# Mathematical Sciences Research Institute

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# Workshop

Recent Developments in Arrangements and Configuration Spaces August 07, 2006 - August 11, 2006
 Registration Deadline: July 31, 2006 over 10 years ago May 07, 2006 over 10 years ago
Organizers Michael Falk (Northern Arizona University), Eva-Maria Feichtner (University of Stuttgart), Hiroaki Terao (Tokyo Metropolitan University)
Speaker(s)

## Show List of Speakers

Description

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.

Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Funding & Logistics

## Show Funding

To apply for funding, you must register by the funding application deadline displayed above.

Students, recent Ph.D.'s, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

## Show Lodging

A block of rooms has been reserved at the Rose Garden Inn. Reservations may be made by calling 1-800-992-9005 OR directly on their website. Click on Corporate at the bottom of the screen and when prompted enter code MATH (this code is not case sensitive). By using this code a new calendar will appear and will show MSRI rate on all room types available.

A block of rooms has been reserved at the Hotel Durant. Reservations may be made by calling 1-800-238-7268. When making reservations, guests must request the MSRI preferred rate. If you are making your reservations on line, please go to this link and enter the promo/corporate code MSRI123. Our preferred rate is \$129 per night for a Deluxe Queen/King, based on availability.

Additional lodging options (short term housing page - Short Term Housing

## Show Visa/Immigration

Schedule
Aug 07, 2006
Monday
 09:45 AM - 10:45 AM The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe Ansatz Alexander Varchenko (University of North Carolina) 11:15 AM - 12:15 PM Resonance and critical points of arrangements Daniel Cohen (Louisiana State University) 02:00 PM - 03:00 PM The homology of real De Concini-Procesi models Eric Rains 03:30 PM - 04:00 PM k-nets and Line Arrangements in P^2 Janis Stipins 04:15 PM - 05:15 PM Tropical Implicitization Bernd Sturmfels (UC Berkeley Math Faculty)
Aug 08, 2006
Tuesday
 09:00 AM - 10:00 AM Fitting ideals and cohomology jump loci Henry Schenck 10:30 AM - 11:00 AM On the monodromy action on Milnor fibers of graphic arrangements Anca Macinic 11:15 AM - 12:15 PM Massey products and monomial ideals Graham Denham 02:00 PM - 03:00 PM Cohomology jumping loci, formality, and quasi-projectivity Alexandru Suciu (Northeastern University) 03:30 PM - 04:30 PM Navigational complexity of collision free motion planning Michael Farber
Aug 09, 2006
Wednesday
 09:00 AM - 10:00 AM Moduli of Representations of Directed Graph Algebras Eric Babson 10:30 AM - 11:00 AM Degeneration varieties Max Wakefield 11:15 AM - 12:15 PM Families of arrangements Richard Randell
Aug 10, 2006
Thursday
 10:30 AM - 11:00 AM The stability of $$A_2$$ and $$B_2$$-type arrangements Takuro Abe 11:15 AM - 12:15 PM Minimal CW-decomposition and applications Masahiko Yoshinaga 02:00 PM - 03:00 PM Genera of complex varieties and singularities of proper maps Laurentiu Maxim (University of Wisconsin-Madison) 04:15 PM - 04:45 PM A remark on Deligne's proof and the Weak Lattice Property Emanuele Delucchi
Aug 11, 2006
Friday
 09:00 AM - 10:00 AM Homology of fiber-type arrangement complements and configuration spaces Daniel Matei 10:30 AM - 11:00 AM Geometry of rank tests Anne Shiu 11:15 AM - 12:15 PM Some results on local system cohomologies of Artin groups Mario Salvetti 02:00 PM - 03:00 PM Asymptotic Regularity of Ideals David Eisenbud (MSRI - Mathematical Sciences Research Institute)