Activities This Week
BGU Probability and Ergodic Theory (PET) seminar
Random temporo-spatial differentiations
May 23, 11:10—12:00, 2024, -101
Speaker
Adian Young (BGU)
Abstract
Temporo-spatial differentiations are ergodic averages on a probabilistic dynamical system $(X, \mu, T)$ taking the form $\left( \frac{1}{\mu(C_k)} \int_{C_k} \frac{1}{k} \sum_{j = 0}^{k - 1} T^j f \mathrm{d} \mu \right)_{k = 1}^\infty $ where $C_k \subseteq X$ are measurable sets of positive measure, and $f \in L^\infty(X, \mu)$. These averages combine both the dynamics of the transformation and the structure of the underlying probability space $(X, \mu)$. We will discuss the motivations behind studying these averages, results concerning the limiting behavior of these averages and, time permitting, discuss generalizations to non-autonomous dynamical systems. Joint work with Idris Assani.
Colloquium
The Toda Lattice, Parallelohedra, and Symplectic Balls
May 28, 14:30—15:30, 2024, Math -101
Speaker
Yaron Ostrover (Tel Aviv University)
Abstract
In this talk, we explain how the classical Toda lattice model, one of the earliest examples of nonlinear completely integrable systems, can be used to demonstrate that certain configurations in the classical phase space are symplectic balls in disguise. No background in symplectic geometry is needed. The talk is based on joint work with Vinicius Ramos and Daniele Sepe.
AGNT
Supersingular elliptic curves, quaternion algebras and some applications to cryptography
May 29, 14:10—15:00, 2024, -101
Speaker
Eyal Goren (McGill University)
Abstract
Part of the talk is expository: I will explain how supersingular isogeny graphs can be used to construct cryptographic hash functions and survey some of the rich mathematics involved. Then, with this motivation in mind, I will discuss two recent theorems by Jonathan Love and myself. The first concerns the generation of maximal orders by elements of particular norms. The second states that maximal orders of elliptic curves are determined by their theta functions.