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 Events
Yale University
Mon 29 May 2017, 10:30am SPECIAL
Hugh Dempster Pavillion Room 110
The Laplacian Matrices of Graphs: Algorithms and Applications
Hugh Dempster Pavillion Room 110
Mon 29 May 2017, 10:30am-11:30am

Details

The Laplacian matrices of graphs arise in many fields, including Machine
Learning, Computer Vision, Optimization, Computational Science, and of
course Network Analysis.  We will explain what these matrices are and why
they appear in so many applications.

We then survey recent ideas that allow us to solve systems of linear
equations in Laplacian matrices in nearly linear time, emphasizing the
utility of graph sparsification---the approximation of a graph by a sparser
one---and a recent algorithm of Kyng and Sachdeva that uses random sampling
to accelerate Gaussian Elimination.

Note for Attendees

Note location at the Hugh Dempster Pavillion.
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Yale University
Mon 29 May 2017, 1:00pm SPECIAL
Department Colloquium
Math Annex 1100
Niven Lecture: Using physical metaphors to understanding networks.
Math Annex 1100
Mon 29 May 2017, 1:00pm-2:00pm

Abstract

Networks describe how things are connected, and are ubiquitous in science and society.  Networks can be very concrete, like road networks  connecting cities or networks of wires connecting computers.  They can represent more abstract connections such as friendship on Facebook.  Networks are widely used to model connections between things that have no real connections. For example, Biologists try to understand how cells work by studying networks connecting proteins that interact with each other, and Economists try to understand markets by studying networks connecting institutions that trade with each other.

Questions we ask about a network include "which components of the network are the most important?", "how well do things like information, cars, or disease spread though the network?", and "does the network have a governing structure?".

I will explain how mathematicians address these questions by modeling networks as physical objects, imagining that the connections are springs, electrical resistors, or pipes that carry fluid, and analyzing the resulting systems.

About the Niven Lectures: Ivan Niven was a famous number theorist and expositor; his textbooks have won numerous awards and have been translated into many languages.  They are widely used to this day. Niven was born in Vancouver in 1915, earned his Bachelor's and Master's degrees at UBC in 1934 and 1936 and his Ph.D. at the University of Chicago in 1938. He was a faculty member at the University of Oregon since 1947 until his retirement in 1982. The annual Niven Lecture, held at UBC since 2005, is funded in part through a generous bequest from Ivan and Betty Niven to the UBC Mathematics Department.

Note for Attendees


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Ailyn Stötzner
Faculty of Mathematics, TU Chemnitz
Tue 30 May 2017, 12:30pm
ESB 4133 (PIMS Lounge)
Optimal Control of Thermoviscoplasticity
ESB 4133 (PIMS Lounge)
Tue 30 May 2017, 12:30pm-1:30pm

Details

Elastoplastic deformations play a tremendous role in industrial forming. Many of these processes happen at non-isothermal conditions. Therefore, the optimization of such problems is of interest not only mathematically but also for applications.

In this talk we will present the analysis of the existence of a global solution of an optimal control problem governed by a thermovisco(elasto)plastic model. We will point out the difficulties arising from the nonlinear coupling of the heat equation with the mechanical part of the model. Finally, we will discuss first numerical results.

The talk is based on joint work with Roland Herzog and Christian Meyer.
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