With funding from an ERC Starting Grant, excellent early career researchers (two to seven years into their post-doc phase) are given the opportunity to pursue an outstanding project idea as part of an independent junior research group.
Funding period
2024–2028
Abstract
Questions involving the scalar curvature bridge many areas inside mathematics including geometric analysis, differential geometry and algebraic topology, and they are naturally related to the mathematical description of general relativity. There are two main flavours of methods to probe the geometry of scalar curvature: One goes back to Lichnerowicz and uses various versions of index theory for the Dirac equation on spinors. The other is broadly based on minimal hypersurfaces and was initiated by Schoen and Yau. On both types of methods there has been tremendous progress over recent years sparked by novel quantitative comparison and rigidity questions due to Gromov and by on-going attempts to arrive at a deeper geometric understanding of lower scalar curvature bounds. In this proposal we view established landmark results, such as the non-existence of positive scalar curvature on the torus, together with the more recent quantitative problems from a conceptually unified standpoint, where a comparison principle for scalar and mean curvature along maps between Riemannian manifolds plays the central role. Guided by this point of view, we aim to develop fundamentally new tools to study scalar curvature that bridge long-standing gaps in between the existing techniques. This includes a far-reaching generalization of the Dirac operator approach expanding upon techniques pioneered by the PI, and novel applications of Bochner-type methods. We will also study analogous comparison problems on domains with singular boundary motivated by a first synthetic characterization of lower scalar curvature bounds in terms of polyhedral domains, and by the general quest for extending the study of scalar curvature beyond smooth manifolds. At the same time, we will treat subtle almost rigidity questions corresponding to the rigidity aspect of our comparison principle.
Funding period
2018–2024
Abstract
The bottom-up assembly of tissue from cellular building blocks constitutes a promising, yet highly challenging approach to engineer complex tissues. The challenge lies in controlling cell-cell interactions, which determine how cells organize with respect to each other, how they work together and consequently whether such a multicellular architecture will be functional. The limited spatial and temporal control over cell-cell interactions current biological and chemical approaches provide severely restricts bottom-up tissue engineering. Here, I propose a new way to control cell-cell interactions. I aim to regulate cell-cell interactions with visible light using proteins that reversibly homo- or heterodimerize under blue or red light. These photoswitchable cell-cell interactions provide sustainable, non-invasive, dynamic and reversible control over cell-cell interactions with unprecedented spatial and temporal resolution. First of all, we will focus on various light dependent protein interactions to mediate cell-cell contacts. The detailed characterization (strength, dynamics, interaction modes and orthogonality) of these new photoswitchable cell-cell interactions will provide the framework for the bottom-up construction of tissue-like structures. Secondly, we will use these photoswitchable cell-cell interactions to assemble cells into multicellular architectures with predictable and programmable organization. The dynamic and reversible nature of the photoswitchable contacts will allow us to locally alter interactions at any point in time, to rearrange and obtain asymmetric multicellular structures, which are typical of tissues. Finally, we will also explore how the photoswitchable cell-cell interactions alter cell behavior and signaling. Ultimately, this will pave the way for the bottom-up assembly of multicellular architectures, enabling us to control precisely and dynamically their organization in space and time as well as regulate how cells work together.
Prof Dr Seraphine Valeska Wegner at the University of Münster
| Year | Recipient | Subject area |
|---|---|---|
| 2016 | Prof Dr Gustavo Fernandez Huertas | chemistry |
| 2015 | Prof Dr Angela Schwering | geoinformatics |
| 2015 | Prof Dr Martin Salinga | physics |
| 2014 | Prof Dr Björn Braunschweig | chemistry |
| 2013 | Prof Dr Gustav Holzegel | mathematics |
| 2013 | Prof Dr Ryan Gilmour | chemistry |
| 2011 | Prof Dr Eva Viehmann | mathematics |
| 2010 | Prof Dr Frank Glorius | chemistry |
| 2009 | Prof Dr Thorsten Quandt | communication sciences |