## Scientific General Events

Combinatorial structures arising as discrete mathematical models of physical phenomena are increasingly found lurking at the interface of mathematics and other sciences. Such models, while apparently simple, are sufficiently rich to play a key role in our understanding of the underlying phenomena being studied.

Computational Geometry

The PIMS YRC is a unique and important opportunity for young graduate students in mathematics and statistics from PIMS universities to meet their peers and discover the wide range of research currently undertaken in Western Canada and the Pacific Northwest. Participants will have opportunities to build and strengthen personal and professional relationships, develop and improve communication skills, and gain valuable experience in the environment of a scientific conference.

This conference has grown from the collaboration between the universities of Alberta and Calgary into a truly inter-PIMS universities project. The PIMS YRC 2012 will offer: An overview of current mathematical research at PIMS universities, an opportunity to present a short talk in a professional context, a panel discussion on employability in both industry and academia, a chance for graduate students to start building their scientific network, and plenary talks by leading mathematical experts in their fields.Since its inception in 2004 by graduate students at the University of Alberta, the PIMS YRC has been held alternately at the University of Alberta, the University of Calgary, and last year in 2011, the PIMS YRC was hosted for the first time outside of Alberta at the University of British Columbia. The conference has become a well-recognized and popular event; in 2007 the CYRC boasted over 90 participants from 11 different universities and in 2008 welcomed participants from six different provinces from across Canada. The PIMS YRC will continue to gain momentum, respect, and popularity among young researchers in mathematics and statistics.

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.