Mathematical Sciences Research Institute - Topology of Arrangements and Applications

This workshop will be part of MSRI's Special Semester in Hyperplane Arrangements and Applications.

The topology of hyperplane arrangements involves a wide range of algebraic
and combinatorial as well as topological methods. The main applications
are to generalized hypergeometric functions, Knizhnik-Zamolodchikov
equations, topology of configuration spaces, and representations of braid
and artin groups. This workshop will focus on these and other topics, including
homotopy type and fundamental groups, higher homotopy groups, cohomology
support loci (resonance and characteristic varieties), Milnor fibers,
cohomology of artin groups, braids and configuration spaces, Gauss-Manin
connections, KZ and qKZ equations.

Confirmed speakers:

Enrique Artal-Bartolo
Anatoly Libgober
Eduard Looijenga
Michael Davis
Fred Cohen
Michael Farber
Toshitake Kohno
Dmitry Panov
Richard Scott
Dev Sinha
Alexander Varchenko

Monday, October 4
9:00-9:45 Registration

9:45-10:00 Welcome and Introduction

10:00-11:00 Peter Orlik
Gauss-Manin connections for arrangements.

11:00-11:15 Morning Tea (Sixth floor)

11:15-12:15 Eduard Looijenga
Arrangements and moduli.

12:15-2:00 Lunch Break

2:00-3:00 Michael Davis
L2-cohomology of artin groups and hyperplane complements.

3:00-3:30 Afternoon Tea (Sixth floor)

3:30-4:30 Stefan Papadima
On a question of Serre: the role of the Alexander invariant.

Tuesday, October 5
9:30-10:30 Dev Sinha
Models for configuration spaces.

10:30-11:00 Morning Tea (Sixth floor)

11:00-12:00 Edward Frenkel
Gaudin model and opers.

12:00-2:00 Lunch Break

2:00-3:00 Alexander Varchenko
Bethe ansatz for arrangements of hyperplanes and the Gaudin model.

3:00-3:30 Afternoon Tea (Sixth floor)

3:30-4:00 Paul Hacking
Moduli of hyperplane arrangements.

4:15-4:45 Karl-Dieter Crisman
Chow groups of zero-cycles relative to hyperplane arrangements.

4:45 - 5:45 Reception (Sixth floor)

Wednesday, October 6
9:30-10:30 Frederick Cohen
Connections between braid groups, homotopy theory,and low dimensional topology.

10:30-11:00 Morning Tea (Sixth floor)

11:00-12:00 Toshitake Kohno
Schlafli functions and iterated integrals on configuration spaces.

12:00-5:00 No scheduled talks

Thurday, October 7
9:30-10:30 Enrique Artal-Bartolo
Fundamental group, topology and combinatorics of line arrangements.

10:30-11:00 Morning Tea (Sixth floor)

11:00-12:00 Anatoly Libgober
Arrangements with isolated non normal crossings.

12:00-2:00 Lunch Break

2:00-3:00 Susumu Tanabe
Weight filtration of the mixed Hodge structure of period integrals and hyperplane arrangement.

3:00-3:30 Afternoon Tea (Sixth floor)

3:30-4:00 Laurentiu Maxim
Intersection homology and Alexander modules of hypersurface complements.

4:15-4:45 Daniel Matei
Homology of resonant local systems.

Friday, October 8
9:30-10:30 Inna Scherbak
Arrangements in the Schubert calculus of Grassmannians.

10:30-11:00 Morning Tea (Sixth floor)

11:00-12:00 Mario Salvetti
On the genus of configuration spaces.

12:00-2:00 Lunch Break

2:00-3:00 Katsuhisa Mimachi
Regularizable cycles associated with a Selberg type integral
under some resonance condition.

3:00-3:30 Afternoon Tea (Sixth floor)

3:30-4:30 Richard Scott
Blow-ups and complements in zonotopal complexes.

Currently Available Videos

Peter Orlik , Gauss-Manin Connections for Arrangements. October 4,2004, 10:00 AM to 11:00 AM
Eduard Looijenga , Arrangements and Moduli. October 4,2004, 11:15 AM to 12:15 PM
Michael Davis , L2-Cohomology of Artin Groups and Hyperplane Complements. October 4,2004, 02:00 PM to 03:00 PM
Stefan Papadima , On a Question of Serre: The Role of the Alexander Invariant. October 4,2004, 03:30 PM to 04:30 PM
Dev Sinha , Models for Configuration Spaces. October 5,2004, 09:30 AM to 10:30 AM
Edward Frenkel , Gaudin Model and Opers. October 5,2004, 11:00 AM to 12:00 PM
Toshitake Kohno , Schlafi Functions and Iterated Integrals on Configuration Spaces. October 5,2004, 11:00 AM to 11:45 AM
Alexander Varchenko , Bethe Ansatz for Arrangements of Hyperplanes and the Gaudin Model. October 5,2004, 02:00 PM to 02:45 PM
Paul Hacking , Moduli of Hyperplane Arrangements. October 5,2004, 03:30 PM to 04:00 PM
Karl-Dieter Crisman , Chow Groups of Zero-Cycles Relative to Hyperplane Arrangements. October 5,2004, 04:00 PM to 04:45 PM
Frederick Cohen , Connections Between Braid Groups, Homotopy Theory, and Low Dimensional Topology. October 6,2004, 09:30 AM to 10:30 AM
Enrique Artal Bartolo , Fundamental Group, Topology and Combinatorics of Line Arrangements. October 7,2004, 09:30 AM to 10:30 AM
Anatoly Libgober , Arrangements with Isolated Non Noraml Crossings. October 7,2004, 11:00 AM to 11:50 AM
Susumu Tanabe , Weight Filtration of the Mixed Hodge Structure of Period Integrals and Hyperplane Arrangements. October 7,2004, 02:00 PM to 02:45 PM
Laurentiu Maxim , Intersection Homology and Alexander Modules of Hypersurface Complements. October 7,2004, 03:30 PM to 04:00 PM
Daniel Matei , Homology of Resonant Local Systems. October 7,2004, 04:00 PM to 04:40 PM
Inna Scherbak , Arrangements in the Schubert Calculus of Grassmannians. October 8,2004, 09:30 AM to 10:30 AM
Mario Salvetti , On the Genus of Configuration Spaces. October 8,2004, 11:00 AM to 11:55 AM
Katsuhisa Mimachi , Regularizable Cycles Associated eith a Selberg Type Integral Under Some Resonance Condition. October 8,2004, 02:00 PM to 02:45 PM
Richard Scott , Blow-ups and Complements in Zonotopal Complexes. October 8,2004, 03:30 PM to 04:30 PM

You can find videos of other workshops and events on our VMath - Streaming Video page.

For more information:
Questions about this workshop should be sent either by email to

268@msri.org

or by regular mail to:

Topology of Arrangements and Applications Mathematical Sciences Research Institute 17 Gauss Way, Berkeley, CA 94720-5070. USA

The Institute is committed to the principles of Equal Opportunity and Affirmative Action.

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