Symplectic geometry combines a broad spectrum of interrelated disciplines lying in the mainstream of modern mathematics. The past two decades have given rise to several exciting developments in this field, which introduced new mathematical tools and opened challenging new questions. Nowadays symplectic geometry reaches out to an amazingly wide range of areas, such as differential and algebraic geometry, complex analysis, dynamical systems, as well as quantum mechanics, and string theory. Moreover, symplectic geometry serves as a basis for Hamiltonian dynamics, a discipline providing efficient tools for modeling a variety of physical and technological processes, such as orbital motion of satellites (telecommunication and GPS navigation), and propagation of light in optical fibers (with significant applications to medicine). The proposed research is composed of several innovative studies in the frontier of symplectic geometry and Hamiltonian dynamics, which are of highly significant interest in both fields. These studies have strong interactions on a variety of topics that lie at the heart of contemporary symplectic geometry, such as symplectic embedding questions, the geometry of Hofer’s metric, Lagrangian intersection problems, and the theory of symplectic capacities. My research objectives are twofold. First, to solve the open research questions described below, which I consider to be pivotal in the field. Some of these questions have already been studied intensively, and progress toward solving them would be of considerable significance. Second, some of the studies in this proposal are interdisciplinary by nature, and use symplectic tools in order to address major open questions in other fields, such as the famous Mahler conjecture in convex geometry. My goal is to deepen the connections between symplectic geometry and these fields, thus creating a powerful framework that will allow the consideration of questions currently unattainable.

Understanding how the Milky Way arrived at its present state requires a large volume of precision measurements of our Galaxy’s current makeup, as well as an empirically based understanding of the main processes involved in the Galaxy’s evolution. Such data are now about to arrive in the flood of quality information from Gaia and SDSS-V. The demography of the stars and of the compact stellar remnants in our Galaxy, in terms of phase-space location, mass, age, metallicity, and multiplicity are data products that will come directly from these surveys. I propose to integrate this information into a comprehensive picture of the Milky Way’s present state. In parallel, I will build a Galactic chemical evolution model, with input parameters that are as empirically based as possible, that will reproduce and explain the observations. To get those input parameters, I will measure the rates of supernovae (SNe) in nearby galaxies (using data from past and ongoing surveys) and in high-redshift proto-clusters (by conducting a SN search with JWST), to bring into sharp focus the element yields of SNe and the distribution of delay times (the DTD) between star formation and SN explosion. These empirically determined SN metal-production parameters will be used to find the observationally based reconstruction of the Galaxy’s stellar formation history and chemical evolution that reproduces the observed present-day Milky Way stellar population. The population census of stellar multiplicity with Gaia+SDSS-V, and particularly of short-orbit compact-object binaries, will hark back to the rates and the element yields of the various types of SNe, revealing the connections between various progenitor systems, their explosions, and their rates. The plan, while ambitious, is feasible, thanks to the data from these truly game-changing observational projects. My team will perform all steps of the analysis and will combine the results to obtain the clearest picture of how our Galaxy came to be.

Electronic skin is seen as the next generation of wearable technology, ideally made of thin, self-powered, self-healing and flexible electronics able to mimic or augment natural skin functionalities. Smart prostheses to give amputees the sense of touch, completely biocompatible skin patches for wound care, or new on-skin drug delivery systems are only few e-skin applications that are being explored by the research community for the last several years. The main problems hindering the e-skin revolution are the lack of fully biocompatible piezoelectric materials, which are the basic component of any e-skin system, and the unavailability of adequate energy harvesting technology, which allows realizing an extremely compact and energy autonomous device. In the PepZoSkin project, we propose to develop an ultra-thin, flexible, self-powered e-skin device that combines innovative piezoelectric materials, microelectronics and sensors for wearable and implantable applications. In the frame of the main ERC Grant, we have synthesized radically new peptide-based materials with exceptional piezoelectric performance, unprecedented mechanical properties, and inherent biocompatibility, and used these materials as an active layer in basic sensing devices. In this PoC project, based on these promising results, we will further develop these basic devices to a TRL5 self-powered biocompatible core technology for an e-skin device. Our vision is to turn our core material into a key component of next generation compact and self-powered wearable and implantable systems, targeting biomedical applications as a market entry point. The e-skin market is expected to be worth more than 15 B$ by 2028. During this PoC project, together with medical, business and industrial stakeholders, we will focus on the validation of the technological and business feasibility of turning our e-skin prototype into a marketable competitive product, which will be developed and commercialized by a spin-off comp

Tissue regeneration has emerged as a promising novel therapy for various disease conditions. A key requirement for the implementation of this advanced approach is the efficient, reliable and reproducible growth of 3D cell cultures, including organoid structures. State-of-the-art 3D culture media support the growth of such cultures, yet exhibit several key setbacks, including low reproducibility and limited modularity. Moreover, no commercial piezoelectric media are currently available, thus prohibiting the option of inducing electrical stimulation of the cells via mechanical stimuli, similar to the in vivo function of several tissues. Here, we aim to develop PiezoGel, a biocompatible, reproducible, controllable and piezoelectric medium for 3D cell cultures. The newly-designed medium will be based on two components, a cell-supporting hydrogel and a piezoelectric self-assembled peptide structure. In the scope of the BISON-694426 Advanced ERC project, we identified promising molecular building blocks for each of these components. The Proof of Concept project will focus both on technological development of the PiezoGel matrix and on business feasibility. Thus, the formulation of the newly-designed cell medium will be optimized, and the resulting matrix will be examined for various properties, including mechanical rigidity and piezoelectricity. The growth of diverse organoid cultures, as well as stem cell differentiation, will be further tested and calibrated. Relevant stakeholders will be approached allowing to map the product requirements and expected features directly from the users. In parallel, the regulatory compliance of the PiezoGel medium will be verified, and the relevant material and methodologies will be patented. We envision diverse applications for the PiezoGel technology, including establishing 3D cell cultures as drug development platforms, basic research exploration, and further advancement of the tissue regeneration field.