In the fiercely competitive arena of the European Research Council’s (ERC) Starting Grants, Junior Professor Manuel Krannich has emerged as a distinguished laureate. As the group head at the Karlsruhe Institute of Technology’s Institute for Algebra and Geometry (IAG), Krannich’s project, titled “Manifolds and Functor Calculus” (MaFC), received a prestigious ERC Starting Grant, securing funding of 1.5 million euros over five years. This accolade highlights not only his academic excellence but also the significant potential of his research, promising to push the boundaries of modern topology and algebra.
Manuel Krannich operates at the cutting edge of algebraic and geometric topology, a realm where the intrinsic properties of spaces that remain invariant under continuous transformations are meticulously studied. His fascination lies primarily with manifolds, intricate structures that locally resemble Euclidean space but globally encapsulate complex shapes akin to the earth’s curvature represented through overlapping maps. His groundbreaking project navigates the interface of manifold theory and functor calculus—a sophisticated mathematical framework that investigates the relationships and transformations between different categories and algebraic structures.
Functor calculus, originally inspired by classical calculus, serves as a powerful tool to analyze functors between categories by approximating them through polynomial-like stages. When applied to manifolds, it unlocks a deeper understanding of their symmetries and structural behaviors in high-dimensional spaces. Krannich’s research delves into the subtle interplay between these symmetries and the algebraic laws governing them, offering new perspectives in both pure mathematics and potentially influencing theoretical physics, particularly in fields like string theory and quantum topology.
Krannich’s approach is notably problem-oriented and methodological innovation lies at the heart of his endeavors. Unlike conventional research that often follows established pathways, his work involves the synthesis of diverse techniques from algebra, geometry, and topology. This synthesis is not merely additive; instead, it reveals unexpected connections and constructs new mathematical apparatuses that deepen our understanding of manifold structures and their algebraic underpinnings. Such a strategy is essential in tackling complex mathematical phenomena that resist straightforward classification or explanation.
The trajectory of Krannich’s career reveals a comprehensive and international academic formation. After receiving his Bachelor’s and Master’s degrees from KIT, he penned his doctoral thesis at the University of Copenhagen, focusing on characteristic classes of bundles of manifolds—objects that encode essential geometric and topological information. His postdoctoral years were spent at internationally renowned institutions, including the University of Cambridge and the University of Münster, where he further honed his expertise in algebraic and geometric topology. In 2022, he solidified his academic role with a junior tenure-track professorship at KIT, leading the Algebraic and Geometric Topology group at IAG.
The ERC Starting Grants aim to empower promising young scientists embarking on independent research careers by providing substantial financial backing and institutional recognition. The 2025 round was notably competitive, with 3,928 applications submitted across Europe. Only 478 projects received funding, reflecting a stringent acceptance rate near 12.2%. Germany was among the leading countries in the program, with 99 recipients. This selectivity underscores the high standards and the transformative potential of the chosen projects, which are envisaged as generating breakthroughs across a wide array of scientific disciplines.
Krannich’s MaFC project stands at the crossroads of manifold theory and higher algebra—fields that underpin much of contemporary mathematics. Manifolds serve as abstract generalizations of curves and surfaces, but in high dimensions, they become vehicles for exploring intricate spatial phenomena and forms. The project’s focus on functor calculus affords an algebraic lens on these complex structures, potentially revealing new invariant properties and symmetry relations. These insights not only enrich theoretical knowledge but may also impact computational topology and geometric analysis.
A critical innovation in Krannich’s work involves the construction of novel invariants of high-dimensional manifolds, linked intricately to the functorial properties of associated algebraic structures. These invariants help classify manifolds and understand their deformation spaces—an area that interfaces with gauge theory, surgery theory, and homotopy theory. The unification of these areas through the technique of functor calculus presents a promising pathway to resolving longstanding open problems in the classification and analysis of manifolds, many of which have resisted previous approaches.
The interdisciplinary nature of Krannich’s research highlights the trend towards the integration of mathematical subfields. By bridging pure algebraic concepts with geometric intuition, the MaFC project exemplifies a paradigm where manifold topology is no longer an isolated discipline but part of a broader algebraic ecosystem that includes category theory, operad theory, and homotopical algebra. Such frameworks provide a language and toolkit to unravel high-dimensional phenomena with greater precision and conceptual clarity.
Beyond theoretical significance, the findings anticipated from the MaFC research may have downstream effects on theoretical physics, especially in areas that model spacetime and fields using manifold structures. The refined understanding of symmetries and algebraic behavior in high-dimensional spaces is key to developing frameworks in quantum field theory, topological quantum computing, and string theory. Thus, Krannich’s research holds the promise of crossing discipline boundaries from pure mathematics to fundamental physics.
The 1.5 million euro funding over five years will enable Krannich to assemble a dynamic research team, procure computational resources, and foster collaborations that accelerate innovation. The ERC grant not only endorses his competence but provides a platform for sustained exploration of mathematically rich, conceptually demanding problems. This support amplifies the impact of his research, increases visibility within the international mathematical community, and cultivates future experts trained under his guidance.
Karlsruhe Institute of Technology (KIT), known as “The Research University in the Helmholtz Association,” offers an inspiring environment for such avant-garde projects. With a multidisciplinary ethos, KIT integrates natural sciences, engineering, economics, and social sciences to address global challenges across energy, mobility, and information technology. Krannich’s appointment and ERC grant reinforce KIT’s standing as an incubator for scientific excellence and innovation, especially within the mathematical sciences.
In sum, Junior Professor Manuel Krannich’s receipt of the ERC Starting Grant for “Manifolds and Functor Calculus” reflects a defining moment in contemporary topology and algebra. His interdisciplinary, methodological, and conceptual contributions promise to push the frontiers of mathematical knowledge and influence related scientific fields, exemplifying the spirit of modern research that transcends traditional boundaries while uncovering the deep structural fabric of mathematical reality.
Subject of Research: Algebraic and geometric topology; manifolds and functor calculus; symmetries and algebraic structures in high-dimensional topology.
Image Credits: Amadeus Bramsiepe, Karlsruhe Institute of Technology (KIT)
Keywords: Manifolds, functor calculus, algebraic topology, geometric topology, ERC Starting Grant, Karlsruhe Institute of Technology, high-dimensional manifolds, algebraic structures, mathematical symmetries, topology, category theory, mathematical research funding
