Department of Mathematics
2011
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Dr. Omer Angel A video of this lecture
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Random Planar Maps |
A planar map is a planar graph embedded in the plane, considered up to continuous deformations. These objects have been studied extensively in combinatorics, physics (as discrete random surfaces) and more recently probability theory. Much progress has been made in recent years in understanding the typical structure of these objects, and glimpses of a deeper theory are visible, particularly connecting the scaling limit of random planar maps with conformally invariant models of statistical physics. I will survey some results and conjectures concerning these objects, and discuss some recent progress in understanding percolation and random walks on these random graphs. Dr. Omer Angel received his Ph.D. from the Weizmann Institute under the supervision of Itai Benjamini and Oded Schramm. Subsequently he's been a Post-doc at Orsay and at UBC. He also spent two years as an assistant professor at the University of Toronto, before returning to UBC. Event Poster can be found HERE. |
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2010
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Dr. William L. Kath A video of this lecture |
Computational Modeling of Neurons |
| With its approximately 100 billion neurons and 200 trillion connections, the human central nervous system is astoundingly complex. Nevertheless, experimental advances are rapidly revealing new insights about the workings of neurons and the networks in which they are connected. Simultaneously, computational models of neurons have grown swiftly in terms of both their capability and utility. When constrained by experimental data, such models greatly enhance the observations and provide tools to construct new experimentally testable predictions. In this talk I will describe how this two-pronged approach has helped explain some of the function of hippocampal CA1 pyramidal neurons, a group of principal cells in a region of the brain that is important for the formation of new memories. The models and experiments indicate that these relatively large neurons integrate and process their inputs in a two-stage manner, in that they first combine inputs in localized parts of the dendritic tree before making an ultimate determination whether or not to signal downstream neurons with an action potential. Bill Kath is a professor in the Departments of Engineering Sciences and Applied Mathematics & Neurobiology and Physiology. From 2005-2010 he was the Co-Director of the Northwestern Institute on Complex Systems at Northwestern University. His research interests include computational neuroscience, nonlinear optics, linear and nonlinear wave propagation and nonlinear dynamics. He received the NSF Presidential Young Investigator Award in 1985, was elected a Fellow of the Optical Society of America in 2007, and elected a Fellow of the Society for Industrial and Applied Mathematics in 2010. He has over 150 peer reviewed publication and 4 US patents. Event poster can be found HERE |
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2009
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Dr. Mark J. Ablowitz |
Extraordinary Waves:
From Beaches to Lasers |
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