Computational Geometric Topology in Arrangement Theory
(July 6-10, 2015)

Picture
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.

Description

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 eco-nomics, 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.

Organizing Committee

  • Nero Budur
    (KU Leuven and University of Notre Dame)
  • Graham Denham
    (Univ. Western Ontario)
  • Anca Daniela Macinic
    (IMAR, Bucharest)
  • Daniel Matei
    (IMAR, Bucharest)
  • Laurentiu Maxim
    (UW-Madison)
  • Hal Schenck
    (UIUC)
  • Max Wakefield
    (US Naval Academy)
  • Nancy Abdallah*
    (Université de Nice Sophia Antipolis)
  • Takuro Abe
    (Kyoto University)
  • Paolo Aluffi*
    (Florida State University)
  • Enrique Artal Bartolo*
    (Universidad de Zaragoza)
  • Pauline Bailet*
    (Université de Nice Sophia Antipolis)
  • Jeremiah Bartz
    (Francis Marion College)
  • Christin Bibby*
    (University of Western Ontario)
  • Pavle Blagojevic *
    (Freie Universität Berlin)
  • Nero Budur
    (KU Leuven)
  • Kevin Casto
    (University of Chicago)
  • Weiyan Chen
    (University of Chicago)
  • JOSE COGOLLUDO
    (UNIVERSITY OF ZARAGOZA)
  • Daniel Cohen*
    (Louisiana State University)
  • Emanuele Delucchi
    (University of Fribourg)
  • Graham Denham*
    (University of Western Ontario)
  • Alperen Ergur
    (Texas A & M University)
  • Michael Falk*
    (Northern Arizona University)
  • Eva Feichtner*
    (Universität Bremen)
  • Nathan Fieldsteel
    (University of Illinois at Urbana-Champaign)
  • Nir Gadish
    (University of Chicago)
  • June Huh*
    (Institute for Advanced Study)
  • Rita Jimenez Rolland
    (National Autonomous University of Mexico (UNAM))
  • Thomas Koberda*
    (Yale University)
  • Yongqiang Liu*
    (University of Science and Technology of China)
  • Diane Maclagan*
    (University of Warwick)
  • Daniel Matei*
    (Institute of Mathematics "Simion Stoilow" of the Romanian Academy)
  • Laurentiu Maxim
    (University of Wisconsin)
  • Mario Salvetti*
    (Università di Pisa)
  • Hal Schenck*
    (University of Illinois at Urbana-Champaign)
  • Yun Su*
    (University of Wisconsin)
  • Alexander Suciu*
    (Northeastern University)
  • Max Wakefield
    (U.S. Naval Academy)
  • Uli Walther*
    (Purdue University)
  • He Wang
    (Northeastern University)
  • KaiHo Wong*
    (University of Wisconsin)
  • Arnold Yim
    (Purdue University)
  • Youngho Yoon
    (Institute for Basic Science, Center for Geometry and Physics)
  • Masahiko Yoshinaga*
    (Hokkaido University)
  • Sergey Yuzvinsky*
    (University of Oregon)
Monday July 6, 2015
Time Description Speaker Location Abstracts Slides
8:30 - 8:55Registration11th Floor Collaborative Space
8:55 - 9:00WelcomeICERM Director11th Floor Lecture Hall
9:00 - 9:30Splines on the Alfeld split of a simplex: approximation theory meets hyperplane arrangementsHal Schenck, University of Illinois at Urbana-Champaign11th Floor Lecture Hall
9:45 - 10:15Chen ranks of arrangement groupsDaniel Cohen, Louisiana State University11th Floor Lecture Hall
PDF
10:30 - 11:00Coffee/Tea Break11th Floor Collaborative Space
11:00 - 11:45Hyperplane arrangements and cohomology jump lociAlex Suciu, Northeastern University 11th Floor Lecture Hall
12:00 - 1:45Break for Lunch
1:45 - 2:30Characteristic classes and arrangements IPaolo Aluffi, Florida State University11th Floor Lecture Hall
PDF
2:45 - 3:15Coffee/Tea Break11th Floor Collaborative Space
3:15 - 4:00 On graphic arrangement groupsMichael Falk, Northern Arizona University11th Floor Lecture Hall
PDF
4:15 - 5:00Annihilators of powers of arrangements.Uli Walther, Purdue University11th Floor Lecture Hall
PDF
5:15 - 6:30Welcome Reception11th Floor Collaborative Space

Tuesday July 7, 2015
Time Description Speaker Location Abstracts Slides
9:00 - 9:30Formality properties, resonance varieties and Chen ranksHe Wang, Northeastern University11th Floor Lecture Hall
9:45 - 10:15Residual finiteness and torsion-freeness of arrangement groupsThomas Koberda, Yale University11th Floor Lecture Hall
PDF
10:30 - 11:00Coffee/Tea Break11th Floor Collaborative Space
11:00 - 11:45Arrangements and tropical geometry IEva Feichtner, Universität Bremen11th Floor Lecture Hall
12:00 - 1:45Break for Lunch
1:45 - 2:30Characteristic classes and arrangements IIPaolo Aluffi, Florida State University11th Floor Lecture Hall
PDF
2:45 - 3:15Coffee/Tea Break11th Floor Collaborative Space
3:15 - 4:00Tropical schemesDiane Maclagan, University of Warwick11th Floor Lecture Hall
PDF
4:15 - 5:00Hodge theory and combinatoricsJune Huh, Institute for Advanced Study11th Floor Lecture Hall
PDF

Wednesday July 8, 2015
Time Description Speaker Location Abstracts Slides
9:00 - 9:30Topology of ComplementsDaniel Matei, Institute of Mathematics "Simion Stoilow" of the Romanian Academy11th FLoor Lecture Hall
9:45 - 10:15Some remarks on local system cohomology over arrangements.Mario Salvetti, Università di Pisa11th Floor Lecture Hall
PDF
10:30 - 11:00Coffee/Tea Break11th Floor Collaborative Space
11:00 - 11:45Hyperplane arrangements and Milnor fibrationsAlex Suciu, Northeastern University 11th Floor Lecture Hall
11:45 - 12:00Group Photo
12:00 - 1:45Break for Lunch
1:45 - 2:30Arrangements and tropical geometry IIEva Feichtner, Universität Bremen11th Floor Lecture Hall
2:45 - 3:30Supersolvable arrangements: higher topological complexity of the complements, randomness.Sergey Yuzvinsky, University of Oregon11th Floor Lecture Hall
3:45 - 5:30Poster Session11th Floor Collaborative Space and Lecture Hall

Thursday July 9, 2015
Time Description Speaker Location Abstracts Slides
9:00 - 9:30Hyperplane arrangements and Eulerian polynomials. Masahiko Yoshinaga, Hokkaido University11th Floor Lecture Hall
PDF
9:45 - 10:15An arithmetic Zariski pair of line arrangements with non-isomorphic fundamental groupEnrique Artal Bartolo, Universidad de Zaragoza11th Floor Lecture Hall
PDF
10:30 - 11:00Coffee/Tea Break11th Floor Collaborative Space
11:00 - 11:30Cohomology of elliptic arrangementsChristin Bibby, University of Western Ontario11th Floor Lecture Hall
PDF
11:45 - 12:15On twisted Alexander invariants and applications to the Milnor fiber of a hyperplane arrangement.KaiHo Wong, University of Wisconsin11th Floor Lecture Hall
PDF
12:30 - 1:45Break for Lunch
1:45 - 2:15Cohomology of Algebraic Plane CurvesNancy Abdallah, Université de Nice Sophia Antipolis11th Floor Lecture Hall
PDF
2:30 - 3:00Degeneration of Orlik-Solomon Algebras and Milnor Fibers of Complex Line Arrangements Pauline Bailet, Université de Nice Sophia Antipolis11th Floor Lecture Hall
PDF
3:15 - 3:45Coffe/Tea Break11th Floor Collaborative Space
3:45 - 5:00Problem Session11th Floor Lecture Hall

Friday July 10, 2015
Time Description Speaker Location Abstracts Slides
9:00 - 9:30Ideal Free Theorem and Saturated Free Filtrations of Affine Weyl ArrangementsHiroaki Terao, Hokkaido University11th Floor Lecture Hall
9:45 - 10:15Resonance and syzygiesGraham Denham, University of Western Ontario11th Floor Lecture Hall
10:30 - 11:00Coffee/Tea Break11th Floor Collaborative Space
11:00 - 11:30Higher-Order Degrees of Complex Hypersurface ComplementsYun Su, University of Wisconsin11th Floor Lecture Hall
11:45 - 12:15Characteristic Varieties of Hypersurface ComplementsYongqiang Liu, University of Science and Technology of China11th Floor Lecture Hall
12:30 - 1:15The Grunbaum-Hadwiger-Ramos hyperplane mass partition problemPavle Blagojevic, Freie Universität Berlin11th Floor Lecture Hall
1:30 - 5:00Open for collaboration