לוח שנה משולב

Let $\mathcal{R} : L^\infty(\mathbb{S}^{n-1}) \rightarrow L^\infty(\mathbb{S}^{n-1})$ denote the spherical Radon transform, defined as $\mathcal{R}(f)(\theta) = \int_{\mathbb{S}^{n-1} \cap \theta^{\perp}} f(u) d\sigma(u)$. A long-standing question in non-linear harmonic analysis due to Lutwak, Gardner, and Fish--Nazarov--Ryabogin--Zvavitch, is to characterize those non-negative $\rho \in L^\infty(\mathbb{S}^{n-1})$ so that $\mathcal{R}(\rho^{n-1}) = c \rho$ when $n\geq 3$. We show that this holds iff $\rho$ is constant, and moreover, $\mathcal{R}(\mathcal{R}(\rho^{n-1})^{n-1}) = c \rho$ iff $\rho$ is either identically zero or is the reciprocal of some Euclidean norm. Our proof recasts the problem in a geometric language using the intersection body operator $I$,  introduced by Lutwak following the work of Busemann, which plays a central role in the dual Brunn-Minkowski theory. We show that for any star-body $K$ in $\mathbb{R}^n$ when $n \geq 3$, $I^2 K = c K$ iff $K$ is a centered ellipsoid, and hence $I K = c K$ iff $K$ is a centered Euclidean ball. To this end, we interpret the iterated intersection body equation as an Euler-Lagrange equation for a certain volume functional under radial perturbations, derive new formulas for the volume of $I K$, and introduce a continuous version of Steiner symmetrization for Lipschitz star-bodies, which (surprisingly) yields a useful radial perturbation exactly when $n\geq 3$.

Joint work with Shahar Shabelman and Amir Yehudayoff.

I will explain the conjectured duality between double-scaled SYKat infinite temperature and the static patch of a particularversion of JT-de Sitter space. The conjectured duality raises thequestion of what particle physics is like in the bulk of the staticpatch.The answer: I will give it in the lecture.

Horizontal gene transfer (HGT) is a central mechanism in bacterial evolution, allowing organisms to exchange genetic material outside of traditional reproduction. This process is a key driver of antibiotic resistance and the emergence of virulence traits.Unlike vertical inheritance, HGT leads to non-tree-like evolutionary relationships, motivating a network-based view of microbial evolution.In this talk I will present a minimal model for HGT and show how it captures distinctive statistical features of bacterial genomes. By combining the model with the genomic data, I infer general properties of the underlying HGT networks. FOR THE LATEST UPDATES AND CONTENT ON SOFT MATTER AND BIOLOGICAL PHYSICS AT THE WEIZMANN, VISIT OUR WEBSITE: https://www.biosoftweizmann.com/ 

2D materials offer vast variability, with nearly unlimited combinations of composition, properties, and structures. This versatility can be further extended through layer stacking and twisting, enabling unique electronic and mechanical behaviours. The diversity in chemical composition necessitates various approaches for their crystal growth and chemical modifications.This discussion will cover the synthesis and crystal growth methods for different classes of 2D materials, including chalcogenides, halides, chalcogen-halides, and beyond. The impact of experimental conditions on their structural and functional properties will also be explored.Exfoliation techniques, particularly those involving intercalation, provide a pathway for obtaining large-area monolayer flakes and bulk intercalated compounds with tailored properties. The effects of these methods on material characteristics will be examined. Additionally, chemical exfoliation methods for materials with layered structures held together by covalent bonds will be presented.Finally, the applications of 2D materials across multiple fields will be discussed, including electronics, energy storage, catalysis, and beyond. This overview aims to highlight the transformative potential of 2D materials from fundamental synthesis to practical technological implementations.

Dr. Asaf Zviran is Experienced entrepreneur, scientist, and executive with over 20 years of product development, business development, and team management in the defense and life science industries. Previously, Dr. Zviran was the Co-Founder, CEO & CSO of C2i Genomics, leading the company from an academy spin-off to a global industry leader and to a successful exit. Currently, Asaf is serving as co-founder and CEO of Prism AI Therapeutics, an AI-driven biomarker discovery company, co-chair of the Multi-Omics & AI working group at the BloodPAC non-profit organization, and on the advisory board of a few companies.