncated from the discretized equations and are the local source of discretization error. The accuracy of the resulting discretization error estimate depends solely on the accuracy of the estimated truncation error. Residualbased methods require only one grid level compared to the more commonly used Richardson extrapolation which requires at least two. Reducing the required number of grid levels reduces computational expense and, since only one grid level is required, can be applied to unstructured grids where multiple quality grid levels are difficult to produce. The two residualbased discretization error estimators of interest are defect correction and error transport equations. The focus of this work is the development, improvement, and evaluation of various truncation error estimation methods considering the accuracy of the truncation error estimate and the resulting discretization error estimates. The minimum requirements for accurate truncation error estimation is specified along with proper treatment for several boundary conditions. The single grid methods require that the continuous operator be modified at the boundary to be consistent with the implemented boundary conditions. The methods are evaluated using various Euler applications. Defect correction showed to be more accurate for areas of larger discretization error; however, the cost was substantial (although cheaper than the primal problem) compared to the cost of solving the ETEs which was essentially free due to the linearization.
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Department of Mathematics, UBC

Thu 9 Apr 2015, 12:30pm
Lunch Series on Teaching & Learning
MATH 126

To the Cloud! Sage Math Cloud as a Cloud Based Learning Management System in MATH 210

MATH 126
Thu 9 Apr 2015, 12:30pm1:30pm
Abstract
Sage Math Cloud (SMC) is an online cloud computing software based on the programming language Sage and founded in 2013. In this seminar, I will discuss using this software package for teaching based on its new 'course' functionality. I will show how easy it is to get set up with SMC and how one can organize a course using this software. In particular, one can easily type in LaTeX, assign and collect assignments, and share lecture notes and demonstrations. I will also show how simple it is to integrate computations into one's lectures, enabling students to make mathematics come alive via computer software. This talk is of particular interest for faculty teaching upper level courses and looking for an intuitive to use learning management system. We will discuss pros and cons of this software, as well as possible integration techniques for other classes.
Pizza and pop will be provided.
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UBC

Thu 9 Apr 2015, 3:30pm
Number Theory Seminar
room MATH 126

Eigenfunction estimate on congruence hyperbolic manifolds

room MATH 126
Thu 9 Apr 2015, 3:30pm4:30pm
Abstract
Understanding the behavior of various L^{p} norms of highenergy eigenstates of the Laplacian on a compact Riemannian manifold is an important and interesting problem lying in the intersection of diverse brunches of mathematics. We will be mainly focusing on the L^{∞} norms and also be discussing on a related problem which is known as Quantum Unique Ergodicity. It is expected that when the manifold has negative sectional curvature and has enough symmetry from underlying congruence subgroup of the isometry group, the L^{∞} norm can be sharpened from the socalled trivial bound. We give a partial result in the case of hyperbolic manifolds of dimension 4 and 5. This is a joint work with my supervisor Lior Silberman.
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UBC

Fri 10 Apr 2015, 3:00pm
Harmonic Analysis Seminar
Math 126 (Note unusual date and time of event)

Weighted Hypergraph Removal Lemma

Math 126 (Note unusual date and time of event)
Fri 10 Apr 2015, 3:00pm4:00pm
Abstract
FurstenbergKatznelson multidimension Szemeredi theorem says that any subsets of Z^d with positive density must contain affine copies of any finite set in Z^d . Green and Tao extended this theorem to P^d where P is the set of primes and d=1, using a pseudorandomness property of primes. Questions of extending GreenTao result to higher dimensions left open for almost 10 years, due to some correlations between its elements. This problem is resolved by three methods in 2013. In this talk, I will describe one of the approaches, by transferring hypergraph regularity and energy increment method to the weighted setting. Then we can use it to prove simplex removal lemma on this weighted hypergraph which would imply multidimensional GreenTao Theorem.
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Department of Applied Mathematics and Theoretical Physics, Cambridge University

Tue 14 Apr 2015, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)

Fast computation of the semiclassical Schrodinger equation

ESB 4133 (PIMS Lounge)
Tue 14 Apr 2015, 12:30pm2:00pm
Abstract
The computation of the semiclassical Schrödinger equation presents a number of difficult challenges because of the presence of high oscillation and the need to respect unitarity. Typical strategy involves a spectral method in space and Strang's splitting in time, but it is of low accuracy and sensitive to high oscillation. In this talk we sketch an alternative strategy, based on highorder symmetric Zassenhaus splittings, combined with spectral collocation, which preserve unitarity and whose accuracy is immune to high oscillation. These splittings, whose analysis requires Liealgebraic techniques, can be implemented with large time steps and allow for an exceedingly affordable computation of underlying exponentials. The talk will be illustrated by the computation of different quantum phenomena.
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UBC

Tue 14 Apr 2015, 1:00pm
Graduate Student Seminar
MATH 126

What is...Machine Learning?

MATH 126
Tue 14 Apr 2015, 1:00pm2:00pm
Abstract
In this gentle introduction to machine learning I will give an overview of the most popular algorithms for supervised and unsupervised learning. You will see that machine learning can be surprisingly simple, yet powerful, while always being mathematically appealing. I will finish by walking us through two example applications using Python's scikitlearn library.
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University of Toronto

Fri 17 Apr 2015, 3:00pm
Department Colloquium
MATX 1100

Rational Points on Elliptic Curves

MATX 1100
Fri 17 Apr 2015, 3:00pm4:30pm
Abstract
The classical problem of Diophantine equations is to solve polynomial equations over the rationals. More generally, we may consider solutions over an extension of the rationals. If the equations define an elliptic curve (or more generally, an Abelian variety), there is more structure. In particular, the set of rational points forms a group which is finitely generated. What happens if we consider the same problem over an infinite extension (or equivalently, over an infinite tower of extensions)? The problem becomes very subtle and is the subject of current research. We shall describe some of the recent results in this area.
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University of Austin

Mon 27 Apr 2015, 2:00pm
SPECIAL
CRG Geometry and Physics Seminar
ESB 2012 (Note that this is not the usual room)

Betti Geometric Langlands

ESB 2012 (Note that this is not the usual room)
Mon 27 Apr 2015, 2:00pm3:00pm
Abstract
The Betti geometric Langlands program is a new physicsinspired variant of the [de Rham] geometric Langlands program, in which the geometry of algebraic curves is replaced by the topology of surfaces. It has close relations to representation theory of quantum groups, Hecke algebras and padic groups. I will describe some features of and progress on this program, following work with David Nadler as well as Adrien Brochier, David Jordan and Anatoly Preygel.
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Scuola Normale Superiore

Mon 27 Apr 2015, 3:30pm
SPECIAL
CRG Geometry and Physics Seminar
ESB 2012 (Note that this is not the usual room)

Cohomological invariants of algebraic stacks (after Robert Pirisi)

ESB 2012 (Note that this is not the usual room)
Mon 27 Apr 2015, 3:30pm4:30pm
Abstract
Galois cohomological invariants for algebraic groups are an arithmetic analogue of characteristic classes in algebraic topology; Totaro and Guillot connected them to unramified étale cohomology and Rost’s higher Chow Groups.
In his PhD thesis, Roberto Pirisi generalizes the theory of Galois cohomological invariants to smooth Artin stacks of finite type over a field, and computes the cohomological invariants for stacks of hyperelliptic curves of even genus. Furthermore he defines Rost’s higher Chow groups for Artin stacks.
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Note for Attendees
Lunch will be provided.