Topology and Geometry in a Discrete Setting
(November 28 - December 2, 2016)

Description

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.

Organizing Committee

= speaker    = poster presenter

Monday November 28, 2016
Time Description Speaker Location Abstracts Slides
8:30 - 8:55Registration11th Floor Collaborative Space
8:55 - 9:00WelcomeICERM Director11th Floor Lecture Hall
9:00 - 9:45Thrifty approximations of convex bodies by polytopesAlexander Barvinok, University of Michigan11th Floor Lecture Hall
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9:50 - 10:20Coffee/Tea Break11th Floor Collaborative Space
10:20 - 11:00Higher-dimensional Expansion and Topological OverlapUli Wagner, IST, Austria11th Floor Lecture Hall
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11:15 - 11:55Topological aspects of Boolean functionsMark Goresky, ICERM and IAS11th Floor Lecture Hall
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12:00 - 2:00Break for Lunch / Free Time
2:00 - 2:40Toric h-vectors and Chow Betti numbers of hypersimplicesJosephine Yu, Georgia Institute of Technology11th Floor Lecture Hall
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2:50 - 3:20Coffee/Tea Break11th Floor Collaborative Space
3:20 - 4:00Tutte chromatic relations, extensions and applicationsSlava Krushkal, University of Virginia11th Floor Lecture Hall
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4:15 - 4:55Mechanism design in discrete settingsNgoc M. Tran, Hausdorff Center UT Austin11th Floor Lecture Hall
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5:00 - 6:30Welcome Reception11th Floor Collaborative Space

Tuesday November 29, 2016
Time Description Speaker Location Abstracts Slides
9:00 - 9:40Points, lines, planes, etc.June Huh, IAS and Princeton University11th Floor Lecture Hall
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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 circleGaiane Panina, St. Petersburg Department of Steklov Institute of Mathematics RAS (PDMI)11th Floor Lecture Hall
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11:15 - 11:55Random triangulations of the two sphereEric Babson, UC Davis11th Floor Lecture Hall
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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
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2:55 - 3:35A toolbox for topologistsPablo Soberón, Northeastern University11th Floor Lecture Hall
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3:45 - 5:00Poster Session and Coffee/Tea Break11th Floor Collaborative Space

Wednesday November 30, 2016
Time Description Speaker Location Abstracts Slides
9:00 - 9:40Lower bound theorems for manifolds and normal pseudomanifoldsIsabella Novik, University of Washington11th Floor Lecture Hall
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9:50 - 10:20Coffee/Tea Break11th Floor Collaborative Space
10:20 - 11:00Lefschetz properties of balanced 3-polytopesMartina Juhnke-Kubitzke, Universität Osnabrück11th Floor Lecture Hall
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11:15 - 11:55Hyperplane Equipartitions Plus ConstraintsSteven Simon, Bard College11th Floor Lecture Hall
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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
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3:10 - 3:40Coffee/Tea Break11th Floor Collaborative Space
3:40 - 4:20Regularity of complete intersections of linesBruno Benedetti, University of Miami11th Floor Lecture Hall
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4:35 - 5:15Matroids over hyperfieldsLaura Anderson, Binghamton University11th Floor Lecture Hall
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Thursday December 1, 2016
Time Description Speaker Location Abstracts Slides
9:00 - 9:40Sum Complexes and their ApplicationsRoy Meshulam, Technion11th Floor Lecture Hall
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9:50 - 10:20Coffee/Tea Break11th Floor Collaborative Space
10:20 - 11:00Prismatic Maps for the Topological Tverberg ConjectureIsaac Mabillard, IST Austria11th Floor Lecture Hall
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11:15 - 11:55Metric reconstruction via optimal transportFlorian Frick, Cornell University11th Floor Lecture Hall
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12:00 - 1:30Break for Lunch / Free Time
1:30 - 2:10Vanishing theorems for highly connected lattices and the subadditivity problemKarim Adiprasito, Hebrew University of Jerusalem11th Floor Lecture Hall
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2:25 - 3:05Colorful simplicial depthZuzana Patáková, IST Austria11th Floor Lecture Hall
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3:20 - 3:50Coffee/Tea Break11th Floor Collaborative Space
6:30 - 8:00Public Lecture - Visualizing the Future of BiomedicineChris R. Johnson, Ph.D, University of Utah11th Floor Lecture Hall

Friday December 2, 2016
Time Description Speaker Location Abstracts Slides
9:00 - 9:40Representation stability in configuration spaces via Whitney homology of the partition latticePatricia Hersh, North Carolina State University11th Floor Lecture Hall
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9:50 - 10:20Coffee/Tea Break11th Floor Collaborative Space
10:20 - 11:00Markoff Surfaces and Strong ApproximationAlexander Gamburd, Graduate Center, CUNY11th Floor Lecture Hall
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11:15 - 11:55High-dimensional Theta NumbersAnna Gundert, University of Cologne11th Floor Lecture Hall
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12:10 - 12:50On Stokes setsYuliy Baryshnikov, University of Illinois at Urbana-Champaign11th Floor Lecture Hall
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1:05 - 3:00Break for Lunch / Free Time