Our Mission:
1. To advance Austrian science
to the forefront
of international research
and to stabilize this position.
2. To strengthen cooperation
with international research centers:

Université Mohammed Premier,
Oujda, Morocco

Australian National University,
Canberra, Capital Territory

Washington and Lee University,
Lexington, Virginia, USA

Aichi University of Education,
Nagoya, Japan

University of Calgary,
Alberta, Canada
International Conferences:
January 13  15, 2018:
3rd International Conference
on Groups and Algebras
ICGA 2018, Sanya, China
Invited Keynote:
Deep Transfers
of pClass Tower Groups
Conference Poster

Progressive Innovations and
Outstanding Scientific Achievements:

3Class Field Towers with Three Stages and their Galois Groups
During the last six years 2012  2018,
many open questions in the context of finite pclass 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 3class 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 3class group Cl_{3}(K) ∼ C(3)×C(3)
and Artin transfer pattern (τ(K),κ(K)) ∼ ((32,21,21,21),(2231))
for which a twostage 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),1^{3},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 sigmagroups [4].
Secondly,
I explored the behavior of real quadratic fields K with these Artin patterns [3]
and found a striking difference because
they admit 3tower groups Gal(F(∞)/K)
with less restrictive requirements for the relation rank,
which necessitated the proof of criteria for distinguishing between
twostage and threestage towers [5].
The final step in illuminating the periodic bifurcations in trees [2]
and the periodic sequences of Schur sigmagroups [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 sigmagroups.
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] 3class field towers of exact length 3
[2] Periodic bifurcations in descendant trees of finite pgroups
[3] Indexp abelianization data of pclass tower groups
[4] Periodic sequences of pclass tower groups
[5] Criteria for threestage towers of pclass fields
[6] Modeling rooted intrees by finite pgroups

Coperiodicity Isomorphisms between coclass forests
arising from infinitely repeated Multifurcations

Artin Limit Patterns for the
Successive Approximation
of the stages of pclass towers and their Galois groups

Fork Topologies
on Structured Descendant Trees and
quantitative measures of Pattern Search Complexity

Fundamental Principles:

Polarization principle

Mainline principle

Monotony principle
Background of Scientific Applications:
Marius Sophus Lie, December 17, 1842, Nordfjordeid  February 2, 1899, Kristiania (Oslo)
Continuous transformation group  Lie group, Tangent space at the identity  Lie algebra
Galilei transformation group → Classical mechanics in Euclidean 3space
Lorentz transformation group → Relativistic mechanics in Minkowski 4space

space  time  translations

proper orthochronous transformations

rotations in Euclidean 3subspace

spatial reflection, time inversion

combined space  time  inversion
Aims of Current Research:
Symmetry groups → Noether Theorem: conservation laws for observables
Poincaré group, Killing groups → General Relativity
Maxwell, Feynman: Quantum Electro Dynamics (QED), Quantum Field Theories
Gauge invariance, nonabelian Yang  Mills theory → Quantum Chromo Dynamics (QCD)

Spectral class O Stars: Theta1 Orionis C1 (Trapezium Cluster)

Luminous Blue Variables (LBV): Deneb, Eta Carinae, PCygni, LMC: SDoradus

WolfRayet Stars (WR): Gamma Velorum, LMC: R136a1

White Dwarf Stars: Sirius B, Prokyon B (Chandrasekhar limit)

Neutron Stars, Pulsars, Magnetars: RX J1856 (Tolman  Oppenheimer  Volkoff limit)

Quark Stars: no proven example is known currently

Black Holes: Cygnus X1

Supermassive Black Holes in Galactic Centers: Milky Way, Andromeda Galaxy

Gamma Ray Bursts (GRB): GRB170817A, GW170817
Publications:
Coperiodicity isomorphisms between forests of finite pgroups
Successive approximation of pclass towers
Deep transfers of pclass tower groups
Modeling rooted intrees by finite pgroups
Recent progress in determining pclass field towers


Principal Investigator and
Project Leader of several
International Scientific Research Lines:
