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Our Mission: 1. To advance European science to the forefront of international research and to stabilize this position. 2. To strengthen cooperation with international research centers: Harish-Chandra Research Institute, Allahabad, India Washington and Lee University, Lexington, Virginia, USA Université Mohammed Premier, Oujda, Morocco Australian National University, Canberra, Capital Territory Aichi University of Education, Nagoya, Japan University of Calgary, Alberta, Canada International Conferences: November 23 - 26, 2022: 6th Journees Algebre, Theorie de Nombres, Applications Universite Mohammed I, Oujda, Morocco Daniel C. Mayer's Plenary Lectures December 24 - 26, 2021: 7th Int. Conf. on Groups and Algebras International Asia-Pacific Convention Center Sanya, Hainan Dao, China Daniel C. Mayer's Invited Key Note: Periodic Schur σ-Groups Conference Header February 27 - 29, 2020: 3rd Int. Conf. on Mathematics and its Applications Université Hassan II, Faculté des Sciences Casablanca, Region Occidental, Morocco Daniel C. Mayer's Invited Key Note: Abstract Pattern Recognition via Artin Transfers Program April 25 - 27, 2019: Conference on Algebra, Number Theory and Their Applications Université Mohammed Premier, Faculté des Sciences Oujda, Region Oriental, Morocco Daniel C. Mayer's 3 Lectures: 1. Proving the Conjecture of Scholz 2. Differential principal factors 3. Pure Metacyclic Fields January 21 - 25, 2019: Asia-Australia Algebra Conference 2019 Western Sydney University, Parramatta City campus Sydney, New South Wales, Australia July 1 - 5, 2019: 31st Journées Arithmétiques Istanbul University, Faculty of Science JA 2019, Istanbul, Turkey Progressive Innovations and Outstanding Scientific Achievements: A Group Theoretic Approach to Cyclic Cubic Fields, 2024 MDPI Mathematics, Basel, Switzerland Trilogy on Periodic Schur σ-Groups, 2021 Non-elementary bicyclic commutator quotients BCF-groups with elevated rank distribution First excited state with moderate rank distribution Classifying Multiplets of Totally Real Cubic Fields, 2021 Electronic Journal of Mathematics, Univ. Hail, Saudi Arabia 3-Rank of Ambiguous Class Groups, 2020 of Cubic Kummer Extensions Periodica Mathematica Hungarica, Akademiai Kiado, Budapest, Magyarorszag 5-Class Field Towers over Cyclic Quartic Mirror Fields arising from Quintic Reflection, 2019 Annales mathématiques du Québec Reliable and Verifiable Invariants of 3-Class Field Towers of Quadratic Number Fields 3-Class Field Towers with Three Stages and their Galois Groups During the last six years 2012 - 2018, many open questions in the context of finite p-class field towers, for an odd prime p, have been answered completely. The clarification commenced in 2012 with the first rigorous proof for the existence of imaginary quadratic fields K having a 3-class tower K = F(0) < F(1) < F(2) < F(3) = F(4) of precise length three, verifying a conjecture by Brink in 1984, respectively by Brink and Gold in 1987. This proof was established in my cooperation with Michael R. Bush and concerned fields K with 3-class group Cl3(K) ∼ C(3)×C(3) and Artin transfer pattern (τ(K),κ(K)) ∼ ((32,21,21,21),(2231)) for which a two-stage tower had been claimed erroneously by Scholz and Taussky in 1934 and by Heider and Schmithals in 1982. Our result was published in the Journal of Number Theory 2015 by Elsevier [1]. We intentionally abstained from most extensive generality in favour of quickly documenting our priority. However, there drowsed two essential capabilities for generalizations. Firstly, I extended the proof for imaginary quadratic fields K to infinitely many distinct Artin patterns (τ(K),κ(K)) with either τ(K) ∼ ((n+1,n),21,21,21) and κ(K) ∈ {(1231),(2231)} or τ(K) ∼ ((n+1,n),13,21,21) and κ(K) ∈ {(1122),(3122)}, where n > 1 denotes an arbitrary integer, based on the remarkable discovery of periodic bifurcations in descendant trees [2] which give rise to the required periodic sequences of Schur σ-groups [4]. Secondly, I explored the behavior of real quadratic fields K with these Artin patterns [3] and found a striking difference because they admit 3-tower groups Gal(F(∞)/K) with less restrictive requirements for the relation rank, which necessitated the proof of criteria for distinguishing between two-stage and three-stage towers [5]. The final step in illuminating the periodic bifurcations in trees [2] and the periodic sequences of Schur σ-groups [4] was completed 2018 in my collaboration with Mike F. Newman [6] by giving an explanation of all phenomena in terms of infinite limit groups whose finite quotients yield the periodic sequences of Schur σ-groups. Since Elsevier denies open access to [1], all further papers [2,…,6] were published with gold open access and can be downloaded free of charge from the publisher's website: [1] 3-class field towers of exact length 3 [2] Periodic bifurcations in descendant trees of finite p-groups [3] Index-p abelianization data of p-class tower groups [4] Periodic sequences of p-class tower groups [5] Criteria for three-stage towers of p-class fields [6] Modeling rooted in-trees by finite p-groups Co-periodicity Isomorphisms between co-class forests arising from infinitely repeated Multifurcations Artin Limit Patterns for the Successive Approximation of the stages of p-class towers and their Galois groups Fork Topologies on Structured Descendant Trees and quantitative measures of Pattern Search Complexity Fundamental Principles: Shockwave Propagation principle of multifurcation Polarization principle of maximal subgroups Mainline principle of pc-presentations Monotony principle of Artin transfer patterns Most Recent Discoveries: Regular Behavior Before the Shockwave Anomalous Behavior Behind the Shockwave Singular Behavior On the Shockwave Regenerative Centres and Sustainable Chains Isogenerative Reproduction of Isoclinism Branches Neogenerative Production of Isoclinism Stems Isoclinic propagation of algebraic invariants Aims of Current Research: Unified Theory of two-generated metabelian p-groups  →  Simply Non-Elementary AQI Sp-Double Orbits of Artin transfer kernels  →  Punctured TKT Preprints of peer reviewed publications: Co-periodicity isomorphisms between forests of finite p-groups Successive approximation of p-class towers Deep transfers of p-class tower groups Modeling rooted in-trees by finite p-groups Recent progress in determining p-class field towers Principal Investigator and Project Leader of several International Scientific Research Lines: Towers of p-Class Fields over Algebraic Number Fields Structured Descendant Trees of Finite p-Groups Lie Groups in General Relativity, Astrophysics, and Particle Physics Supported by the Austrian Science Fund (FWF) J0497-PHY and P 26008-N25 and by the Research Executive Agency of the European Union (EUREA) Our Services to the Mathematical Community: Mathematical Reviews (MR) Data Base