פעילויות השבוע

In their paper, Frączyk and Gelander prove a conjecture by Margulis: for a higher-rank simple Lie group $G$, a discrete subgroup has an infinite injectivity radius if and only if it has infinite covolume. The novel methods used to resolve this rely on ergodic theory—specifically, analyzing random walks on the space of discrete subgroups, alongside new stiffness and rigidity results for these stationary measures. In this talk, I will introduce the foundational definitions and present an outline of the main arguments used to prove the conjecture.

Link to paper

The covering radius of a shift space is a quantity of interest for information-theoretic applications of data transmission over noisy channels. In this talk we will explain what is the covering radius of a sofic shift and why people care about it. We will outline a proof that the covering radius of a primitive sofic shift is always a rational number, and outline an algorithm to compute the covering radius from a labeled graph presentation. We will also briefly explain how these results relate to dynamics, to a certain zero-sum two-player game and to an old meta-conjecture about typical ground states in statistical mechanics. The notions will be defined, no specific background assumed. Based on joint work with Aidan Young as in https://arxiv.org/abs/2603.21449, and previous joint work with Dor Elimelech and Moshe Schwartz as in https://ieeexplore.ieee.org/document/10360152

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.