# Mathematics

## Nonlocal equations from various perspectives - lecture 2

Speaker:

Enrico Valdinoci
Date:

Tue, Jun 14, 2016
Location:

PIMS, University of British Columbia
Conference:

PIMS Workshop on Nonlocal Variational Problems and PDEs Abstract:

We would like to give a detailed presentation of some equations which exhibit some nonlocal phenomena. Often, the nonlocal effect is modelled by a diffusive operator which is (in some sense) elliptic and fractional. Natural example arise from probability, geometry, quantum physics, phase transition theory and crystal dislocation dynamics. We will try to discuss some of the mathematical tools that are useful to deal with these problems, explain in detail some of the main motivations, describe some recent results on these topics and list some open problems.

## Nonlocal equations from various perspectives - lecture 1

Speaker:

Enrico Valdinoci
Date:

Mon, Jun 13, 2016
Location:

PIMS, University of British Columbia
Conference:

PIMS Workshop on Nonlocal Variational Problems and PDEs Abstract:

## Operational Research and the Criminal Justice System

Speaker:

Alexander Rutherford
Date:

Wed, Mar 30, 2016
Location:

PIMS, Simon Fraser University
Conference:

Lunchbox Lecture Series Abstract:

The Criminal Justice System is responsible for upholding public safety through the enforcement of laws, the apprehension, prosecution, and judging of suspects, and the administration of community and custodial sentences. It is highly complex, with interactions between police, prosecutors, judges, the court, and correctional services. Effective and efficient administration of justice is important for maintaining public safety.
We present an overview of operational research modelling applied to the Criminal Justice System. Two case studies are considered: a systems dynamics model of the impact of the 2010 impaired driving legislation in British Columbia and a queue network model of the impact of the Truth in Sentencing Act of Canada.

## A glamorous Hollywood star, a renegade composer, and the mathematical development of spread spectrum communications.

Speaker:

Mark Goresky
Date:

Mon, May 30, 2016
Location:

PIMS, University of British Columbia
Conference:

2016 Niven Lecture Abstract:

During World War II Hedy Lamarr, a striking Hollywood actress, together with George Antheil, a radical composer, invented and patented a secret signaling system for the remote control of torpedoes. The ideas in this patent have since developed into one of the ingredients in modern digital wireless communications. The unlikely biography of these two characters, along with some of the more modern developments in wireless communications will be described.

## Bayesian study design for nonlinear systems: an animal disease transmission experiment case study

Speaker:

Rob Deardon
Date:

Tue, May 3, 2016
Location:

PIMS, University of Calgary
Conference:

Lunchbox Lecture Series Abstract:

Experimental design is a branch of statistics focused upon designing experimental studies in a way that maximizes the amount of salient information produced by the experiment. It is a topic which has been well studied in the context of linear systems. However, many physical, biological, economic, financial and engineering systems of interest are inherently non-linear in nature. Experimental design for non-linear models is complicated by the fact that the optimal design depends upon the parameters that we are using the experiment to estimate. A Bayesian, often simulation-based, framework is a natural setting for such design problems. We will illustrate the use of such a framework by considering the design of an animal disease transmission experiment where the underlying goal is to identify some characteristics of the disease dynamics (e.g. a vaccine effect, or the infectious period).

## Multivariable Operator Theory and Dilation Theory

Speaker:

Kenneth R. Davidson
Date:

Tue, Apr 5, 2016
Location:

PIMS, University of Manitoba
Conference:

PIMS-UManitoba Distinguished Lecture Abstract:

This will be a general talk about the role of dilation theory in studying operators on Hilbert space, illustrated in part by some recent work of mine with Raphaël Clouâtre on multivariable operator theory.

## Combinatorial Matrices

Speaker:

Richard A. Brualdi
Date:

Tue, Mar 1, 2016
Location:

PIMS, University of Manitoba
Conference:

PIMS-UManitoba Distinguished Lecture Abstract:

Matrices contain combinatorial information. They may provide alternative representations of combinatorial ideas. Examples include permutation matrices as representations of permutations of a finite set, and adjacency matrices as representations of a finite graph. The linear algebraic properties of these matrices may provide useful combinatorial information, and combinatorial information about a matrix may impact its linear algebraic properties. At the same time, some combinatorial constructs are defined by matrices. A notable example is the alternating sign matrices which arise in a number of ways including from the partial order on permutations called the Bruhat order. In this talk we will explore various connections between combinatorics and matrices, combinatorial matrices.

## Optimal Strategic Sizing of Energy Storage Facilities in Restructured Electricity Markets

Author:

Hamidreza Zareipour

Date:

Wed, Apr 6, 2016

Location:

PIMS, University of Calgary

Conference:

Lunchbox Lecture Series

Abstract:

In this seminar we will discuss a new model for strategic investment model for a merchant energy storage facility. The facility's actions impact market-clearing outcomes, and thus it is a price-maker facility. We consider the uncertainties associated with other generation units offering strategies and future load levels in the proposed model. Thestrategic investment decisions include the sizes of charging device,discharging device, and energy reservoir. The proposed model is astochastic bi-level optimization problem where planning and operation decisions of the energy storage facility are made in the upper level, and market clearing is modeled in the lower level under different operating conditions. To make the proposed model computationally tractable, an iterative solution technique based on Benders¹ decomposition is implemented. This provides a master problem and a set of subproblems for each scenario. Each subproblem is recast as a Mathematical Programs with Equilibrium Constraints (MPEC). Numerical results based on real-lifemarket data from Alberta's electricity market will be provided.

## It’s a Mathematical World

Speaker:

Cristian Rios
Date:

Thu, Apr 16, 2015
Location:

Calgary Place Tower (Shell)
Conference:

Shell Lunchbox Lectures Abstract:

Description:
The “language" of mathematics has been developed since the dawn of humanity to describe and comprehend the surrounding world and its phenomena. Mathematics as a science and a school subject is widely identified with the mechanical rules of algebra or calculus, and with the symbolic writings native to this discipline. In this talk I will attempt to bring a perspective of mathematics as a natural, everyday endeavour, which each one of us lives and performs every day, most of the time without even realizing that we do so. I will present several examples in which the pervasiveness of mathematics in our everyday life will be illustrated, and I will also show some interesting mathematical applications through modelling. This particular feature, that the universe can be modelled "by the use of a minimum of primary concepts and relations” (A. Einstein) is one of the most puzzling properties of our universe. Finally, I will discuss some of these historic reflections on the nature of mathematics and its connection to the “real” world.

## Lang's conjecture and level structures on abelian varieties

Speaker:

Anthony Várilly-Alvarado
Date:

Thu, Apr 7, 2016
Location:

PIMS, Simon Fraser University
Conference:

PIMS CRG in Explicit Methods for Abelian Varieties Abstract:

Before Mazur proved his theorem on the possible torsion groups on elliptic curves over Q, Manin had shown in 1969 that for a fixed number field K and prime p, the p-primary torsion of elliptic curves over K was uniformly bounded. We will explain a result in this direction for more general abelian varieties, subject to Lang's conjecture on rational points on varieties of general type. This is joint work with Dan Abramovich.