Organizing Committee
Abstract

This workshop will explore topological properties of random and quasi-random phenomena in physical systems, stochastic simulations/processes, as well as optimization algorithms. Practitioners in these fields have written a great deal of simulation code to help understand the configurations and scaling limits of both the physically observed and computational phenomena. However, mathematically rigorous theories to support the simulation results and to explain their limiting behavior are still in their infancy.

Randomness is inherent to models of the physical, biological, and social world. Random topology models are important in a variety of complicated models including quantum gravity and black holes, filaments of dark matter in astronomy, spatial statistics, and morphological models of shapes, as well as models appearing in social media. The probabilistic method, theory of point processes, and ideas from stochastic and integral geometry have been central tools for proofs and efficient algorithms to measure topological quantities, such as Betti numbers of random geometric complexes.

The workshop topics include: random simplicial complexes, topological invariants in Gaussian random fields, and topological aspects of phase transitions, and geometry and topology of hard disks. A major theme of this workshop will center around computational issues and numerical experiments based on existing models and implementations.

Confirmed Speakers & Participants

Workshop Schedule

Monday, October 17, 2016
TimeEventLocationMaterials
9:00 - 9:30Registration11th Floor Collaborative Space 
9:30 - 9:35Welcome - ICERM Director11th Floor Lecture Hall 
9:35 - 10:20A Parisi formula for the ground state energy of the Sherrington-Kirkpatrick model - Antonio Auffinger, Northwestern University11th Floor Lecture Hall
10:35 - 11:00Coffee/Tea Break11th Floor Collaborative Space 
11:00 - 11:45Universality of Jamming in Continuous Constrained Satisfaction - Silvio Franz, LPTMS Universite Paris-Saclay11th Floor Lecture Hall
12:00 - 2:00Break for Lunch / Free Time  
2:00 - 2:45Configuration space topology as cause or signature of slow dynamics - Yoav Kallus, Santa Fe Institute11th Floor Lecture Hall
3:00 - 3:15Coffee/Tea Break11th Floor Collaborative Space 
3:15 - 4:00Self-similarity in the eigenvalues of random matrices - Elizabeth Meckes, Case Western Reserve University11th Floor Lecture Hall
4:15 - 5:00Spaces of planar embeddings - Richard Kenyon, Brown University11th Floor Lecture Hall
5:15 - 6:45Welcome Reception11th Floor Collaborative Space 
Tuesday, October 18, 2016
TimeEventLocationMaterials
9:00 - 9:45Topology of large random spaces - Michael Farber, Queen Mary, University of London11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15Generalized statistical honeycomb and void percolation. - Benoit Charbonneau, University of Waterloo11th Floor Lecture Hall
11:30 - 12:15Property (T) in simplicial complexes and the spectral evolution of random graphs - Elliot Paquette, The Ohio State University11th Floor Lecture Hall
12:30 - 2:30Break for Lunch / Free Time  
2:30 - 3:15Persistence Diagrams in Probability and Statistics: From Materials TDA View- points - Yasu Hiraoka, Tohoku University11th Floor Lecture Hall
3:30 - 5:00Poster Session and Coffee/Tea Break11th Floor Collaborative Space 
Wednesday, October 19, 2016
TimeEventLocationMaterials
9:00 - 9:45Random gluing polygons - Sergei Chmutov, Ohio State University at Mansfield11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15Continumm Percolation and Duality with Hard-Particle Systems Across Dimensions - Salvatore Torquato, Princeton11th Floor Lecture Hall
11:30 - 12:15Topology of Random Geometric Complexes - Omer Bobrowski, Technion - Israel Institute of Technology11th Floor Lecture Hall 
12:30 - 12:40Group Photo 11th Floor Lecture Hall 
12:40 - 2:30Break for Lunch / Free Time  
2:30 - 3:15Percolating length scales in persistence diagrams from porous materials - Vanessa Robins, The Australian National University11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45Random Clique Complexes - Christopher Hoffman, University of Washington11th Floor Lecture Hall
Thursday, October 20, 2016
TimeEventLocationMaterials
9:00 - 9:45A probabilistic approach to real enumerative geometry. - Antonio Lerario, SISSA11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15Random signed measures constructed using Euler characteristics - Katharine Turner, EPFL11th Floor Lecture Hall
11:30 - 12:15Algorithmic Self-Assembly and Self-Similar Structures - Natasa Jonoska, USF11th Floor Lecture Hall
12:30 - 2:30Break for Lunch / Free Time  
2:30 - 3:15Random Steiner complexes - Ron Rosenthal, Technion11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
6:30 - 8:00ICERM Public Lecture: Voting Insecurity - Barbara SimonsBrown University's Salomon Center  
Friday, October 21, 2016
TimeEventLocationMaterials
9:00 - 9:45Random lemniscates - Erik Lundberg, Florida Atlantic University11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15Connectivity and distributions of three dimensional tilings. - Caroline Klivans, Brown University11th Floor Lecture Hall
11:30 - 12:15Recent progress in random groups - Moon Duchin, Tufts University11th Floor Lecture Hall
12:30 - 2:30Break for Lunch / Free Time  
2:30 - 3:15Gaussian Random Knots - Eric Babson, UC - Davis11th Floor Lecture Hall

Associated Semester Workshops

Topology in Motion
Unusual Configuration Spaces
Topology and Geometry in a Discrete Setting

Lecture Videos

Random lemniscates

Erik Lundberg
Florida Atlantic University
October 21, 2016

Random gluing polygons

Sergei Chmutov
Ohio State University at Mansfield
October 19, 2016

Topology of large random spaces

Michael Farber
Queen Mary, University of London
October 18, 2016