Integrated Calendar

<p>To reach real sustainability for today’s preferred ‘sustainable’ types of energy, viz. electrical ones as solar (photovoltaic, PV, &amp; wind; thermal solar &amp; hydroelectric, which also store) and chemical ones as reduced CO2 [food], H2 &amp; batteries,<em> also the enabling&nbsp;materials&nbsp;need to be sustainable</em>. Alas, mostly they are not, and that is a problem.&nbsp; As sustainability implies long life spans, it is thought to be incompatible with modern society’s pillars of&nbsp;<em>continuing growth &amp; consumerism. </em>This is a serious issue that, while outside the scope of this lecture<em>,</em> adds to the science &amp; technology challenge to return to repairable&nbsp;devices, and&nbsp;repair-friendly designs, with as best option <em>self-healing</em>,** the most relevant option for micro- and macro-electronic device materials. The sustainable materials challenge is reminiscent of the sustainable energy one, i.e., we need to go from science fiction to reality. Starting&nbsp;with&nbsp;bio-solar conversion, via ionics and organic material self-healing, we get to inorganic light&nbsp;ßà&nbsp;electricity conversion compounds. Emphasis will be on PV materials, as in hindsight those already provide (confirm) some material self-healing criteria. Once (many) more experimental properties data will become available (&amp; accessible), deep learning may guide further discovery.</p>

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.

<p>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 &amp; 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 &amp; AI working group at the BloodPAC non-profit organization, and on the advisory board of a few companies.&nbsp;</p><p>&nbsp;</p>