Scientific

Hot Topics in Computational Criminology

Conference: 
Hot Topics in Computational Criminology
Date: 
Wed, Sep 19, 2012
Class: 
Scientific
Applied
Subject: 
Applied Mathematics
Social Sciences

Iwahori-Hecke algebras are Gorenstein (part II)

Speaker: 
Peter Schneider
Date: 
Tue, Oct 23, 2012 to Wed, Oct 24, 2012
Location: 
PIMS, University of British Columbia
Conference: 
PIMS Speaker series
Abstract: 

n the local Langlands program the (smooth) representation theoryof p-adic reductive groups G in characteristic zero plays a key role. For any compact open subgroup K of G there is a so called Hecke algebra H(G,K). The representation theory of G is equivalent to the module theories over all these algebras H(G,K). Very important examples of such subgroups K are the Iwahori subgroup and the pro-p Iwahori subgroup. By a theorem of Bernstein the Heckealgebras of these subgroups (and many others) have finite global dimension.

In recent years the same representation theory of G but over an algebraically closed field of characteristic p has become more and more important. But little is known yet. Again one can define analogous Hecke algebras. Their relation to the representation theory of G is still very mysterious. Moreover they are no longer of finite global dimension. In joint work with R. Ollivier we prove that over any field the algebra H(G,K), for K the (pro-p) Iwahori subgroup, is Gorenstein.

Class: 
Scientific
Subject: 
Mathematics
Group Theory

Iwahori-Hecke algebras are Gorenstein (part I)

Speaker: 
Peter Schneider
Date: 
Wed, Oct 17, 2012 to Thu, Oct 18, 2012
Location: 
PIMS, University of British Columbia
Conference: 
PIMS Speaker series
Abstract: 

N.B. Due to problems with our camera, there is some audio distortion on this file and a small portion of the video has been removed.



This lecture is the first of a two part series (part II).

In the local Langlands program the (smooth) representation theory
of p-adic reductive groups G in characteristic zero plays a key role. For any
compact open subgroup K of G there is a so called Hecke algebra H(G,K). The
representation theory of G is equivalent to the module theories over all these
algebras H(G,K). Very important examples of such subgroups K are the Iwahori
subgroup and the pro-p Iwahori subgroup. By a theorem of Bernstein the Hecke
algebras of these subgroups (and many others) have finite global dimension.

In recent years the same representation theory of G but over
an algebraically closed field of characteristic p has become more and more important. But little is known yet. Again one can define analogous Hecke algebras. Their relation to the representation theory of G is still very mysterious. Moreover
they are no longer of finite global dimension. In joint work with R. Ollivier
we prove that over any field the algebra H(G,K), for K the (pro-p) Iwahori
subgroup, is Gorenstein.

Class: 
Scientific
Subject: 
Mathematics
Group Theory

Alan Turing and the Patterns of Life

Speaker: 
Przemysław Prusinkiewicz
Date: 
Tue, Oct 9, 2012 to Wed, Oct 10, 2012
Location: 
PIMS, University of Calgary
Conference: 
Alan Turing Year
Abstract: 

In 1952, Turing published his only paper spanning chemistry and biology: "The chemical basis of morphogenesis". In it, he proposed a hypothetical mechanism for the emergence of complex patterns in chemical reactions, called reaction-diffusion. He also predicted the use of computational models as a tool for understanding patterning. Sixty years later, reaction-diffusion is a key concept in the study of patterns and forms in nature. In particular, it provides a link between molecular genetics and developmental biology. The presentation will review the concept of reaction-diffusion, the tumultuous path towards its acceptance, and its current place in biology.

Class: 
Scientific
Subject: 
Mathematics
Mathematical Biology

Quadratic forms and finite groups

Speaker: 
Eva Bayer
Date: 
Fri, Sep 28, 2012
Location: 
PIMS, University of British Columbia
Conference: 
PIMS/UBC Distinguished Colloquium
Abstract: 

The study of quadratic forms is a classical and important topic of algebra and number theory. A natural example is the trace form of a finite Galois extension. This form has the additional property of being invariant under the Galois group,leading to the notion of "self-dual nornal basis", introduced by Lenstra. The aim of this talk is to give a survey of this area, and to present some recent joint results with Parimala and Serre.

Class: 
Scientific
Subject: 
Mathematics
Group Theory

24th Canadian Conference on Computational Geometry Proceedings

Author: 
Greg Aloupis
David Bremner
Date: 
Wed, Aug 8, 2012
Location: 
Charlottetown, PEI
Conference: 
24th Canadian Conference on Computational Geometry
Abstract: 

This volume contains the official proceedings of the 24th Canadian Conference on Computational Geometry (CCCG’12), held in Charlottetown on August 8-10, 2012. These papers are also available electronically at http://www.cccg.ca and at http://2012.cccg.ca.

We thank the staff at Holland College, and in particular Tina Lesyk, Marsha Doiron and Tracey Campbell, for preparing the conference site.

We are grateful to the Program Committee for agreeing to a rigorous review process. They, and other reviewers, thoroughly examined all submissions and provided excellent feedback. Out of 75 papers submitted, 49 are contained in these proceedings. We thank the authors of all submitted papers, all those who have registered, and in particular Günter Ziegler, Pankaj Agarwal and Joseph Mitchell for presenting plenary lectures.

We also thank Sébastien Collette, who prepared these proceedings, as well as Perouz Taslakian and Narbeh Bedrossian who designed the conference logo.
Last but not least, we are grateful for sponsorship from AARMS, the Mprime Network, PIMS and the Fields Institute. Their financial support has helped us to cover many costs as well as provide significant funding to over 50 students and postdocs, including waivers of their registration fees.

Notes: 
PDF icon e-proceedings.pdf
Class: 
Scientific
Subject: 
Mathematics

2012 IGTC Summit: Prof. Steve Krone (Part II)

Author: 
Prof. Steve Krone
Date: 
Sun, Oct 14, 2012
Location: 
Naramata Centre
Abstract: 

Spontaneous pattern formation in spatial populations with cyclic dynamics

There are many examples in nature where a system goes through a succession of states that are cyclically related. Examples include ecological succession in a forest and SIRS models of epidemics. When such populations are spatially arranged (as are *all* populations to some degree), these cyclic dynamics can sometimes lead to the spontaneous formation of spatial patterns such as spiral waves. We will explore this phenomenon via interacting particle system models and related differential equations.

Notes: 
PDF icon krone_Naramata_cyclic_2012.pdf
Class: 
Scientific
Subject: 
Mathematics
Mathematical Biology

2012 IGTC Summit: Prof. Steve Krone (Part I)

Author: 
Prof. Steve Krone
Date: 
Sat, Oct 13, 2012
Location: 
Naramata Centre
Abstract: 

Individual-based stochastic spatial models and population biology

These talks will provide an introduction to individual-based stochastic spatial models (sometimes called interacting particle systems or stochastic cellular automata). We will proceed from very simple basic models to more elaborate ones, illustrating the ideas with examples of spatial biological population dynamics. We will compare these models and results with analogous differential equations (ODE and PDE) and see how they are connected. Biological topics will include spatial population growth and spread, epidemics, evolution of pathogens, and antibiotic resistance plasmids. Throughout, we will point out situations in which spatial structure can dramatically influence the ecology and evolution of populations.

Notes: 
PDF icon krone_Naramata_symp_Oct2012.pdf
Class: 
Scientific
Subject: 
Mathematics
Mathematical Biology

IGTC 2012 Math Bio Summit

2012 IGTC Summit in Naramata
Lecture notes from Prof. Krone are available at http://www.mathtube.org/date/lecture_notes/2012.

Conference: 
IGTC 2012 Summit
Date: 
Fri, Oct 12, 2012
Class: 
Scientific
Subject: 
Mathematics
Mathematical Biology

On the Sylvester-Gallai Theorem

Speaker: 
Ben Green
Date: 
Wed, Sep 26, 2012
Location: 
PIMS, University of British Columbia
Conference: 
PIMS/UBC Distinguished Colloquium
Abstract: 

The Sylvester-Gallai Theorem states that, given any set P of n points in the plane not all on one line, there is at least one line through precisely two points of P. Such a line is called an ordinary line. How many ordinary lines must there be? The Sylvester-Gallai Theorem says that there must be at least one but, in recent joint work with T. Tao, we have shown that there must be at least n/2 if n is even and at least 3n/4 - C if n is odd, provided that n is sufficiently large. These results are sharp

Photos of this event are also available.

Class: 
Scientific
Subject: 
Mathematics
Algebraic Geometry

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