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

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, November 28, 2016
TimeEventLocationMaterials
8:30 - 8:55am ESTRegistration11th Floor Collaborative Space 
8:55 - 9:00am ESTWelcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:45am ESTThrifty approximations of convex bodies by polytopes - Alexander Barvinok, University of Michigan11th Floor Lecture Hall
9:50 - 10:20am ESTCoffee/Tea Break11th Floor Collaborative Space 
10:20 - 11:00am ESTHigher-dimensional Expansion and Topological Overlap - Uli Wagner, IST, Austria11th Floor Lecture Hall
11:15 - 11:55am ESTTopological aspects of Boolean functions - Mark Goresky, ICERM and IAS11th Floor Lecture Hall
12:00 - 2:00pm ESTBreak for Lunch / Free Time  
2:00 - 2:40pm ESTToric h-vectors and Chow Betti numbers of hypersimplices - Josephine Yu, Georgia Institute of Technology11th Floor Lecture Hall
2:50 - 3:20pm ESTCoffee/Tea Break11th Floor Collaborative Space 
3:20 - 4:00pm ESTTutte chromatic relations, extensions and applications - Slava Krushkal, University of Virginia11th Floor Lecture Hall
4:15 - 4:55pm ESTMechanism design in discrete settings - Ngoc M. Tran, Hausdorff Center UT Austin11th Floor Lecture Hall
5:00 - 6:30pm ESTWelcome Reception11th Floor Collaborative Space 
Tuesday, November 29, 2016
TimeEventLocationMaterials
9:00 - 9:40am ESTPoints, lines, planes, etc. - June Huh, IAS and Princeton University11th Floor Lecture Hall
9:50 - 10:20am ESTCoffee/Tea Break11th Floor Collaborative Space 
10:20 - 11:00am ESTDiscrete 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 - 11:55am ESTRandom triangulations of the two sphere - Eric Babson, UC Davis11th Floor Lecture Hall
12:00 - 2:00pm ESTBreak for Lunch / Free Time  
2:00 - 2:40pm ESTDiscrete invariants of Hamiltonian torus actions. - Yael Karshon, University of Toronto.11th Floor Lecture Hall
2:55 - 3:35pm ESTA toolbox for topologists - Pablo Soberón, Northeastern University11th Floor Lecture Hall
3:45 - 5:00pm ESTPoster Session and Coffee/Tea Break11th Floor Collaborative Space 
Wednesday, November 30, 2016
TimeEventLocationMaterials
9:00 - 9:40am ESTLower bound theorems for manifolds and normal pseudomanifolds - Isabella Novik, University of Washington11th Floor Lecture Hall
9:50 - 10:20am ESTCoffee/Tea Break11th Floor Collaborative Space 
10:20 - 11:00am ESTLefschetz properties of balanced 3-polytopes - Martina Juhnke-Kubitzke, Universität Osnabrück11th Floor Lecture Hall
11:15 - 11:55am ESTHyperplane Equipartitions Plus Constraints - Steven Simon, Bard College11th Floor Lecture Hall
12:10 - 12:20pm ESTGroup Photo11th Floor Lecture Hall 
12:20 - 2:20pm ESTBreak for Lunch / Free Time  
2:20 - 3:00pm ESTTopology and combinatorics of toric arrangements. - Emanuele Delucchi, University of Fribourg (Switzerland)11th Floor Lecture Hall
3:10 - 3:40pm ESTCoffee/Tea Break11th Floor Collaborative Space 
3:40 - 4:20pm ESTRegularity of complete intersections of lines - Bruno Benedetti, University of Miami11th Floor Lecture Hall
4:35 - 5:15pm ESTMatroids over hyperfields - Laura Anderson, Binghamton University11th Floor Lecture Hall
Thursday, December 1, 2016
TimeEventLocationMaterials
9:00 - 9:40am ESTSum Complexes and their Applications - Roy Meshulam, Technion11th Floor Lecture Hall
9:50 - 10:20am ESTCoffee/Tea Break11th Floor Collaborative Space 
10:20 - 11:00am ESTPrismatic Maps for the Topological Tverberg Conjecture - Isaac Mabillard, IST Austria11th Floor Lecture Hall
11:15 - 11:55am ESTMetric reconstruction via optimal transport - Florian Frick, Cornell University11th Floor Lecture Hall
12:00 - 1:30pm ESTBreak for Lunch / Free Time  
1:30 - 2:10pm ESTVanishing theorems for highly connected lattices and the subadditivity problem - Karim Adiprasito, Hebrew University of Jerusalem11th Floor Lecture Hall
2:25 - 3:05pm ESTColorful simplicial depth - Zuzana Patáková, IST Austria11th Floor Lecture Hall
3:20 - 3:50pm ESTCoffee/Tea Break11th Floor Collaborative Space 
6:30 - 8:00pm ESTPublic Lecture - Visualizing the Future of Biomedicine - Chris R. Johnson, Ph.D, University of Utah11th Floor Lecture Hall 
Friday, December 2, 2016
TimeEventLocationMaterials
9:00 - 9:40am ESTRepresentation stability in configuration spaces via Whitney homology of the partition lattice - Patricia Hersh, North Carolina State University11th Floor Lecture Hall
9:50 - 10:20am ESTCoffee/Tea Break11th Floor Collaborative Space 
10:20 - 11:00am ESTMarkoff Surfaces and Strong Approximation - Alexander Gamburd, Graduate Center, CUNY11th Floor Lecture Hall
11:15 - 11:55am ESTHigh-dimensional Theta Numbers - Anna Gundert, University of Cologne11th Floor Lecture Hall
12:10 - 12:50pm ESTOn Stokes sets - Yuliy Baryshnikov, University of Illinois at Urbana-Champaign11th Floor Lecture Hall
1:05 - 3:00pm ESTBreak for Lunch / Free Time  

Associated Semester Workshops

Topology in Motion
Image for "Topology in Motion"
Unusual Configuration Spaces
Image for "Unusual Configuration Spaces"
Stochastic Topology and Thermodynamic Limits
Image for "Stochastic Topology and Thermodynamic Limits "

Lecture Videos

High-dimensional Theta Numbers

Anna Gundert
University of Cologne
December 2, 2016

Colorful simplicial depth

Zuzana Patáková
Hebrew University of Jerusalem
December 1, 2016

Matroids over hyperfields

Laura Anderson
Binghamton University
November 30, 2016

Lefschetz properties of balanced 3-polytopes

Martina Juhnke-Kubitzke
University of Osnabrück
November 30, 2016

A toolbox for topologists

Pablo Soberón
Northeastern University
November 29, 2016

Points, lines, planes, etc.

June Huh
Princeton University
November 29, 2016

Mechanism design in discrete settings

Ngoc Mai Tran
University of Texas at Austin
November 28, 2016

Topological aspects of Boolean functions

Mark Goresky
Institute for Advanced Study, School of Mathematics
November 28, 2016