Mathematical Sciences Research Institute - Recent Developments in Arrangements and Configuration Spaces

Organized By: Michael Falk (Northern Arizona University), Eva-Maria Feichtner (University of Stuttgart), Hiroaki Terao (Tokyo Metropolitan University)

Participant List:

View a List of Registered Participants

The purpose of this workshop is to assess and build upon progress in the theory of hyperplane arrangements and configuration spaces since the 2004 MSRI program Hyperplane Arrangements and Applications. The theory of arrangements is typified by its interdisciplinarity, an aspect that has become even more pronounced since the 2004 program. Topics covered in the workshop will range accordingly through combinatorics, commutative algebra, algebraic geometry, algebraic topology, singularity theory, representation theory, and geometric group theory.

Specific topics to be covered may include: arrangements of hyperplanes, subspaces, tori, and rational varieties; freeness of arrangements, reflection groups, Artin groups, discriminants; configuration spaces, wonderful compactifications, moduli spaces and the related tropical theory, local systems, characteristic and resonance varieties, and invariants of fundamental groups and higher homotopy groups, applications, including generalized hypergeometric functions and the Bethe Ansatz, and topological robotics.

The workshop is dedicated to Sergey Yuzvinsky, on the occasion of his 70th birthday.

Schedule

Monday, August 7
9:00 – 9:30 Registration
9:30 – 9:45 Welcome and Introduction
9:45 – 10:45 Alexander Varchenko, The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe Ansatz
10:45 – 11:15 Morning Tea
11:15 – 12:15 Daniel Cohen, Resonance and critical points of arrangements
12:15 – 2:00 Lunch Break
2:00 – 3:00 Eric Rains, The homology of real De Concini-Procesi models
3:00 – 3:30 Afternoon Tea
3:30 – 4:00 Janis Stipins, k-nets and Line Arrangements in P^2
4:15 – 5:15 Bernd Sturmfels: Tropical Implicitization

Tuesday, August 8
9:00 – 10:00 Hal Schenck: Fitting ideals and cohomology jump loci
10:00 – 10:30 Morning Tea
10:30 – 11:00 Anca Macinic, On the monodromy action on Milnor fibers of graphic arrangements
11:15 – 12:15 Graham Denham, Massey products and monomial ideals
12:15 – 2:00 Lunch break
2:00 – 3:00 Alex Suciu, Cohomology jumping loci, formality, and quasi-projectivity
3:00 – 3:30 Afternoon Tea
3:30 – 4:30 Michael Farber, Navigational complexity of collision free motion planning
5:00 – 7:00 Social Event

Wednesday, August 9
9:00 – 10:00 Eric Babson: TBA
10:00 – 10:30 Morning Tea
10:30 – 11:00 Max Wakefield: Degeneration varieties
11:15 – 12:15 Dick Randell: Families of arrangements
12:15 – 5:00 No scheduled talks

Thursday, August 10
9:00 – 10:00 Anne Shepler: Hochschild cohomology and graded Hecke Algebras
10:00 – 10:30 Morning Tea
10:30 – 11:00 Takuro Abe, The stability of $A_2$ and $B_2$-type arrangements
11:15 – 12:15 Masahiko Yoshinaga: Minimal CW-decomposition and applications
12:15 – 2:00 Lunch break
2:00 – 3:00 Laurentiu Maxim: Genera of complex varieties and singularities of proper maps
3:00 – 3:30 Afternoon Tea
3:30 – 4:00 Stefan Tohaneanu: Line-conic arrangements in P2
4:15 – 4:45 Emanuele Delucchi: A remark on Deligne's proof and the Weak Lattice Property

Friday, August 11
9:00 – 10:00 Daniel Matei: Homology of fiber-type arrangement complements and configuration spaces
10:00 – 10:30 Morning Tea
10:30 – 11:00 Anne Shiu: Geometry of rank tests
11:15 – 12:15 Mario Salvetti: Some results on local system cohomologies of Artin groups
12:15 – 2:00 Lunch break
2:00 – 3:00 David Eisenbud (tentative): Asymptotic Regularity of Ideals
3:00 – 3:30 Afternoon Tea

A block of rooms has been reserved at the Hotel Durant. Please mention the workshop name and reference the following code when making reservations via phone, fax or e-mail: JU0000. The cut-off date for reservations is July 7, 2006.

A block of rooms has been reserved at the Rose Garden Inn. Please reference the following Group Code when making reservations via phone, e-mail or web (if booking via web, put the code in the Guest Comment field): CGMS27. The cut-off date for reservations is July 7, 2006.

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Currently Available Videos

Alexander Varchenko , The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe Ansatz August 7,2006, 09:45 AM to 10:45 AM
Daniel Cohen , Resonance and critical points of arrangements August 7,2006, 11:15 AM to 12:15 PM
Eric Rains , The homology of real De Concini-Procesi models August 7,2006, 02:00 PM to 03:00 PM
Janis Stipins , k-nets and Line Arrangements in P^2 August 7,2006, 03:30 PM to 04:00 PM
Bernd Sturmfels , Tropical Implicitization August 7,2006, 04:15 PM to 05:15 PM
Henry Schenck , Fitting ideals and cohomology jump loci August 8,2006, 09:00 AM to 10:00 AM
Vilislav Boutchaktchiev , On the monodromy action on Milnor fibers of graphic arrangements August 8,2006, 10:30 AM to 11:00 AM
Graham Denham , Massey products and monomial ideals August 8,2006, 11:15 AM to 12:15 PM
Alexandru Suciu , Cohomology jumping loci, formality, and quasi-projectivity August 8,2006, 02:00 PM to 03:00 PM
Michael Farber , Navigational complexity of collision free motion planning August 8,2006, 03:30 PM to 04:30 PM
Eric Babson , Moduli of Representations of Directed Graph Algebras August 9,2006, 09:00 AM to 10:00 AM
Max Wakefield , Degeneration varieties August 9,2006, 10:30 AM to 11:00 AM
Richard Randell , Families of arrangements August 9,2006, 11:15 AM to 12:15 PM
Anne Shepler , Hochschild cohomology and graded Hecke Algebras August 10,2006, 09:00 AM to 10:00 AM
Takuro Abe , The stability of $A_2$ and $B_2$-type arrangements August 10,2006, 10:30 AM to 11:00 AM
Masahiko Yoshinaga , Minimal CW-decomposition and applications August 10,2006, 11:15 AM to 12:15 PM
Laurentiu Maxim , Genera of complex varieties and singularities of proper maps August 10,2006, 02:00 PM to 03:00 PM
Stefan Tohaneanu , Line-conic arrangements in P2 August 10,2006, 03:30 PM to 04:00 PM
Emanuele Delucchi , A remark on Deligne's proof and the Weak Lattice Property August 10,2006, 04:15 PM to 04:45 PM
Daniel Matei , Homology of fiber-type arrangement complements and configuration spaces August 11,2006, 09:00 AM to 10:00 AM
Anne Shiu , Geometry of rank tests August 11,2006, 10:30 AM to 11:00 AM
Mario Salvetti , Some results on local system cohomologies of Artin groups August 11,2006, 11:15 AM to 12:15 PM
David Eisenbud , Asymptotic Regularity of Ideals August 11,2006, 02:00 PM to 03:00 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

389@msri.org

or by regular mail to:

Recent Developments in Arrangements and Configuration Spaces Mathematical Sciences Research Institute 17 Gauss Way, Berkeley, CA 94720-5070. USA

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