Organizing Committee
Abstract

While the semester program as a whole is inspired by the original view of topology as analysis situs fueled by applications in natural sciences and engineering, this workshop emphasizes the impact of topology and geometry on discrete structures.

Combinatorially inspired configuration spaces, such as arrangements of points, lines, hyperplanes, polytopes, and the like, provide intricate material and ongoing challenge for topological and geometric techniques. The latter have often gone through a process of adjustment towards their discrete, stratified objects, as in the case of discrete Morse theory or application of Fourier analysis. Notably, the recent solution of the log-concavity conjecture for matroids by Adiprasito, Huh and Katz was achieved by developing Hodge theory for combinatorial geometries which opens up most exciting perspectives on further applications. The construction of higher dimensional expanders is yet another promising direction. Inspired by the rich theory of graph expanders and drawing on the techniques of combinatorial algebraic topology, the goal is to design high-dimensional simplicial complexes with strong connectivity properties. New applications abound, like the impact of discrete geometry on social choice and mathematical economics through balancing theorems and equilibrium configurations.

This workshop is about building bridges - providing intricate, combinatorially inspired spaces to the topologist and geometer, and versatile geometric tools to the combinatorialist. Computational and algorithmic aspects as well as experimental evidence are crucial for this purpose.

Confirmed Speakers & Participants

Workshop Schedule

Monday, November 28, 2016
TimeEventLocationMaterials
8:30 - 8:55Registration11th Floor Collaborative Space 
8:55 - 9:00Welcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:45Thrifty approximations of convex bodies by polytopes - Alexander Barvinok, University of Michigan11th Floor Lecture Hall
9:50 - 10:20Coffee/Tea Break11th Floor Collaborative Space 
10:20 - 11:00Higher-dimensional Expansion and Topological Overlap - Uli Wagner, IST, Austria11th Floor Lecture Hall
11:15 - 11:55Topological aspects of Boolean functions - Mark Goresky, ICERM and IAS11th Floor Lecture Hall
12:00 - 2:00Break for Lunch / Free Time  
2:00 - 2:40Toric h-vectors and Chow Betti numbers of hypersimplices - Josephine Yu, Georgia Institute of Technology11th Floor Lecture Hall
2:50 - 3:20Coffee/Tea Break11th Floor Collaborative Space 
3:20 - 4:00Tutte chromatic relations, extensions and applications - Slava Krushkal, University of Virginia11th Floor Lecture Hall
4:15 - 4:55Mechanism design in discrete settings - Ngoc M. Tran, Hausdorff Center UT Austin11th Floor Lecture Hall
5:00 - 6:30Welcome Reception11th Floor Collaborative Space 
Tuesday, November 29, 2016
TimeEventLocationMaterials
9:00 - 9:40Points, lines, planes, etc. - June Huh, IAS and Princeton University11th Floor Lecture Hall
9:50 - 10:20Coffee/Tea Break11th Floor Collaborative Space 
10:20 - 11:00Discrete Morse theory for moduli spaces of flexible polygons, or solitaire game on the circle - Gaiane Panina, St. Petersburg Department of Steklov Institute of Mathematics RAS (PDMI)11th Floor Lecture Hall
11:15 - 11:55Random triangulations of the two sphere - Eric Babson, UC Davis11th Floor Lecture Hall
12:00 - 2:00Break for Lunch / Free Time  
2:00 - 2:40Discrete invariants of Hamiltonian torus actions. - Yael Karshon, University of Toronto.11th Floor Lecture Hall
2:55 - 3:35A toolbox for topologists - Pablo Soberón, Northeastern University11th Floor Lecture Hall
3:45 - 5:00Poster Session and Coffee/Tea Break11th Floor Collaborative Space 
Wednesday, November 30, 2016
TimeEventLocationMaterials
9:00 - 9:40Lower bound theorems for manifolds and normal pseudomanifolds - Isabella Novik, University of Washington11th Floor Lecture Hall
9:50 - 10:20Coffee/Tea Break11th Floor Collaborative Space 
10:20 - 11:00Lefschetz properties of balanced 3-polytopes - Martina Juhnke-Kubitzke, Universität Osnabrück11th Floor Lecture Hall
11:15 - 11:55Hyperplane Equipartitions Plus Constraints - Steven Simon, Bard College11th Floor Lecture Hall
12:10 - 12:20Group Photo11th Floor Lecture Hall 
12:20 - 2:20Break for Lunch / Free Time  
2:20 - 3:00Topology and combinatorics of toric arrangements. - Emanuele Delucchi, University of Fribourg (Switzerland)11th Floor Lecture Hall
3:10 - 3:40Coffee/Tea Break11th Floor Collaborative Space 
3:40 - 4:20Regularity of complete intersections of lines - Bruno Benedetti, University of Miami11th Floor Lecture Hall
4:35 - 5:15Matroids over hyperfields - Laura Anderson, Binghamton University11th Floor Lecture Hall
Thursday, December 1, 2016
TimeEventLocationMaterials
9:00 - 9:40Sum Complexes and their Applications - Roy Meshulam, Technion11th Floor Lecture Hall
9:50 - 10:20Coffee/Tea Break11th Floor Collaborative Space 
10:20 - 11:00Prismatic Maps for the Topological Tverberg Conjecture - Isaac Mabillard, IST Austria11th Floor Lecture Hall
11:15 - 11:55Metric reconstruction via optimal transport - Florian Frick, Cornell University11th Floor Lecture Hall
12:00 - 1:30Break for Lunch / Free Time  
1:30 - 2:10Vanishing theorems for highly connected lattices and the subadditivity problem - Karim Adiprasito, Hebrew University of Jerusalem11th Floor Lecture Hall
2:25 - 3:05Colorful simplicial depth - Zuzana Patáková, IST Austria11th Floor Lecture Hall
3:20 - 3:50Coffee/Tea Break11th Floor Collaborative Space 
6:30 - 8:00Public Lecture - Visualizing the Future of Biomedicine - Chris R. Johnson, Ph.D, University of Utah11th Floor Lecture Hall 
Friday, December 2, 2016
TimeEventLocationMaterials
9:00 - 9:40Representation stability in configuration spaces via Whitney homology of the partition lattice - Patricia Hersh, North Carolina State University11th Floor Lecture Hall
9:50 - 10:20Coffee/Tea Break11th Floor Collaborative Space 
10:20 - 11:00Markoff Surfaces and Strong Approximation - Alexander Gamburd, Graduate Center, CUNY11th Floor Lecture Hall
11:15 - 11:55High-dimensional Theta Numbers - Anna Gundert, University of Cologne11th Floor Lecture Hall
12:10 - 12:50On Stokes sets - Yuliy Baryshnikov, University of Illinois at Urbana-Champaign11th Floor Lecture Hall
1:05 - 3:00Break for Lunch / Free Time  

Associated Semester Workshops

Topology in Motion
Unusual Configuration Spaces
Stochastic Topology and Thermodynamic Limits

Lecture Videos

High-dimensional Theta Numbers

Anna Gundert
University of Cologne
December 2, 2016

Colorful simplicial depth

Zuzana Patáková
IST Austria
December 1, 2016

Matroids over hyperfields

Laura Anderson
Binghamton University
November 30, 2016

Lefschetz properties of balanced 3-polytopes

Martina Juhnke-Kubitzke
Universität Osnabrück
November 30, 2016

A toolbox for topologists

Pablo Soberón
Northeastern University
November 29, 2016

Discrete Morse theory for moduli spaces of flexible polygons, or solitaire game on the circle

Gaiane Panina
St. Petersburg Department of Steklov Institute of Mathematics RAS (PDMI)
November 29, 2016

Points, lines, planes, etc.

June Huh
IAS and Princeton University
November 29, 2016

Mechanism design in discrete settings

Ngoc M. Tran
Hausdorff Center UT Austin
November 28, 2016