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PROGEOCOM Report Summary

Project ID: 320924
Funded under: FP7-IDEAS-ERC
Country: Israel

Mid-Term Report Summary - PROGEOCOM (Avenues in Probabilistic and Geometric Combinatorics)

The study of noise in stochastic systems turned out to be useful in many different areas: It is crucial for understanding correlation inequalities related to classical questions in extremal combinatorics, the study of random graphs, and to the study of small quantum systems designed to allow superior computational powers. We explored some of these directions yielding promising fruits of theoretical and applied nature. This represent a main effort of our proposal in the direction of probabilistic combinatorics. We explored some avenues in geometric combinatorics, making progress on face number of embedded complexes, studying high dimensional analog for minors and induced graphs, and trying to apply geometric and homological methods for extremal combinatorial problems.

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