Organizing Committee
Abstract

This workshop will bring together mathematicians working on combinatorial, geometric and topological properties of arrangements. In addition to fundamental open problems in the area, we will emphasize connections to tropical geometry, configuration spaces, and applications (coding theory, statistical economics, topological robotics), building bridges between those working on different aspects of the area. The main aim of the workshop is to discuss computational issues that arise in studying topological and combinatorial invariants of arrangements.

The workshop will be comprised of two main activities: A series of short courses by leading experts and research or expository talks. The short courses will be aimed at a broad audience; in particular they will be appropriate for advanced graduate students and early career mathematicians. In addition to theory, talks will highlight computational aspects of the problems, and the state of the art on the main open conjectures in the field. We will also have a pair of research talks each afternoon.

Image for "Computational Geometric Topology in Arrangement Theory"
The Simpson lines of a triangle trace out a deltoid. If you divide the circle into 3n number of intervals, draw the corresponding Simpson lines, and alternate three colors then the result is a 3-net (or web). The existence of nets are a crux in understanding various topological properties in arrangement theory.

Confirmed Speakers & Participants

Talks will be presented virtually or in-person as indicated in the schedule below.

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, July 6, 2015
TimeEventLocationMaterials
8:30 - 8:55am EDTRegistration11th Floor Collaborative Space 
8:55 - 9:00am EDTWelcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:30am EDTSplines on the Alfeld split of a simplex: approximation theory meets hyperplane arrangements - Hal Schenck, University of Illinois at Urbana-Champaign11th Floor Lecture Hall 
9:45 - 10:15am EDTChen ranks of arrangement groups - Daniel Cohen, Louisiana State University11th Floor Lecture Hall
10:30 - 11:00am EDTCoffee/Tea Break11th Floor Collaborative Space 
11:00 - 11:45am EDTHyperplane arrangements and cohomology jump loci - Alex Suciu, Northeastern University 11th Floor Lecture Hall 
12:00 - 1:45pm EDTBreak for Lunch   
1:45 - 2:30pm EDTCharacteristic classes and arrangements I - Paolo Aluffi, Florida State University11th Floor Lecture Hall
2:45 - 3:15pm EDTCoffee/Tea Break11th Floor Collaborative Space 
3:15 - 4:00pm EDT On graphic arrangement groups - Michael Falk, Northern Arizona University11th Floor Lecture Hall
4:15 - 5:00pm EDTAnnihilators of powers of arrangements. - Uli Walther, Purdue University11th Floor Lecture Hall
5:15 - 6:30pm EDTWelcome Reception11th Floor Collaborative Space 
Tuesday, July 7, 2015
TimeEventLocationMaterials
9:00 - 9:30am EDTFormality properties, resonance varieties and Chen ranks - He Wang, Northeastern University11th Floor Lecture Hall 
9:45 - 10:15am EDTResidual finiteness and torsion-freeness of arrangement groups - Thomas Koberda, Yale University11th Floor Lecture Hall
10:30 - 11:00am EDTCoffee/Tea Break11th Floor Collaborative Space 
11:00 - 11:45am EDTArrangements and tropical geometry I - Eva Feichtner, Universität Bremen11th Floor Lecture Hall 
12:00 - 1:45pm EDTBreak for Lunch   
1:45 - 2:30pm EDTCharacteristic classes and arrangements II - Paolo Aluffi, Florida State University11th Floor Lecture Hall
2:45 - 3:15pm EDTCoffee/Tea Break11th Floor Collaborative Space 
3:15 - 4:00pm EDTTropical schemes - Diane Maclagan, University of Warwick11th Floor Lecture Hall
4:15 - 5:00pm EDTHodge theory and combinatorics - June Huh, Institute for Advanced Study11th Floor Lecture Hall
Wednesday, July 8, 2015
TimeEventLocationMaterials
9:00 - 9:30am EDTTopology of Complements - Daniel Matei, Institute of Mathematics "Simion Stoilow" of the Romanian Academy11th FLoor Lecture Hall 
9:45 - 10:15am EDTSome remarks on local system cohomology over arrangements. - Mario Salvetti, Università di Pisa11th Floor Lecture Hall
10:30 - 11:00am EDTCoffee/Tea Break11th Floor Collaborative Space 
11:00 - 11:45am EDTHyperplane arrangements and Milnor fibrations - Alex Suciu, Northeastern University 11th Floor Lecture Hall 
11:45 - 12:00pm EDTGroup Photo  
12:00 - 1:45pm EDTBreak for Lunch   
1:45 - 2:30pm EDTArrangements and tropical geometry II - Eva Feichtner, Universität Bremen11th Floor Lecture Hall 
2:45 - 3:30pm EDTSupersolvable arrangements: higher topological complexity of the complements, randomness. - Sergey Yuzvinsky, University of Oregon11th Floor Lecture Hall 
3:45 - 5:30pm EDTPoster Session11th Floor Collaborative Space and Lecture Hall 
Thursday, July 9, 2015
TimeEventLocationMaterials
9:00 - 9:30am EDTHyperplane arrangements and Eulerian polynomials. - Masahiko Yoshinaga, Hokkaido University11th Floor Lecture Hall
9:45 - 10:15am EDTAn arithmetic Zariski pair of line arrangements with non-isomorphic fundamental group - Enrique Artal Bartolo, Universidad de Zaragoza11th Floor Lecture Hall
10:30 - 11:00am EDTCoffee/Tea Break11th Floor Collaborative Space 
11:00 - 11:30am EDTCohomology of elliptic arrangements - Christin Bibby, University of Western Ontario11th Floor Lecture Hall
11:45 - 12:15pm EDTOn twisted Alexander invariants and applications to the Milnor fiber of a hyperplane arrangement. - KaiHo Wong, University of Wisconsin11th Floor Lecture Hall
12:30 - 1:45pm EDTBreak for Lunch   
1:45 - 2:15pm EDTCohomology of Algebraic Plane Curves - Nancy Abdallah, Université de Nice Sophia Antipolis11th Floor Lecture Hall
2:30 - 3:00pm EDTDegeneration of Orlik-Solomon Algebras and Milnor Fibers of Complex Line Arrangements - Pauline Bailet, Université de Nice Sophia Antipolis11th Floor Lecture Hall
3:15 - 3:45pm EDTCoffe/Tea Break11th Floor Collaborative Space 
3:45 - 5:00pm EDTProblem Session11th Floor Lecture Hall 
Friday, July 10, 2015
TimeEventLocationMaterials
9:00 - 9:30am EDTIdeal Free Theorem and Saturated Free Filtrations of Affine Weyl Arrangements - Hiroaki Terao, Hokkaido University11th Floor Lecture Hall
9:45 - 10:15am EDTResonance and syzygies - Graham Denham, University of Western Ontario11th Floor Lecture Hall 
10:30 - 11:00am EDTCoffee/Tea Break11th Floor Collaborative Space 
11:00 - 11:30am EDTHigher-Order Degrees of Complex Hypersurface Complements - Yun Su, University of Wisconsin11th Floor Lecture Hall
11:45 - 12:15pm EDTCharacteristic Varieties of Hypersurface Complements - Yongqiang Liu, University of Science and Technology of China11th Floor Lecture Hall
12:30 - 1:15pm EDTThe Grunbaum-Hadwiger-Ramos hyperplane mass partition problem - Pavle Blagojevic, Freie Universität Berlin11th Floor Lecture Hall
1:30 - 5:00pm EDTOpen for collaboration   

Lecture Videos

The Grunbaum-Hadwiger-Ramos hyperplane mass partition problem

Pavle Blagojevic
Freie Universität Berlin
July 10, 2015
Computational Geometric Topology in Arrangement Theory
Play     Abstract

Characteristic Varieties of Hypersurface Complements

Yongquiang Liu
University of Science and Technology in China
July 10, 2015
Computational Geometric Topology in Arrangement Theory
Play     Abstract

Higher-Order Degrees of Complex Hypersurface Complements

Yun Su
University of Wisconsin - Madison
July 10, 2015
Computational Geometric Topology in Arrangement Theory
Play     Abstract

Resonance and syzygies

Graham Denham
University of Western Ontario
July 10, 2015
Computational Geometric Topology in Arrangement Theory
Play

Degeneration of Orlik-Solomon Algebras and Milnor Fibers of Complex Line Arrangements

Pauline Bailet
Université Nice Sophia Antipolis (UNS)
July 9, 2015
Computational Geometric Topology in Arrangement Theory
Play     Abstract

Cohomology of Algebraic Plane Curves

Nancy Abdallah
Institut Universitaire de France, Univ. de Nice
July 9, 2015
Computational Geometric Topology in Arrangement Theory
Play     Abstract

On twisted Alexander invariants and applications to the Milnor fiber of a hyperplane arrangement.

Kaiho Wong
University of Wisconsin - Madison
July 9, 2015
Computational Geometric Topology in Arrangement Theory
Play     Abstract

Cohomology of elliptic arrangements

Christin Bibby
University of Western Ontario
July 9, 2015
Computational Geometric Topology in Arrangement Theory
Play     Abstract

An arithmetic Zariski pair of line arrangements with non-isomorphic fundamental group

Enrique Artal Bartolo
University of Zaragoza
July 9, 2015
Computational Geometric Topology in Arrangement Theory
Play     Abstract

Hyperplane arrangements and Eulerian polynomials.

Masahiko Yoshinaga
Hokkaido University
July 9, 2015
Computational Geometric Topology in Arrangement Theory
Play     Abstract

Supersolvable arrangements: higher topological complexity of the complements, randomness.

Sergey Yuzvinsky
University of Oregon
July 8, 2015
Computational Geometric Topology in Arrangement Theory
Play     Abstract

Arrangements and tropical geometry II

Eva Marie Feichtner
University of Bremen
July 8, 2015
Computational Geometric Topology in Arrangement Theory
Play

Hyperplane arrangements and Milnor fibrations

Alexandru Suciu
Northeastern University
July 8, 2015
Computational Geometric Topology in Arrangement Theory
Play

Topology of Complements

Daniel Matei
Institute of Mathematics at the Romanian Academy
July 8, 2015
Computational Geometric Topology in Arrangement Theory
Play     Abstract

Some remarks on local system cohomology over arrangements.

Mario Salvetti
Universita' di Pisa
July 8, 2015
Computational Geometric Topology in Arrangement Theory
Play     Abstract

Hodge theory and combinatorics

June Huh
Princeton University
July 7, 2015
Computational Geometric Topology in Arrangement Theory
Play     Abstract

Tropical schemes

Diane Maclagan
University of Warwick
July 7, 2015
Computational Geometric Topology in Arrangement Theory
Play     Abstract

Characteristic classes and arrangements II

Paolo Aluffi
Florida State University
July 7, 2015
Computational Geometric Topology in Arrangement Theory
Play     Abstract

Arrangements and tropical geometry I

Eva Marie Feichtner
University of Bremen
July 7, 2015
Computational Geometric Topology in Arrangement Theory
Play

Residual finiteness and torsion-freeness of arrangement groups

Thomas Koberda
Yale University
July 7, 2015
Computational Geometric Topology in Arrangement Theory
Play     Abstract

Formality properties, resonance varieties and Chen ranks

He Wang
Northeastern University
July 7, 2015
Computational Geometric Topology in Arrangement Theory
Play

On graphic arrangement groups

Michael Falk
Northern Arizona University
July 6, 2015
Computational Geometric Topology in Arrangement Theory
Play     Abstract

Characteristic classes and arrangements I

Paolo Aluffi
Florida State University
July 6, 2015
Computational Geometric Topology in Arrangement Theory
Play     Abstract

Hyperplane arrangements and cohomology jump loci

Alexandru Suciu
Northeastern University
July 6, 2015
Computational Geometric Topology in Arrangement Theory
Play

Chen ranks of arrangement groups

Daniel Cohen
University of Louisiana
July 6, 2015
Computational Geometric Topology in Arrangement Theory
Play     Abstract

Splines on the Alfeld split of a simplex: approximation theory meets hyperplane arrangements

Hal Schenck
University of Illinois Urbana-Champaign
July 6, 2015
Computational Geometric Topology in Arrangement Theory
Play     Abstract