Algebraic Geometry

Algebraic Stacks and the Inertia Operator

Submitted by root on Fri, 2015-03-27 17:25
Speaker: 
Kai Behrend
Date: 
Fri, Mar 27, 2015
Location: 
PIMS, University of British Columbia
Conference: 
CRM-Fields-PIMS Prize Lecture
Abstract: 

Motivated by subtle questions in Donaldson-Thomas theory, we study the spectrum of the inertia operator on the Grothendieck module of algebraic stacks. We hope to give an idea of what this statement means.  Along the way, we encounter some elementary, but apparently new, questions about finite groups and matrix groups.  Prerequisites for this talk: a little linear algebra, and a little group theory. 

 

Embedded Video: 
File Algebraic Stacks and the Inertia Operator - Kai Behrend
Class: 
Scientific
Subject: 
Mathematics
Algebraic Geometry

Algebraic groups and maximal tori

Submitted by root on Mon, 2015-03-23 16:01
Speaker: 
Vladimir Chernousov
Date: 
Mon, Mar 23, 2015
Location: 
PIMS, University of British Columbia
Conference: 
Geometry and Physics Seminar
Abstract: 

We will survey recent developments dealing with characterization of absolutely almost simple algebraic groups having the same isomorphism/isogeny classes of maximal tori over the field of definition. These questions arose in the analysis of weakly commensurable Zariski-dense subgroups. While there are definitive  results over number fields (which we will briefly review), the  theory over general fields is only emerging. We will formulate the  existing conjectures, outline their potential applications, and  report on recent progress. Joint work with A. Rapinchuk and  I. Rapinchuk.

Embedded Video: 
File Algebraic groups and maximal tori
Class: 
Scientific
Subject: 
Mathematics
Algebraic Geometry

The Work of Misha Gromov, a Truly Original Thinker

Speaker: 
Jean-Pierre Bourguignon
Date: 
Fri, Apr 5, 2013
Location: 
PIMS, University of British Columbia
Conference: 
Special Lecture
Abstract: 

The work of Misha Gromov has revolutionized geometry in many respects, but at the same time introduced a geometric point of view in many questions. His impact is very broad and one can say without exaggeration that many fields are not the same after the introduction of Gromov's ideas.I will try and explain several avenues that Gromov has been pursuing, stressing the changes in points of view that he brought in non-technical terms.Here is a list of topics that the lecture will touch:

  1. The h-Principle
  2. Distance and Riemannian Geometry
  3. Group Theory and Negative Curvature
  4. Symplectic Geometry
  5. A wealth of Geometric Invariants
  6. Interface with other Sciences
  7. Conceptualizing Concept Creation
Class: 
Scientific
Subject: 
Algebraic Geometry
Differential Geometry and Geometric Analysis

Ben Green: the Sylvester-Gallai Theorem

These pictures are of a lecture given by Ben Green on the Sylvester-Gallai Theorem

Conference: 
PIMS/UBC Distinguished Colloquium
Date: 
Thu, Sep 6, 2012
Class: 
Scientific
Subject: 
Mathematics
Algebraic Geometry

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

Expanders, Group Theory, Arithmetic Geometry, Cryptography and Much More

Speaker: 
Eyal Goran
Date: 
Tue, Apr 6, 2010
Location: 
University of Calgary, Calgary, Canada
Abstract: 

This is a lecture given on the occasion of the launch of the PIMS CRG in "L-functions and Number Theory".

The theory of expander graphs is undergoing intensive development. It finds more and more applications to diverse areas of mathematics. In this talk, aimed at a general audience, I will introduce the concept of expander graphs and discuss some interesting connections to arithmetic geometry, group theory and cryptography, including some very recent breakthroughs.

Class: 
Scientific
Subject: 
Mathematics
Algebraic Geometry
Group Theory
Number Theory

Frozen Boundaries and Log Fronts

Speaker: 
Andrei Okounkov
Date: 
Mon, Oct 16, 2006
Location: 
University of British Columbia, Vancouver, Canada
Conference: 
PIMS 10th Anniversary Lectures
Abstract: 

In this talk, based on joint work with Richard Kenyon and Grisha Mikhalkin, Andrei Okounkov discusses a binary operation on plane curves which

  1. generalizes classical duality for plane curves and
  2. arises naturally in probabilistic context,

namely as a facet boundary in certain random surface models.

Class: 
Scientific
Subject: 
Algebraic Geometry

Hyperplane Arrangements and Applications

Some photos from the Hyperplane Arrangements and Applications conference which took place at UBC Vancouver, August 8-12. This conference was held in honour of Hiroaki Terao.

Conference: 
Hyperplane Arrangements and Applications
Date: 
Mon, Aug 8, 2011
Class: 
Scientific
Subject: 
Algebraic Geometry
Combinatorics
Algebra
Topology

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