Continuous Tasks and the Asynchronous Computability Theorem

The celebrated 1999 Asynchronous Computability Theorem (ACT) of Herlihy and Shavit characterized distributed tasks that are wait-free solvable and uncovered deep connections with combinatorial topology. We provide an alternative characterization of those tasks by means of the novel concept of continuous tasks, which have an input/output specification that is a continuous function between the geometric realizations of the input and output complex: We state and prove a precise characterization theorem (CACT) for wait-free solvable tasks in terms of continuous tasks. Its proof utilizes a novel chromatic version of a foundational result in algebraic topology, the simplicial approximation theorem, which is also proved in this paper. Apart from the alternative proof of the ACT implied by our CACT, we also demonstrate that continuous tasks have an expressive power that goes beyond classic task specifications, and hence open up a promising venue for future research: For the well-known approximate agreement task, we show that one can easily encode the desired proportion of the occurrence of specific outputs, namely, exact agreement, in the continuous task specification

Geometric, Algebraic, and Topological Combinatorics

The 2019 Oberwolfach meeting "Geometric, Algebraic and Topological Combinatorics" was organized by Gil Kalai (Jerusalem), Isabella Novik (Seattle), Francisco Santos (Santander), and Volkmar Welker (Marburg). It covered a wide variety of aspects of Discrete Geometry, Algebraic Combinatorics with geometric flavor, and Topological Combinatorics. Some of the highlights of the conference included (1) Karim Adiprasito presented his very recent proof of the $g$-conjecture for spheres (as a talk and as a "Q\&A" evening session) (2) Federico Ardila gave an overview on "The geometry of matroids", including his recent extension with Denham and Huh of previous work of Adiprasito, Huh and Katz

Graph Theory

This workshop focused on recent developments in graph theory. These included in particular recent breakthroughs on nowhere-zero flows in graphs, width parameters, applications of graph sparsity in algorithms, and matroid structure results

Bestvina–Brady Morse theory on hyperbolic manifolds

Inspired by the work of Jankiewicz, Norin, and Wise, in this thesis we describe that given a hyperbolic right-angled polytope, a colouring and a set of moves, it produces a hyperbolic manifold M with a map f: M→S¹. We apply this to a family of hyperbolic polytopes studied by Potyagailo and Vinberg, and by analyzing the resulting map we obtain a 5-manifold fibering over the circle, a 6-manifold with a perfect circle-valued Morse function, and a 7-manifold and a 8-manifold which fiber algebraically. These results are joint work with Giovanni Italiano and Bruno Martelli

Third International Conference on Technologies for Music Notation and Representation TENOR 2017

The third International Conference on Technologies for Music Notation and Representation seeks to focus on a set of specific research issues associated with Music Notation that were elaborated at the first two editions of TENOR in Paris and Cambridge. The theme of the conference is vocal music, whereas the pre-conference workshops focus on innovative technological approaches to music notation