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:

HarishChandra 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:
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:
AsiaAustralia 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:

Reliable and Verifiable Invariants
of 3Class Field Towers
of Quadratic Number Fields

3Rank of Ambiguous Class Groups
of Cubic Kummer Extensions
Periodica Mathematica Hungarica, Akademiai Kiado Budapest Magyarorszag

5Class Field Towers over Cyclic Quartic Mirror Fields
arising from Quintic Reflection
Annales mathématiques du Québec

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 σgroups [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 σgroups [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 σgroups.
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:

Shockwave Propagation principle of multifurcation

Polarization principle of maximal subgroups

Mainline principle of pcpresentations

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 twogenerated metabelian pgroups → Simply NonElementary AQI
S_{p}Double Orbits of Artin transfer kernels → Punctured TKT
Preprints of peer reviewed 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:
Supported by the
Austrian Science Fund (FWF)
J0497PHY and P 26008N25
and by the
Research Executive Agency of the
European Union (EUREA)
Our Services to the Mathematical Community:
