The 2013 SFU Symposium on Mathematics and Computation was a showcase of research in computational mathematics at SFU, UBC, and UVic.

Program Schedule

Date: Wednesday, August 7th, 2013 Location: The IRMACS Centre, Simon Fraser University 

Roberto Armenta

High-Order Finite-Difference Methods for Modelling Electromagnetic Wave Propagation

Finite-difference methods are a popular choice for solving systems of partial differential equations (PDEs) numerically. Throughout my work, I employ finite-difference methods to solve the various systems of PDEs that arise in common electromagnetic problems. One of the most important recent developments in finite-difference methods has been the use of finite-difference approximations with an increasable order of accuracy. The ability to increase the order of accuracy of the employed approximations can considerably improve performance; however, to exploit high-order approximations effectively, it is necessary to clearly understand how to incorporate boundary conditions. This issue, which stands as the biggest barrier to the widespread adoption of high-order methods, will be the subject of the talk.

Robert Bridson

Simulating Smoke without Volumes

In computer graphics, and visual effects in particular, smoke simulation has become a standard tool. Typically it is modeled with incompressible fluid flow on a 3D grid, tracking soot concentration and velocity in the air, and calculating buoyancy and pressure forces to evolve it forward; volume renderers can take the soot concentration as input to produce the final images. However, this doesn't scale very well, particularly to real-time applications like video games where even the volume rendering alone is unacceptably expensive relative to the rest of the application. This calls for a little more mathematical analysis and algorithmic creativity! In many circumstances, we can model the soot concentration as uniformly smoky inside a region sharply bounded by a dynamically evolving surface; vorticity likewise provides a much more efficient representation of the velocity field. Avoiding any use of volume data, we can get to interactive simulation and highly efficient real-time rendering.

Alexandre Bouchard-Côté

Inference algorithms for continuous time Markov chains over large state spaces

Continuous time Markov chains (CTMCs) is a fundamental modeling tool in time series analysis, phylogenetics and many other areas of statistics. In most applications, simplifying assumptions are typically made to reduce the state space of the CTMCs to a finite and typically small collection of objects (in phylogenetics, for example, the four nucleotides). However, new questions and new data types motivate the development of CTMCs over strings, graphs and other countably infinite spaces. In this talk, I will describe some of our recent work on models and algorithms for analyzing CTMCs over countably infinite space. The first part of the talk will be devoted to the Poisson Indel Process, a model for string-valued CTMCs, and the second part, on inference on CTMCs over other countably infinite spaces. I will focus on applications in phylogenetics, but many of the algorithms and models have potential uses in other branches of applied statistics.

Pavol Hell

Combinatorial dichotomy classifications

In classifying the complexity of certain homomorphism problems, it sometimes turns out that it is the presence of a combinatorial obstruction in the target structure that causes a problem to become intractable. I will discuss several recent results of this type, including recent joint work with Egri, Larose, and Rafiey.

Lily Yen

Automation for the generating series of coloured set partitions

The equidistribution of many crossing and nesting statistics exists in several combinatorial objects like matchings, set partitions, permutations, and embedded labelled graphs. The enumeration of such objects according to their crossing or nesting number has been a challenge, often resulting in hard to solve functional equations.  When both nesting and crossing numbers are bounded, the generating series are rational for (arc-)colouredmatchings, set partitions, and permutations shown by Chen and Guo, Marberg, and Yen respective. We describe algorithms implemented in Maple that give the rational generating series for non-crossing, non-nesting, c-coloured set partitions and permutations. The success of the implementation leads to the possibility of automation for more complicated structures and provides new directions of attack for previously unsolved functional equations.

Poster Information

The SFU Mathematics Department invites undergraduate and graduate research students, postdoctoral fellows and faculty members to participate in the 2013 SFU Symposium on Mathematics and Computation Poster Session.

The only requirement is that the poster has mathematics in it. It may be applied, pure, computational or experimental mathematics. If you have already prepared a poster for a presentation at another scientific meeting this year, and you would like to present it to members of the Department, this is an appropriate venue. If you wish to present a computer demo this is also possible.

Prizes

There will be one prize of $200 (winner) and one prize of $100 (runner-up) for the best undergraduate poster, and one prize of $200 (winner) and one prize of $100 (runner-up) for the best graduate poster. Judging will be based on both content and presentation.

Submission Details

Poster titles must be submitted via the online registration form by August 1st, 2013. Presenters are responsible for printing their own poster.

Display Details

The posters will be displayed in the IRMACS atrium. Poster presenters can set up their posters as early as 9:00am on August 7th, 2013. The poster and demo session will take place from 11:15am to 1:15pm. Awards will be made at 4:30pm, followed by a presentation of the winning undergraduate and winning graduate poster.

Details

• A registration fee of $30 per participant will be charged to all participants except invited speakers and invited guests. The registration fee includes the cost of a buffet lunch at IRMACS.
• Students may wish to ask their supervisor to pay for their registration fee.
• The registration fee may be paid by cash or cheque at the registration desk on the day of the event (receipt will be provided at registration) or through an SFU account (journal voucher).
• Participants who need assistance with the payment should contact Paul Tupper. 
• If you are submitting a poster click on "Poster Submissions Details" to reveal the poster form.

Thank you to our Sponsors

	The IRMACS Centre is a unique, interdisciplinary research facility that enables collaborative interaction - intellectually, physically and virtually. IRMACS focuses on facilitating the human interactions that are critical in interdisciplinary research by providing the technologies and technical support to promote effective interactions (computational, networking, human-computer interaction, remote collaboration, and visualization). By removing the traditional boundaries between scientific disciplines and physical boundaries due to distance, IRMACS creates a synergistic environment on an international scale.
	PIMS promotes research in and applications of the mathematical sciences, facilitates the training of highly qualified personnel, enriches public awareness of and education in the mathematical sciences, and creates mathematical partnerships with similar organizations in other countries.
	The Department of Mathematics currently numbers 39 faculty. In a typical semester the ranks of regular faculty are augmented with up to 20 post-doctoral fellows and Visiting Professors. At present the Department has a graduate enrolment around 80. The Department has earned a national and international reputation as one of the most forward-looking and broad-based mathematical sciences departments in Canada. Undergraduate and graduate students thrive in the highly interactive and personalized environment which characterizes the Department and is typical of the unique character of Simon Fraser University. We offer a broad program of training in contemporary Mathematics, but also specialize in various areas for which we are internationally recognized.