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Organizing Committee
University of Bremen
MIT
Hebrew U and Yale
Moscow Phys-Tech Institute
University of California, Berkeley
University of California at Los Angeles
Belgrade University
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.
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.
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Workshop Schedule
Monday, November 28, 2016
8:30 - 8:55 AM EST
Registration
Location: 11th Floor Collaborative Space
8:55 - 9:00 AM EST
Welcome - ICERM Director
Location: 11th Floor Lecture Hall
9:50 - 10:20 AM EST
Coffee/Tea Break
Location: 11th Floor Collaborative Space
12:00 - 2:00 PM EST
Break for Lunch / Free Time
2:50 - 3:20 PM EST
Coffee/Tea Break
Location: 11th Floor Collaborative Space
5:00 - 6:30 PM EST
Welcome Reception
Location: 11th Floor Collaborative Space
Lecture Videos
Alexander Barvinok
University of Michigan
November 28, 2016 • 12:00 AM
Mark Goresky
Institute for Advanced Study, School of Mathematics
November 28, 2016 • 12:00 AM
Josephine Yu
Georgia Institute of Technology
November 28, 2016 • 12:00 AM
Gaiane Panina
St. Petersburg Institute of Informatics
November 29, 2016 • 12:00 AM
Pablo Soberón
Northeastern University
November 29, 2016 • 12:00 AM
Isabella Novik
University of Washington
November 30, 2016 • 12:00 AM
Martina Juhnke-Kubitzke
University of Osnabrück
November 30, 2016 • 12:00 AM
Bruno Benedetti
University of Miami
November 30, 2016 • 12:00 AM
Laura Anderson
Binghamton University
November 30, 2016 • 12:00 AM
Florian Frick
Cornell University
December 1, 2016 • 12:00 AM
Ngoc Mai Tran
University of Texas at Austin
November 28, 2016 • 12:00 AM
Yael Karshon
Univerity of Toronto
November 29, 2016 • 12:00 AM
Zuzana Patáková
Hebrew University of Jerusalem
December 1, 2016 • 12:00 AM
Patricia Hersh
North Carolina State University
December 2, 2016 • 12:00 AM
Anna Gundert
University of Cologne
December 2, 2016 • 12:00 AM
