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Philipp LückeView profile

Researcher

• Mathematical Logic
• Set Theory
• Large Cardinals
• +6 more

Philipp Lücke is a Heisenberg Fellow and Privatdozent at the Department of Mathematics, University of Hamburg, where he conducts research in mathematical logic and set theory. He is a member of the research group Mathematical Logic and Interdisciplinary Applications of Logic . Research Interests: His work centers on advanced topics in set theory, including large cardinals, infinitary combinatorics, definability at higher cardinals, and structural reflection. He investigates interactions between strong axioms of infinity, forcing, inner model theory, and descriptive set-theoretic methods in generalized Baire spaces. The most recent publications reflect a consistent focus on the interplay between definability, reflection principles, and large cardinal axioms. Key trends include the analysis of structural reflection across the large cardinal hierarchy, Σ₁-definability at uncountable cardinals, and the behavior of ideals and clubs under forcing extensions. His work often connects model-theoretic and combinatorial properties with foundational questions in set theory. Scientific Awards and Recognition: Heisenberg Fellowship from the German Research Foundation (DFG) Member of the Editorial Board of Zeitschrift für Mathematische Logik und Grundlagen der Mathematik Supervision and Grants: Lücke supervises doctoral students, including Dr. Ana Njegomir. He leads multiple funded research projects, such as the DFG project Complexity and Definability at Higher Cardinals (LU2020/1-1), the Heisenberg Project Definability and Singular Cardinals , and the MSCA project Strong Axioms of Infinity - Frameworks, Interactions and Applications (SAIFIA) . These projects highlight his role as an independent principal investigator in foundational mathematics. Laboratories and Research Groups: He is an active member of the Mathematical Logic and Interdisciplinary Applications of Logic research group at the University of Hamburg, contributing to seminars, workshops, and collaborative research in set theory and logic.

• Differential Geometry
• Geometric Topology
• Classical Field Theories
• +3 more

Modesto Ramon Salgado Seco is a Professor in the Department of Mathematics at the University of Santiago de Compostela's Faculty of Mathematics. He is affiliated with the Galician Mathematical Research and Technology Center (CITMAga) and specializes in Geometry and Topology, particularly Differential Geometry and k-Symplectic Field Theories. He earned his doctorate from USC in 1984 with a thesis on differential geometry under the supervision of Dr. Manuel de Leon. His research focuses on differential geometric structures applied to classical field theories, with expertise in k-symplectic manifolds, Lagrangian mechanics, and geometric approaches to field equations. Primary research areas include: Symplectic and polysymplectic manifold reduction techniques Hamilton-Jacobi theory in field contexts Nonholonomic constraint systems Symmetry analysis in Lagrangian formalisms Geometric structures in higher-order tangent bundles His publications demonstrate consistent focus on geometric methods in mathematical physics, particularly developing formal frameworks for field theories using symplectic geometry. Recent work (2010-2016) emphasizes k-symplectic and k-cosymplectic approaches to field equations, constraint systems, and reduction theory, while earlier foundational work established geometric structures for higher-order tangent manifolds.

• Complex Systems
• Chaos Theory
• Network Science
• +16 more

Murilo da Silva Baptista is a Reader at the Institute for Complex Systems and Mathematical Biology , within the School of Natural and Computing Sciences at the University of Aberdeen . He has been with the university since 2009, initially as a Senior Lecturer and promoted to Reader in 2014. He is actively accepting PhD students in Physics, Mathematics, and Engineering, and his research is internationally recognized in the fields of complex systems and chaos theory. His research focuses on understanding the relationship between function—such as information processing, collective behavior, and synchronization—and structure in large networked complex systems. He applies analytical methods, data science, nonlinear time series analysis, and machine learning to model systems in neuroscience, smart engineering, and Earth sustainability. He is a leading scientist in chaos-based communication, demonstrating how chaotic signals can enable smart and secure wireless and underwater communication systems. His work includes theoretical developments in phase definition in chaotic oscillators, chaos-based cryptography using Poincaré return times, and the discovery of phenomena like Collective Almost Synchronization, which enhances machine learning for EEG signal prediction. His recent publications (2023–2025) span a wide range of applications, including chaotic image and 3D model encryption, UAV surveillance using chaotic paths, causal feature selection in health systems, modeling neurological disorders, and socio-environmental analysis in Brazil. These works reflect a strong trend toward applying nonlinear dynamics and network science to real-world engineering, biomedical, and societal challenges. Scientific Contributions and Recognition: Proved a conjecture on the analytical calculation of Poincaré first return times using unstable periodic orbits. Contributed foundational work to chaos-based cryptography. Proposed a formula linking mutual information to Lyapunov exponents, supporting the Infomax theory of brain evolution. Discovered the phenomenon of Collective Almost Synchronization in complex networks. Demonstrated that causality is a space-time phenomenon, not purely temporal. Advising and Research Support: He is currently supervising PhD students in Physics, Maths, and Engineering, indicating active mentorship. His research is supported by analytical developments and data-driven modeling. He leads work on optimal wireless chaos communication, synapse modeling, brain network changes post-surgery, and socio-economic causality in Brazil. His collaborations span institutions in the USA, Brazil, Germany, and Portugal. Labs and Research Groups: He is affiliated with the Institute for Complex Systems and Mathematical Biology at Aberdeen, a hub for interdisciplinary research in nonlinear dynamics, network theory, and their applications across physical, biological, and social systems.

Christoph GellhausView profile

Professor

• Complex Analysis
• Symplectic Geometry
• Mathematical Physics
• +3 more

Christoph Gellhaus is a Professor of Mathematics at the Georg Agricola University of Applied Sciences, specifically within the School of Electrical and Information Technology and Industrial Engineering. His academic career spans both theoretical research and industrial application, with a focus on complex manifolds and symplectic geometry. He has also contributed to telecommunications software development at Siemens AG. Dr. Gellhaus' research interests include Complex Analysis, Symplectic Geometry, and Mathematical Physics, particularly the study of (almost-)complex manifolds and their applications. His publications reflect this, covering topics like Holomorphic Group Actions, DECT Protocols, and Hamiltonian Vector Fields. His recent work trends include interdisciplinary applications of mathematics in telecommunications and wireless communication protocols. Notable areas include DECT protocol design, network protocols, and interface specification. He is actively involved in teaching, covering subjects such as Higher Mathematics and Object-Oriented Programming in Java. His academic journey began with a diploma in Complex Analysis at Ruhr University Bochum, followed by a 1988 PhD in the theory of compact complex manifolds with holomorphic vector fields.

José Antonio Prado-BassasView profile

Professor

• Complex Analysis
• Functional Analysis
• Operator Theory
• +5 more

José Antonio Prado-Bassas is a Professor in the Department of Mathematical Analysis at the Faculty of Mathematics, University of Seville, where he also serves as Vice Dean of Teaching Innovation and Scientific Disclosure. His academic career spans over two decades with continuous teaching appointments across multiple mathematics and physics degree programs. His research focuses on complex variable approximation, universal functions (cluster set theory), hypercyclicity of operators, and lineability. He has developed significant contributions to understanding the algebraic and topological structures of function spaces, particularly regarding convergence modes and dimension properties of continuous functions. His work bridges pure mathematical analysis with dynamical systems and functional analysis. Analysis of his 15 most recent publications reveals sustained exploration of lineability phenomena across diverse mathematical contexts, with increasing sophistication in handling infinite-dimensional structures. His work consistently connects classical complex analysis with modern functional analytic techniques, particularly in studying convergence behaviors and dimensional properties of pathological function sets. Premio Extraordinario de Doctorado 2021 (University of Seville) First Prize for Science in Action 2019 (Mathematics Laboratory category) Dissemination Award from University of Seville 2020 Member of RSME Disclosure Committee Prado-Bassas actively supervises doctoral students, with his first PhD student (Pablo J. Gerlach-Mena) achieving Cum Laude and International Mention. He teaches across multiple programs including Mathematical Analysis for Physics degrees and Mathematical Methods courses, while leading innovation initiatives through his Vice Dean role. His outreach extends through the "Spy Workshop" project and extensive public engagement. He maintains active laboratory work through the "Análisis Funcional No Lineal" research group under Tomás Domínguez Benavides, focusing on nonlinear functional analysis problems. His current projects integrate mathematical theory with cryptographic applications and science communication initiatives.

Ayse SahinView profile

Professor

• Ergodic theory
• Dynamical systems
• Amenable groups
• +2 more

Ayse Sahin serves as Professor and Dean of the College of Science and Mathematics at Wright State University in Dayton, Ohio, where she provides academic leadership while maintaining an active research program in pure mathematics. Her administrative role encompasses oversight of all academic departments and programs within the college. Her educational foundation includes: B.A. in Mathematics (1988) from Mount Holyoke College M.A. in Mathematics (1992) from University of Maryland at College Park Ph.D. in Mathematics (1994) from University of Maryland at College Park Dr. Sahin's research centers on ergodic theory and dynamical systems, with specialized expertise in actions of amenable groups. Her work investigates structural properties of multi-dimensional dynamical systems through combinatorial and geometric approaches, particularly examining recurrence phenomena, entropy characteristics, and equivalence relations in measure-preserving systems. She has made significant contributions to understanding Kakutani equivalence, directional dynamics in Z d actions, and tiling-based representations of group actions. Analysis of her publication trajectory reveals consistent focus on foundational aspects of dynamical systems, evolving from one-dimensional systems to higher-dimensional and continuous group actions. Her recent work increasingly incorporates geometric structures like Robinson tilings and Heisenberg group actions, demonstrating interdisciplinary connections between ergodic theory, combinatorics, and geometric group theory. As Dean, she bridges administrative responsibilities with scholarly contributions, maintaining an active research profile while shaping the academic direction of the College of Science and Mathematics.