Activities This Week
AGNT
Quadratic Chabauty, p-adic adelic metrics and local contributions, Part II
Feb 14, 14:10—15:00, 2024, -101
Speaker
Amnon Besser (Ben Gurion University)
Abstract
Continuing with the topics of last week’s talk, I will explain how one can use this to compute the “local contributions away from p” for Quadratic Chabauty, which are crucial for computations.
BGU Probability and Ergodic Theory (PET) seminar
On the Girth of Graph Lifts
Feb 15, 11:10—12:00, 2024, -101
Speaker
Shlomo Hoory
Abstract
The size of the smallest $k$-regular graph of girth $g$ is denoted by the well studied function $n(k,g)$. We suggest generalizing this function to $n(H,g)$, defined as the smallest size girth $g$ graph covering the, possibly non-regular, graph $H$. We prove that the two main combinatorial bounds on $n(k,g)$, the Moore lower bound and the Erdos-Sachs upper bound, carry over to the new setting of lifts, even in their non-asymptotic form.
We also consider two other generalizations of $n(k,g)$: i) The smallest size girth $g$ graph sharing a universal cover with $H$. We prove that it is the same as $n(H,g)$ up to a multiplicative constant. ii) The smallest size girth $g$ graph with a prescribed degree distribution. We discuss this known generalization and argue that the new suggested definitions are superior.
We conclude with experimental results for a specific base graph and with some conjectures and open problems.
Operator Algebras and Operator Theory
Isometric dilations for representations of product systems
Feb 19, 14:00—15:00, 2024, 201
Speaker
Sibaprasad Barik (Technion)
Abstract
In this talk, I will discuss isometric dilations of completely contractive representations (in short c.c. representation) of product systems (of $W^∗$-correspondences) over the semigroup $\mathbb{Z}^n_{+}$. It is known that for $n = 1, 2$, c.c. representations of such product systems always have isometric dilations and the result fails for $n > 2$, in general. We will see that under certain positivity and pureness conditions c.c. representations of product systems over $\mathbb{Z}^n_{+}$ have isometric dilations, also we will see an explicit form of the dilations. If time permits, I will discuss some applications of it.
This talk is based on joint work with Monojit Bhattacharjee and Baruch Solel.