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• Arithmetic Geometry
• Coding Theory
• Galois Representations
• +3 more

Jérémy Le Borgne is an Assistant Professor in the Department of Mathematics at ENS Rennes, where he has held faculty positions since 2012. He is a core member of IRMAR's Geometry and Effective Algebra Team, contributing to France's national mathematics research infrastructure through this CNRS-affiliated institute. His dual role encompasses advanced teaching from undergraduate to Agrégation levels and active research at the intersection of algebra, geometry, and computation. His educational foundation includes: ENS Cachan - Antenne de Bretagne (2005-2009) PhD in Mathematics, University of Rennes 1 (2009-2012), supervised by Xavier Caruso and David Lubicz Le Borgne's research pioneers computational approaches to arithmetic geometry, with seminal work on Ore polynomials enabling breakthroughs in Gabidulin code construction for error correction. His investigations into p-adic Galois representations bridge number theory and algorithm design, while recent studies of Hall bases for free Lie algebras reveal deep combinatorial structures applicable to differential equations. This tripartite focus creates synergies between theoretical mathematics and practical computation. Analysis of his 2010-2023 publications reveals consistent progression from foundational number theory (Ax-Sen-Tate theorem optimization) toward increasingly computational work, with 2022-2023 papers emphasizing algorithmic Lie algebra structures and nonlinear system expansions. His research demonstrates strong continuity in non-commutative algebra applications while expanding into new combinatorial territories. No formal awards are documented in public materials, though his publication record in high-impact journals like Journal of Algebra and Comptes Rendus Mathématique indicates peer recognition. His teaching portfolio spans advanced algebra courses and Agrégation preparation, with documented outreach including Lebesgue lectures and Olympiad training. As a research supervisor, Le Borgne integrates students through IRMAR's collaborative environment, though specific advisee counts aren't public. His Geometry and Effective Algebra Team provides infrastructure for computational mathematics projects, with recent work suggesting active funding for skew polynomial and Lie algebra research. The lab maintains close ties with University of Rennes 1's mathematics department, facilitating resource sharing across Rennes' academic ecosystem.

• Computational mechanics
• Finite element method
• Uncertainty quantification
• +6 more

Prof. Dr.-Ing. habil. Kai Willner is a distinguished Professor at the Chair of Engineering Mechanics within the Department of Mechanical Engineering at Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU). His research spans multiple domains of computational mechanics with significant contributions to structural dynamics, uncertainty quantification, and biomechanics. His current work focuses on innovative applications of fuzzy arithmetic in engineering systems and the mechanics of brain tissue. Principal Investigator for SFB 1540 EBM (Erforschung der Mechanik des Gehirns) Lead researcher on multiple DFG-funded projects including polymorphic uncertainty modeling Active participant in international collaborations on structural dynamics Member of the research group FOR 2271 on process-oriented tolerance management Willner's research interests center on computational mechanics with emphasis on uncertainty quantification , fuzzy-stochastic finite element methods , contact mechanics , and brain biomechanics . His work addresses fundamental challenges in modeling systems with uncertain parameters, particularly in heterogeneous materials and biological systems. His research group develops advanced computational frameworks that integrate fuzzy arithmetic with traditional finite element methods to handle epistemic and aleatoric uncertainties simultaneously, with applications ranging from microstructural analysis to brain mechanics. Analysis of his recent publications reveals a strong trend toward interdisciplinary research, particularly at the intersection of computational mechanics and neuroscience. His work on brain mechanics within the SFB 1540 EBM project represents a significant shift toward biomedical applications of traditional mechanical engineering methods. His publications consistently demonstrate expertise in vibration analysis, structural dynamics, and uncertainty quantification, with increasing focus on applying these methods to biological systems and complex material behaviors. Prof. Willner has secured substantial third-party funding from the German Research Foundation (DFG), including multiple collaborative research center (SFB/TRR) projects, research units (FOR), and individual grants. His current major projects include the SFB 1540 EBM (2023-2026) investigating brain mechanics, and continuing work on polymorphic uncertainty modeling in heterogeneous materials. Within the SFB 1540 EBM consortium, Willner leads research on model-based matching of ex vivo and in vivo test data (project X01), focusing on resolving contradictions in mechanical properties of ultraweak brain tissue materials across different testing modalities. His team develops continuum-based simulation models to unify various experimental observations into a coherent mechanical framework for brain tissue.

Panagiotis ManoliosView profile

Professor

• Formal Methods
• Program Verification
• Theorem Proving
• +5 more

Panagiotis (Pete) Manolios is a Professor in the Department of Computer Science within Northeastern University's College of Engineering in Boston. He leads the Northeastern University Formal Methods (NUFM) research group and maintains an active research program with multiple current PhD students. His primary affiliation is with the College of Computer Science (CCS) at Northeastern University, where he holds a tenured faculty position. Manolios' research focuses on formal methods with particular emphasis on program verification, theorem proving, and safety analysis of systems. His work spans several key areas including floating-point program analysis, resource-aware program verification, protocol verification, and safety-critical systems. He has developed significant tools and methodologies such as ACL2s (a powerful theorem prover) and pioneered approaches for analyzing numeric stability in compiler optimizations. His recent publications demonstrate substantial activity in formal verification, with particular focus on numeric stability analysis, invariant discovery through gamification, and model-based safety analysis of complex system architectures. These works reflect a consistent research trajectory toward making formal verification more practical and applicable to real-world systems, especially those with safety-critical requirements. Manolios has received recognition through multiple NSF grants including the SaTC: CORE: Medium collaborative project on bridging the gap between protocol design and implementation. His work on confidentiality and integrity of deep neural networks represents cutting-edge research at the intersection of formal methods and AI security. He has successfully mentored numerous PhD students who have gone on to positions at major technology companies including Google, Facebook, Intel, and MathWorks. His students' dissertations cover diverse topics within formal methods, from rank-polymorphic programming languages to resource-aware program analysis. Manolios directs several significant research projects including ACL2s (a powerful theorem prover), CID: Confidentiality and Integrity of Deep Neural Networks, Compilation-Dependent Security Properties of Software, and Platform Dependencies of Floating-Point Programs. These projects address fundamental challenges in making formal verification more practical and applicable to real-world systems.