## Scientific General Events

The stability of coherent structure and patterns.

Stability plays an essential role in many branches of science and engineering, including several aspects of fluid mechanics, high-speed transmission of information, and feasibility of MHD fusion devices. The objective of the workshop is to give an overview of current state-of-the-art methods for examining stability, as well as to present some widely applicable new techniques. The format will consist of three invited speakers giving a series of lectures at a level aimed at graduate students but useful for researchers from a variety of disciplines, such as mathematics, engineering, biology, etc.

There will be two main courses, given by Omer Angel and Gregory Miermont. There will be a number of invited talks. Participants will have an option of giving a presentation as well.

**Omer Angel**- Interacting particle systemsParticles attempt to follow a simple dynamic (random walk, constant flow, etc) in some space (interval, line, cycle, arbitrary graph). Add a simple interaction between particles, and the behaviour can change completely. The resulting dynamical systems are far more complex than the ingredients suggest. These processes (interchange process, TASEP, sorting networks, etc) have diverse to many topics: growth processes, queuing theory, representation theory, algebraic combinatorics. I will discuss recent progress on and open problems arising from several models of interacting particle systems.

**Gregory Miermont**- Planar MapsThe study of maps, that is of graphs embedded in surfaces, is a popular subject that has implications in many branches of mathematics, the most famous aspects being purely graph-theoretical, such as the four-color theorem. The study of random maps has met an increasing interest in the recent years. This is motivated in particular by problems in theoretical physics, in which random maps serve as discrete models of random continuum surfaces. The probabilistic interpretation of bijective counting methods for maps happen to be particularly fruitful, and relates random maps to other important combinatorial random structures like the continuum random tree and the Brownian snake. This course will survey these aspects and present recent developments in this area.

This is a satellite event to the 2012 Summer Meeting of the Canadian Mathematical Society that will take place from June 2 to 4, and it will continue into that meeting as a Special Session on the same topic.

This workshop will introduce participants to current research topics in the intersection of Algebra and Geometry

The symposium encompasses all aspects of

multiple-valued logic, including but not limited to:- Algebra

and Formal Aspects - ATPG

and SAT - Automatic

Reasoning - Circuit/Device

Implementation - Communication

Systems - Computer

Arithmetic - Data

Mining

- Fuzzy

Systems and Soft Computing - Image

Processing - Logic

Design and Switching Theory - Logic

Programming - Machine

Learning and Robotics - Mathematical

Fuzzy Logic - Nano

Technology

- Philosophical

Aspects - Quantum

Computing - Quantum

Cryptography - Signal

Processing - Spectral

Techniques - Verification

- Algebra
Abstracts for the talks:

1. Toti Daskalapoulos

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Title: Ancient solutions of the Yamabe flow

Abstract: We construct new ancient compact solutions of the Yamabe flow. Our approach involves a parabolic analogue of the gluing method of solutions to the rescaled flow with constant scalar curvature.

2. Eric Bahuaud

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Title: The Yamabe flow of an incomplete edge metric

Abstract: In this talk I will describe recent work to understand the behaviour of the Yamabe flow in a singular setting modeled by an incomplete edge metric. I will discuss the background estimates obtained from the heat kernel, conditions for short-time existence and prospects for long-time existence. This is ongoing work with Boris Vertman.

3. Martin Li

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Title: Minimal Surfaces with Free Boundary and Geometric Applications

Abstract: Minimal surfaces have been a very useful tool in studying 3-manifold topology and geometry since the pioneering work of Schoen-Yau. When the 3-manifold M possess a boundary, it is natural to look at minimal surfaces with free boundary. In this talk, I will first describe a very general existence result for properly embedded minimal surfaces with free boundary. When the 3-manifold satisfies some curvature and boundary convexity assumptions, we show that the space of these minimal surfaces with a fixed topological type is compact in a very strong sense. As a geometric application, we prove a rigidity result for bounded convex domains in R^3 in terms of the area of a minimal surface which realize the "width" of the convex domain. If time permits, I will indicate some potential applications to mean curvature flow in R^3.

3. John Lott

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Title : Collapsing with a lower bound on the curvature operator

Abstract : Cheeger and Gromov characterized bounded curvature collapse in terms of F-structures. I'll describe how some of the Cheeger-Gromov results extend to collapse with just a lower bound on the curvature operator, in terms of fibered F-structures.

4. Jiaping Wang

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Title: Analysis on smooth metric measure spaces and applications

Abstract: We intend to explain some joint work with Ovidiu Munteanu concerning the analysis on smooth manifolds with densities.Applications to the Ricci gradient solitons will also be discussed.

The Alberta Colleges Mathematics Conference presents talks about the teaching issues specific to the colleges and their math course offerings. This is an opportunity to meet with colleagues from Alberta’s post-secondary institutions primarily, discuss teaching, technology, and curriculum, and to share perspectives on experiences and common interests of mathematics in Alberta.

The North/South Dialogue, also sponsored by PIMS, will take place Friday, running concurrently with the Colleges Mathematics Conference. This year we will feature two parallel sessions (program details will follow).

This event will celebrate Dale Rolfsen's 70th birthday.

There will be a special conference dinner.During the last few years, the workshop has facilitated discussions on a variety of topics of interest to college and university faculty. Topics in the past have included connections between automorphic forms and other areas or mathematics, how to find the right job, encouraging and retaining under-represented groups in number theory, grant writing, how to choose the right journal, and balancing a career with a personal life.

Based on the success of previous sessions, we plan to hold discussions again this year.

**Abstract:**Central to Alan Turing's posthumous reputation is his work with British codebreaking during the Second World War. This relationship is not well understood, largely because it stands on the intersection of two technical fields, mathematics and cryptology, the second of which also has been shrouded by secrecy. This lecture will assess this relationship from an historical cryptological perspective. It treats the mathematization and mechanization of cryptology between 1920-50 as international phenomena. It assesses Turing's role in one important phase of this process, British work at Bletchley Park in developing cryptanalytical machines for use against Enigma in 1940-41. It focuses on also his interest in and work with cryptographic machines between 1942-46, and concludes that work with them served as a seed bed for the development of his thinking about computers.

**Cellular reconstitution: Rebuilding biological systems from the bottom-up**Abstract:Understanding the molecular basis of cellular behaviour is a central goal in biology and a critical guide for medical research. Increasing knowledge of the essential proteins in a complex process such as crawling motility raises the tantalizing question: Do we know enough to build it? In vitro reconstitution provides an import tool for identifying the roles of individual molecules, but defining components is not enough. Progress towards reconstitution of micron-scale cellular structures and processes has been limited by the challenges of generating in vitro reconstitutions that capture the spatial organization, physical constraints, and dynamics of living cells. This talk will describe on-going efforts to create functional reconstitutions of cytoskeletal and membrane processes involved in cellular protrusions and membrane transport. The lessons of what works – and what doesn’t – are helping to guide efforts to build biological systems from molecular parts.