This talk deals with product systems over closed, convex cones in $\mathbb{R}^{d}$.
In this talk, we describe the structure of a decomposable product system over a closed convex cone in $\mathbb{R}^{d}$. We explicitly compute the cohomology groups involved in the description of a decomposable product system for a specific example.
We show that the CAR functor which maps an isometric representation of a cone to the corresponding CAR flow is injective. We also characterise type $I$ CAR flows associated to isometric representations with commuting range projections. Finally, we compute the gauge group and index of these type $I$ CAR flows.
This is pre-synopsis seminar.
The size of the nucleus scales robustly with cell size so that the nuclear-to-cell size—the N/C ratio—is maintained during growth in many cell types. To address the fundamental question of how cells maintain the size of their organelles despite the constant turnover of proteins and biomolecules, we consider a model based on osmotic force balance predicts a stable nuclear-to-cell size ratio, in good agreement with experiments on the fission yeast Schizosaccharomyces pombe. We model the synthesis of macromolecules during growth using chemical kinetics and demonstrate how the N/C ratio is maintained in homeostasis. We compare the variance in the N/C ratio predicted by the model to that observed experimentally.
meet.google.com/bgr-jyoj-wdc
Biology Seminar | IMSc Webinar
Oct 21 14:00-15:00
Bharatram Rangarajan | Hebrew University of Jerusalem
Expansion in groups (or their Cayley graphs) is a valuable and well-studied notion in both mathematics and computer science, and describes a robust form of connectivity of graphs (a gap property of fixed points of representations of groups). It can also be interpreted as a graph on which connectivity is efficiently locally testable.
Group stability, on the other hand, is concerned with another robustness property- but of homomorphisms (or representations). Namely, is an almost-homomorphism of a group necessarily a small deformation of a homomorphism? This too can be interpreted as a local testability property
of group homomorphisms in the right settings.
Expansion in groups (or property (T)) had been classically reformulated in the language of algebraic topology- in terms of the vanishing of the first cohomology of the group. In this talk we will see approaches in capturing group stability in terms of the vanishing of a second cohomology of the group, motivating higher-dimensional generalizations of expansion.
Based on joint (previous and ongoing) work with Monod, Glebsky, Lubotzky, Fournier-Facio, Dogon.