Mathematics Dept.
  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.
hide
Mon 29 May 2017, 11:15am SPECIAL
MATH 125
Mathematics Grad Reception
MATH 125
Mon 29 May 2017, 11:15am-12:45pm

Details

This is a lunch followed by the awards presentation.
hide
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.

hide
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.
hide
Ph.D. Candidate: Benjamin Wallace
Mathematics
Fri 2 Jun 2017, 12:30pm SPECIAL
Room 207, Anthropology and Sociology Bldg. UBC
Examination: Renormalization Group Analysis of Self-Interacting Walks and Spin Systems
Room 207, Anthropology and Sociology Bldg. UBC
Fri 2 Jun 2017, 12:30pm-2:30pm

Details

ABSTRACT
The central concern of this thesis is the study of critical behaviour in models of statistical physics in the upper-critical dimension. We study a generalized n-component lattice |φ|4 model and a model of weakly self-avoiding walk with nearest-neighbour contact self-attraction on the Euclidean lattice Zd. By utilizing a supersymmetric integral representation involving boson and fermion fields, the two models are studied in a unified manner.
Our main result, which is contingent on a small coupling hypothesis, identifies the precise leading-order asymptotics of the two-point function, susceptibility, and finite-order correlation length of both models in d = 4. In particular, we show that the critical two-point function satisfies mean-field scaling whereas the near-critical susceptibility and finite-order correlation length exhibit logarithmic corrections to mean-field behaviour. The proof employs a renormalisation group method of Bauerschmidt, Brydges, and Slade based on a finite-range covariance decomposition and requires two extensions to this method.
The first extension, which is required for the computation of the finite-order correlation length (even for the ordinary weakly self-avoiding walk and |φ|4 model), is an improvement of the norms used to control the evolution of the renormalisation group. This allows us to obtain improved error estimates in the massive regime of the renormalisation group flow.
The second extension involves the identification of critical parameters for models initialized with a non-zero error coordinate coupled to a marginal/relevant coordinate. This allows us, for example, to realize the two-point function and susceptibility for the walk with self-attraction as a small perturbation of the corresponding quantities without self-attraction, whose asymptotic behaviour was determined by Bauerschmidt, Brydges, and Slade. This establishes a form of universality
hide