Mathematics

The Lasso: A Brief Review and a New Significance Test

Speaker: 
Rob Tibshirani
Date: 
Thu, Apr 10, 2014
Location: 
PIMS, University of British Columbia
Conference: 
Constance van Eeden Invited Speaker, UBC Statistics Department
Abstract: 

Tibshirani will review the lasso method and show an example of its utility in cancer diagnosis via mass spectometry. He will then consider testing the significance of the terms in a fitted regression, fit via the lasso. He will present a novel test statistic for this problem and show that it has a simple asymptotic null distribution. This work builds on the least angle regression approach for fitting the lasso, and the notion of degrees of freedom for adaptive models (Efron 1986) and for the lasso (Efron et. al 2004, Zou et al 2007). He will give examples of this procedure, discuss extensions to generalized linear models and the Cox model, and describe an R language package for its computation.


This work is joint with Richard Lockhart (Simon Fraser University), Jonathan Taylor (Stanford) and Ryan Tibshirani (Carnegie Mellon).

Oceans and Multiplicative Ergodic Theorems

Speaker: 
Anthony Quas
Date: 
Tue, Mar 25, 2014
Location: 
Calgary Place Tower (Shell)
Conference: 
Shell Lunchbox Lectures
Abstract: 

In many physical processes, one is interested in mixing and obstructions to mixing: warm air currents mixing with cold air; pollutant dispersal etc. Analogous questions arise in pure mathematics in dynamical systems and Markov chains. In this talk, I will describe the relationship between obstructions to mixing and eigenvectors of transition operators; in particular I will focus on recent work on the non-stationary case: when the Markov chain or dynamical system is non-homogeneous, or when the physical process is driven by external factors.

I will illustrate my talk with analysis of and data from ocean mixing.

The Emerging Roles and Computational Challenges of Stochasticity in Biological Systems

Speaker: 
Linda Petzold
Date: 
Fri, Mar 28, 2014
Location: 
PIMS, University of British Columbia
Conference: 
PIMS/UBC Distinguished Colloquium
Abstract: 

In recent years it has become increasingly clear that stochasticity plays an important role in many biological processes. Examples include bistable genetic switches, noise enhanced robustness of oscillations, and fluctuation enhanced sensitivity or “stochastic focusing". Numerous cellular systems rely on spatial stochastic noise for robust performance. We examine the need for stochastic models, report on the state of the art of algorithms and software for modeling and simulation of stochastic biochemical systems, and identify some computational challenges.

Finite Simple Groups and Applications

Speaker: 
Robert Guralnick
Date: 
Fri, Mar 14, 2014
Location: 
PIMS, University of British Columbia
Conference: 
PIMS/UBC Distinguished Colloquium
Abstract: 

The classification of finite simple groups is of fundamental importance in mathematics. It is also one of the longest and most complicated proofs in mathematics.

 

We will very briefly discuss the result and a bit of history and then explain how it can and has been used to solve problems in many areas. We will end with mentioning some specific and perhaps surprising consequences in various fields.

Sparse - Dense Phenomena

Speaker: 
Jaroslav Nesetril
Date: 
Fri, Feb 28, 2014
Location: 
PIMS, University of British Columbia
Conference: 
PIMS/UBC Distinguished Colloquium
Abstract: 

The dichotomy between sparse and dense structures is one of the profound, yet fuzzy, features of contemporary mathematics and computer science. We present a framework for this phenomenon, which equivalently defines sparsity and density of structures in many different yet equivalent forms, including effective decomposition properties. This has several applications to model theory, algorithm design and, more recently, to structural limits.

Test HTML5

Speaker: 
Ian Allison
Date: 
Fri, Jan 31, 2014
Location: 
PIMS, University of British Columbia
Abstract: 

HTML 5 test

Explicit isogenies and endomorphisms of low-genus Jacobians: theory and applications

Author: 
Benjamin Smith
Date: 
Wed, Jun 19, 2013 - Fri, Jun 21, 2013
Location: 
PIMS, University of Calgary
Conference: 
Workshop on Curves and Applications
Abstract: 

Explicit isogenies and endomorphisms of low-genus Jacobians: theory and applications

Notes: 

The state-of-the-art in hyperelliptic curve cryptography

Author: 
Craig Costello
Date: 
Wed, Jun 19, 2013 - Fri, Jun 21, 2013
Location: 
PIMS, University of Calgary
Conference: 
Workshop on Curves and Applications
Abstract: 

The state-of-the-art in hyperelliptic curve cryptography

Notes: 

Splitting of Abelian varieties

Author: 
V. Kumar Murty
Date: 
Wed, Jun 19, 2013 - Fri, Jun 21, 2013
Location: 
PIMS, University of Calgary
Conference: 
Workshop on Curves and Applications
Abstract: 

Splitting of Abelian varieties

Notes: 
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