![]() ![]() 2D Euclidean geometry is defined by rigid transformations (modeled as the isometry group) that preserve areas, distances, and angles, and thus also parallelism. K lein’s Erlangen Programme approached geometry as the study of properties remaining invariant under certain types of transformations. Importantly, the Erlangen Programme was limited to homogeneous spaces and initially excluded Riemannian geometry. ![]() Thus, the group of rigid motions leads to the traditional Euclidean geometry, while affine or projective transformations produce, respectively, the affine and projective geometries. Klein used the formalism of group theory to define such transformations and use the hierarchy of groups and their subgroups in order to classify different geometries arising from them. The breakthrough insight of Klein was to approach the definition of geometry as the study of invariants, or in other words, structures that are preserved under a certain type of transformations ( symmetries). However, these constructions had quickly diverged into independent and unrelated fields, with many mathematicians of that period questioning how the different geometries are related to each other and what actually defines a geometry. For the first time in nearly two thousand years after Euclid, the construction of projective geometry by Poncelet, hyperbolic geometry by Gauss, Bolyai, and Lobachevsky, and elliptic geometry by Riemann showed that an entire zoo of diverse geometries was possible. The nineteenth century had been remarkably fruitful for geometry. Image: Wikipedia/University of Michigan Historical Math Collections. The team’s initial focus is on development of therapeutics that enhance host tolerance to infections, as part of a DARPA-funded THoR research program.Felix Klein and his Erlangen Programme. His independent laboratory (2000-2007 at Forsyth Institute, Harvard 2008-present at Tufts University) develops new molecular-genetic and conceptual tools to probe large-scale information processing in regeneration, embryogenesis, and cancer suppression.Īt the Wyss Institute, he collaborates with Donald Ingber and James Collins on a program focused on development of a highly multiplexed, microfluidic, Xenopus embryo culture system that will enable discovery of new drug targets and development of therapeutics when combined with multi-omics and an integrated bioinformatics pipeline. He did post-doctoral training at Harvard Medical School (1996-2000), where he began to uncover a new bioelectric language by which cells coordinate their activity during embryogenesis. degrees, in CS and in Biology and then received a PhD from Harvard University. To explore the algorithms by which the biological world implemented complex adaptive behavior, he got dual B.S. He attended Tufts University, interested in artificial intelligence and unconventional computation. ![]() Prior to college, Michael Levin worked as a software engineer and independent contractor in the field of scientific computing. Using these insights to enable new capabilities in regenerative medicine and engineering.Creating next-generation AI tools for helping scientists understand top-down control of pattern regulation (a new bioinformatics of shape) and.Understanding how somatic cells form bioelectrical networks for storing and recalling pattern memories that guide morphogenesis.His group’s focus is on understanding the biophysical mechanisms that implement decision-making during complex pattern regulation, and harnessing endogenous bioelectric dynamics toward rational control of growth and form. Recent honors include the Scientist of Vision award and the Distinguished Scholar Award. Michael Levin, a Distinguished Professor in the Biology department at Tufts, holds the Vannevar Bush endowed Chair and serves as director of the Allen Discovery Center at Tufts and the Tufts Center for Regenerative and Developmental Biology.
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