Mathematics

How Does Google Google?

Speaker:

Margot Gerritsen

Date:

Thu, Jan 17, 2013

Location:

PIMS, University of Calgary

Conference:

Mathematics of Planet Earth 2013

Abstract:

Abstract: We all Google. You may even have found this talk by Googling. What you may not know is that behind the Google's and other search engines is beautiful and elegant mathematics. In this talk, I will try to explain the workings of page ranking and search engines using only rusty calculus.

Bio: Dr. Margot Gerritsen is the Director of the Institute for Computational and Mathematical Engineering at Stanford University. She is also the chair of the SIAM Activity group in Geoscience, the co-director and founder of the Stanford Center of Excellence for Computational Algorithms in Digital Stewardship, and the director of Stanford Yacht Research. She has been appointed to several prestigious positions, including Magne Espedal Professorship at Bergen University, Aldo Leopold Fellow, Faculty Research Fellow at the Clayman Institute and she is also a Stanford Fellow. She is the editor of the Journal of Small Craft Technology and an associate editor of Transport in Porous Media. We are delighted to have Dr. Gerritsen participate in the Mathematics of Planet Earth series.

Class:

Scientific

Subject:

Mathematics

Data Structures and Algorithmic Databases

Computer Science

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A Computational Mathematician Combusts

Speaker:

Margot Gerritsen

Date:

Fri, Jan 18, 2013

Location:

PIMS, University of Calgary

Conference:

Mathematics of Planet Earth 2013

Abstract:

Large scale production of very heavy oil is gaining momentum because of the decline of easy to produce reservoirs, the increasing oil demand and subsequent rising oil price, which makes such resources more economical. Considering the pressure on the oil market and our still very heavy dependence on oil, this move to heavy oil production seems inevitable. Typically, heavy oil reservoirs are stimulated thermally. Injecting steam that is generated at the surface is not always viable or desirable. An alternative technique for production is In-Situ Combution (ISC) where a steam drive is generated in the reservoir itself. In this process, (enriched) air is injected in the reservoir. After ignition a combustion front develops in-situ that burns a small percentage of the oil in place and slowly moves through the reservoir producing steam along the way. A side benefit of this process is that the heat thus generated often cracks the oil into heavy, undesirable components (the "guck") that stay behind in the reservoir and lighter, more valuable components that can be brought up to the surface. Performance prediction of ISC projects is rather tricky and poses many computational challenges. In this talk I'll discuss our work in ISC simulation, which is centered around the design of upscaling methods for kinetics and critical reservoir heterogeneities supported by laboratory experimentation.

Class:

Subject:

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Recent Results on Bootstrap Percolation

Speaker:

Béla Bollobás

Date:

Fri, Feb 15, 2013 to Sat, Feb 16, 2013

Location:

PIMS, University of British Columbia

Conference:

PIMS/UBC Distinguished Colloquium

Abstract:

Bootstrap percolation, one of the simplest cellular automata, can be viewed as an oversimplified model of the spread of an infection on a graph. In the past three decades, much work has been done on bootstrap percolation on finite grids of a given dimension in which the initially infected set A is obtained by selecting its vertices at random, with the same probability p, independently of all other choices. The focus has been on the critical probability, the value of p at which the probability of percolation (eventual full infection) is 1/2.

The first half of my talk will be a review of some of the fundamental results concerning critical probabilities proved by Aizenman, Lebowitz, Schonman, Cerf, Cirillo, Manzo, Holroyd and others, and by Balogh, Morris, Duminil-Copin and myself. The second half will about about the very recent results I have obtained with Holmgren, Smith, Uzzell and Balister on the time a random initial set takes to percolate.

Class:

Scientific

Subject:

Mathematics

Discrete Mathematics