פעילויות השבוע

We will survey basic tools of project scheduling including Gannt charts, CPM and PERT. We will then consider a new point of view that takes into account the different resources that different potential contractors may have when scheduling the same project. We will also consider the aspects of policies for many similar projects. We will do so taking into account only operational considerations. Nonetheless, we will show that this purely application driven approach can lead to a lot of interesting and diverse mathematics and physics including enumerative combinatorics, Lorentzian geometry, Kardar-Parisi-Zhang processes (Integrable probability) and wave propagation in hyperbolic media. The talk will be self contained.

In this talk I will present some enhancements and generalizations of a criterion for six-functor formalisms first sketched by Voevodsky in 2001. This principle was then implemented by Ayoub in order to show that the stable motivic homotopy theory of quasi-projective schemes has the structure of a six-functor formalism, although it has later been generalized by works of Cisinski, Déglise, Hoyois, Khan, and Ravi, leading to a six-functor formalism of genuine stable motivic homotopy theory on qcqs derived algebraic stacks with separated diagonals and nice stabilizers.

In our framework, we produce six-functor formalism using the cohomological behaviour of smooth maps, closed immersions, and smooth proper maps (where the relevant cohomological property is expressed by a version of Atiyah duality). This is related to recent results of Dauser-Kuijper and Cnossen-Lenz-Linskens, which enhances work of Mann following Liu-Zheng on the construction of six-functor formalisms using the cohomological behaviour of étale maps and proper maps. Our general results are then used to produce a six-functor formalism of complex analytic stable motivic homotopy theory, as well as equivariant analytification functors that are compatible with the six operations.

Tits‘ independence property (P) and geometric density are two properties a group action on a tree can have; Tits showed that the combination of these properties yields interesting simple groups. However, constructing and detecting these properties remained unclear. Burger and Mozes‘s introduction of universal groups gave one rich ”local-to-global“ way to construct groups with (P) by defining their action locally around each vertex. I will present a paper by Colin Reid and Simon Smith which defines local action diagrams, greatly generalizing the Burger-Mozes construction. Local action diagrams turn out to completely classify groups with property (P), as well as to be able to detect geometric density and other global properties of group actions on trees.

Link to the paper: https://link.springer.com/article/10.1007/s00208-026-03412-w

(This talk will be the second part of the Colloquium-Lecture the same week)

We will survey basic tools of project scheduling including Gannt charts, CPM and PERT. We will then consider a new point of view that takes into account the different resources that different potential contractors may have when scheduling the same project. We will also consider the aspects of policies for many similar projects. We will do so taking into account only operational considerations. Nonetheless, we will show that this purely application driven approach can lead to a lot of interesting and diverse mathematics and physics including enumerative combinatorics, Lorentzian geometry, Kardar-Parisi-Zhang processes (Integrable probability) and wave propagation in hyperbolic media. The talk will be self contained.