8-9 September 2016 Place: Centro De Giorgi, Pisa. List of Speakers: -Toshiyuki Akita (Hokkaido University) -Pauline Bailet (Bremen University) -Filippo Callegaro (Pisa University) -Emanuele Delucchi (Fribourg University) -Mario Salvetti (Pisa University) -Simona Settepanella (Hokkaido University) Timetable: THURSDAY 8 15.00-16.00 Simona Settepanella 16.30-18.00 Emanuele Delucchi FRIDAY 9 10.00-11.00 Pauline Bailet 11.30-12.30 Filippo Callegaro 14.00-15.00 Toshiyuki Akita 15.30-16.30: Mario Salvetti Titles and abstracts: -Toshiyuki Akita (Hokkaido University) Title: Cohomology of Coxeter groups and related groups. Abstract: After a brief introduction of group cohomology, I will explain what is known about the cohomology of Coxeter groups and related groups, including my recent results. -Pauline Bailet (Bremen University) Title: Aomoto complexes and monodromy of Milnor fibers of hyperplane arrangements Abstract: In the first part of the course, I will recall some geometrical and combinatorial objects associated to an hyperplane arrangement such as complement, Milnor fiber, Orlik-Solomon algebra and Aomoto complex. Then I will talk about local system cohomology of complements, cohomology of Milnor fibers and monodromy. In the second part of the course, we will study a graph which is determined by the arrangement's combinatorics. It has been conjectured by Salvetti and Serventi that the connectivity of this graph implies the triviality of the monodromy on the Milnor fiber for a complex line arrangement. We will discuss some particular cases, relying on a key inequality du to Papadima and Suciu, that involves local system cohomology of complements and cohomology of Aomoto complexes with finite field coefficients. -Filippo Callegaro (Pisa University) Title: Cohomology of braid groups and generalizations Abstract: Braid groups appear in strict relations with hyperplane arrangements and their construction can be extended to many generalisations. In this talk we will introduce classical braid groups and their generalization associated to complex hyperplane arrangements, presenting some methods for the computation of their cohomology. We will start with a survey on classical results and reserve some time for more recent computations. -Emanuele Delucchi (Fribourg University) Title: Matroids and more. Abstract: Matroid theory is a structurally rich branch of combinatorics with pervasive connections with geometry, topology, and algebra. In this expository talk I will gently introduce the notion of matroid and illustrate some of applications. Then — with an view towards topological applications — I will go on to more refined combinatorial structures such as oriented matroids. I will conclude with a recent and already thriving new character among matroidal theories: Baker's matroids over hyperfields. Time permitting, I will also outline some of the main open research directions revolving around these objects. -Mario Salvetti (Pisa University) Title: A group-theoretical approach to the monodromy of arrangements. Abstract: The complement to an arrangement of central hyperplanes in the complex space fibers over C^* with Milnor fiber F whose homology is not known in general. The arrangement will be called "a-monodromic" if the geometric monodromy acts trivially on the first homology of the Milnor fiber. We consider the problem of determining the a-monodromicity of the arrangement, giving some conjecture, and using a group theoretical approach to solve it in some cases. -Simona Settepanella (Hokkaido University) Title: Discrete Morse Theory and minimal CW-complex. Abstract: A number of questions in mathematics lead to the problem of analysing the topology of simplicial (and CW) complexes. As an answer to this, Forman introduced at the beginning of 2000 the Discrete Morse Theory. In this talk, we will introduce the basic facts on this theory that provided to be incredibly useful. Organizers: Giovanni Gaiffi (Pisa University), Michele Torielli (Hokkaido University). Contact: Michele Torielli (torielli [at] math.sci.hokudai.ac.jp) |