Lorentz Center - DIAMANT meets GQT from 27 Oct 2008 through 31 Oct 2008
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    DIAMANT meets GQT
    from 27 Oct 2008 through 31 Oct 2008

 
Preliminary Program

Preliminary Program

 

 

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Monday October 27th 2008

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09.00 09.55 Coffee/Tea

 

09.55 10.00 Introduction of the Lorentz Center and a few words by the organizers

 

10.00 12.00 Presentation of Problems

12.30 - 13.30 Lunch

13.30 - 17.30 Working on Problems

17.30 Wine and Cheese Party

 

 

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Tuesday October 28th 2008

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Morning: Working on Problems

 

12.30 - 13.30 Lunch

Afternoon: Working on Problems

 

17.00 Intermediate Evaluation of Results

 

 

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Wednesday October 29th 2008

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Morning: Working on Problems; Preparation of Final Presentations

 

12.30 - 13.30 Lunch

 

Afternoon: Working on Problems; Preparation of Final Presentations

 

 

Parallel Program

(for teachers and other participants interested)

 

 

10.00 - 12.30 Workshop wiskunde D-modules

12.30 - 13.30 Lunch

 

14.30 - 17.00 Workshop wiskunde D-modules

17.00 Drinks get together

 

 

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Thursday October 30th 2008

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10.00 - 11.00 Lisa Carbone (Rutgers): Lattices, buildings and Kac-Moody groups

 

Abstract: A Kac-Moody Lie algebra is the most natural generalization to infinite

dimensions of a finite dimensional simple Lie algebra. Kac-Moody groups and algebras

of affine type are known to have wide applications in physical theories and have

concrete mathematical and physical realizations. Hyperbolic Kac-Moody theory

naturally generalizes the theory of finite dimensional and affine Kac-Moody groups and

algebras, and their symmetries in high energy physics have recently been discovered,

though many fundamental questions regarding these structures remain open. In this

talk we discuss a program to study forms of hyperbolic Kac-Moody groups over finite

fields, their lattices and actions on their hyperbolic buildings.

 

11.00 - 12.30 Presentation Results of Working on Problems

12.30 13.30 Lunch

13.30 - 14.00 Bas Spitters (Nijmegen): Geometric aspects of topos approaches to

quantum theory

14.00 14.30 Roel Willems (Nijmegen): Polynomial automorphisms of 3-space over

F_2 viewed as bijections of 3-space of field extensions of F_2

 

14.30 15.00 Coffee/Tea

15.00 15.30 Jorge Plazas (Utrecht): Galois theory meets quantum statistical

Mechanics

 

15.30 - 16.30 Pierre-Emmanuel Caprace (IHES):

Metric spaces of non-positive curvature and their isometry groups

 

Abstract: Non-positively curved metric spaces were introduced by A. D. Alexandrov and

popularised by M. Gromov, and play a prominent role in geometric group theory. They

provide a framework for the development of some form of generalised differential

geometry, whose objects encompass Riemannian manifolds of non-positive sectional

curvature as well as large families of singular spaces including Euclidean buildings and

many other polyhedral complexes. In particular the geometries naturally associated to

the semi-simple Lie groups over both the real and p-adic numbers fit into this context.

The talk will be devoted to an overview of recent results which, on the one hand,

extend classical results on Hadamard manifolds to this broad geometric setting, and,

on the other hand, highlight properties that single out semi-simple groups and their

discrete subgroups.

16.45 Departure by bus for Boat Trip and Conference Dinner (until 22.00)

 

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Friday October 31st 2008

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09.00 10.00 Ravi Vakil (Stanford): Generalizing the cross ratio: The moduli space

of N points on the projective line up to projective equivalence.

 

Abstract: Four ordered points on the projective line, up to projective equivalence, are

classified by the cross ratio, a notion introduced by Cayley. This theory can be

extended to more points, leading to one of the first important examples of an invariant

theory problem, studied by Kempe, Hilbert, and others. Instead of the cross ratio (a

point on the projective line), we get a point in a larger projective space, and the

equations necessarily satisfied by such points exhibit classical combinatorial and

geometric structure. For example, the case of six points is intimately connected to the

outer automorphism of S_6. We extend this picture to an arbitrary number of points,

completely describing the equations of the moduli space. This is joint work with Ben

Howard, John Millson, and Andrew Snowden. This talk is intended for a general

mathematical audience, and much of the talk will be spent discussing the problem, and

an elementary graphical means of understanding it.

 

10.00 - 10.30 Jan Willem de Jong (Utrecht): Graphs and Dirac zeta functions

 

10.30 11.00 Coffee/Tea

11.00 - 11.30 Frank Vallentin (CWI): Fourier analysis, linear programming, and distance avoiding

sets in real n-space

 

11.30 - 12.30 Bert Gerards (CWI): On the Structure of Binary Matroids

 

AbstractI will describe the structure of minor-closed classes of binary matroids. This

result has been obtained recently together with Jim Geelen University of Waterloo,

Ontario) and Geoff Whittle (Victoria University of Wellington, New Zealand).

Many combinatorial optimization problems can be modeled by graphs or matrices.

Algorithms of these problems often rely on the picture we have of such model. For

instance it may help if we know that the graph is planar or if the matrix is totally

unimodular. Such desirable properties are often "minor-closed". This raises

the question if we can test minor-closed properties in polynomial time. Answering this

computational question requires a structural study of the graphs or matrices at hand.

For graphs this has been the Robertson Seymour Graph Minor Project. One of its major

outcomes is that minor-closed graph properties can be verified in polynomial time and

that graphs are well-quasi-ordered by the minor-order. With Jim Geelen and Geoff

Whittle, we carry out the same program for matroids over finite fields. (Matroids abstract

the relevant combinatorial properties of matrices.)The work horse of Robertson and

Seymour's theory is the Graph Minor Structure Theorem. The result I will describe today

is such a structure theorem for binary matroids. With this result proving well--quasi-

ordering of binary matroids and the related computational conjectures are well within

reach. (Actually most of this structural work does apply to other finite fields, but more

work is needed there, in particular for composite fields.)

12.30 - 14.00 Lunch

14.00 - 14.30 Jakub Byszewski (Utrecht): Devissage for local deformation functors

 

14.30 - 15.00 Koen Thas (Gent): Gassman-Sunada theory, isospectrality and finite

simple groups

 

15.00 15.30 Coffee/Tea

 

15.30 16.00 Liza Huijse (Amsterdam): What can cohomology tell us about a many-

particle quantum system?

 

16.00 17.00 Irene Bouw (Ulm): Existence of covers of curves in positive

characteristic

 

Abstract: This talk discusses the question of the existence of covers of curves with

prescribed ramification both in characteristic zero and characteristic p. The available

techniques are deformation and degeneration of covers and the linear-series method.

We illustrate these methods in the concrete case of (non-Galois) degree-p covers from

the projective line to itself. This is joint work with Brian Osserman.

 

 

 

=== end of workshop ===



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