

Scientists/Scholars
Daniel C. MAYER, Ph. D.,
Austrian citizen, born in Graz, Styria, Austria
…
28.05.1956
Address: Naglergasse 53, 8010 Graz, Austria
Web site: www.algebra.at
Research interests:
Towers of pclass fields with nonabelian higher pclass groups as Galois groups,
GolodShafarevich cohomology theory,
generator rank and relation rank of pgroups,
Galois action,
Schur σgroups and generalizations,
bivariate polynomial ideals as annihilator modules of the main commutator of twogenerated metabelian pgroups,
uniserial padic space groups,
infinite prop groups,
coclass graphs of finite pgroups,
periodicity of pruned branches of coclass trees,
parametrized presentations for infinite sequences of pgroups,
pgroup generation algorithm,
quadratic, cubic, quartic, quintic, dihedral, metacyclic and Frobenius extensions of algebraic number fields,
Voronoi's algorithms for computing lattice minima, fundamental systems of units, and class group structure,
multiplicities of discriminants,
ring and ray class fields,
differential principal factorizations and ambiguous principal ideals.
See also:
Wikiscientist.
Curriculum vitae:
(1)
University:
Ph. D. studies of mathematics, physics, and chemistry
Faculty of natural sciences,
KarlFranzensUniversity, Graz
…
01.10.1975  05.07.1983
Ph. D. Thesis
in functional analysis and differential equations
…
05.1983
Rigorous exams in mathematics, physics, and philosophy
…
06.1983
Dissertation:
The theory of formal power series mappings
between Banach spaces
and its application to
formal vector fields,
Jordan decompositions and group embeddings
of formal transformations,
Austrian National Library,
1983.
Graduation:
Promotion to Ph. D. (Doctor of Philosophy)
… 05.07.1983
In my graduate years of study at the KarlFranzensUniversity in Graz,
I was introduced to modular and automorphic functions by Ludwig Reich,
who was the supervisor of my Ph. D. thesis from 1981 to 1983.
Alexander Aigner and his former student Franz HalterKoch
acquainted me with analytic and algebraic number theory.
(2)
University assistant:
Institute for mathematics,
KarlFranzensUniversity, Graz
Studying assistant
…
01.03.1982  14.07.1983
Assistant with contract
…
15.07.1983  31.10.1983
University assistant
…
01.11.1983  31.10.1990
Conference presentations:

Jordan decompositions and analytic iterations
of formal power series mappings,
3. Austrian Mathematicians Meeting,
University of Salzburg
…
28.09.1983

Sharp bounds for the
partition function of integer sequences,
11. Austrian Math. Congress and
95. Annual Meeting of the DMV 1985,
University of Graz
…
19.09.1985

On differential principal factors
among the lattice minima in the Minkowski image of orders
in simply real cubic number fields,
4. Austrian Math. Meeting,
Bressanone, Italy
…
21.09.1987

Ambiguous principal ideals in nonGalois number fields
with dihedral normal field,
12. Austrian Math. Congress and
99. Annual DMV Meeting 1989,
University of Technology, Vienna
…
18.09.1989

Multiplicities of cubic discriminants,
5. Austrian Math. Meeting, University of Klagenfurt
…
24.09.1991
Teaching experience in university lectures and courses:

Elliptic and Automorphic Functions
…
fall term 1983/84

Functional Analysis and Spectral Theory
…
spring term 1984

Linear Algebra 1 and 2
…
fall term 1984/85
and spring term 1985

Algebraic Number Theory
…
fall term 1985/86

Linear Algebra
…
spring term 1986

Analysis 1  2 (Differential and Integral Calculus)
…
fall term 1986/87
and spring term 1987

Linear Algebra and Analytic Geometry
…
fall term 1987/88
and spring term 1988

Higher Algebra
…
fall term 1988/89

Arithmetically Equivalent Number Fields
…
spring term 1989

Modular Functions and Complex Multiplication
…
fall term 1989/90

Voronoi's 1 and 2Dimensional Unit Algorithms
…
spring term 1990
My main working areas as a University Assistant from 1983 to 1990 were
generalized continued fraction algorithms for number fields of
unit rank 1 and 2 by G. F. Voronoi and A. Brentjes.
At conferences I became acquainted with Michael Pohst and Johannes Buchmann in 1986.
Together with Hugh C. Williams, whom I met in 1987,
I investigated conditions for generators of ambiguous principal ideals
and integral multiples of units to appear among the lattice minima
of the geometric Minkowski image of orders in quadratic and cubic fields,
e. g. in
Differential principal factors and units in pure cubic number fields,
Inst. for Math., KarlFranzensUniv. Graz, 1988,
and
Lattice minima and units in real quadratic number fields,
Publ. Math. Debrecen
39 (1991), 19  86.
(3)
Postgraduate visiting research assistant,
conducting the research project Galois number fields with S_{3}group
on my own responsibility:
Department of Computer Science,
University of Manitoba, Winnipeg, Canada
…
01.09.1990  28.08.1991
supported by Erwin Schrödinger Grant Nr. J0497PHY
from the Austrian Science Fund
Presentations at international conferences:

Classification of cubic number fields,
20th Manitoba Conference on Numerical Mathematics and Computing,
University of Manitoba,
Winnipeg, Manitoba, Canada
…
29.09.1990

Multiplicities and classification of dihedral discriminants,
1990 Westcoast Number Theory,
Asilomar Conference Grounds, Pacific Grove, Monterey, California, USA
…
20.12.1990

Dihedral fields from quadratic infrastructure,
101. Annual Meeting of the DMV 1991,
University of Bielefeld, Germany
…
19.09.1991

Dihedral fields from quadratic invariants,
1992 Westcoast Number Theory Conference,
Oregon State University, Corvallis, Portland, Oregon, USA
…
18.12.1992
University lectures and courses:

Galois Cohomology and Class Field Theory
…
fall term 1990/91

Selected Topics on Dihedral Field Extensions
…
spring term 1991
Aside from fulfilling standard teaching duties
I tried to offer access to advanced areas for students.
However, due to a low number of participants,
cancellation of special courses aiming at research topics
became inavoidable, repeatedly.
Therefore, I asked H. C. Williams for the opportunity
to launch a research project with title
Galois number fields with S_{3}group
at the University of Manitoba, Winnipeg, Canada,
and I applied for an Erwin Schrödinger grant
at the Austrian Science Fund in 1990.
Inspired by errors in the table of complex cubic fields
by G. W. Fung and H. C. Williams,
I developed my theory of multiplicities of discriminants
in the course of this Schrödinger Project.
In collaboration with Pierre Barrucand at Paris,
I extended the multiplicity theory from dihedral to metacyclic fields.
(4)
Secondary university studies:
Teachership in mathematics and physics
Faculty of natural sciences,
University of Regensburg
…
12.04.1994  18.12.1995
Graduations
and authorization to take the title LehramtsAssessor:
1^{st} State Exam for teachership at high schools
…
18.12.1995
2^{nd} State Exam for teachership at high schools
…
09.12.1997
Several deficiencies in the daily routine of lectures at universities,
a considerable gap between teaching and research,
and the lack of impressive graphical visualizations
convinced me to start second studies at the University of Regensburg, Germany.
In particular, I paid attention to the
cognitive psychology of perception, attention, motivation, memory, learning, and language,
and to technical didactics, from elementary school to high school and university.
With Theodor Bröcker, Klaus Jänich, and Ernst Kunz I probed deeper into
differential topology, algebraic topology and algebraic geometry.
Professional qualification:
Exam in Austrian School Laws
…
28.06.1999
Approval of Bavarian State Exams by the
Federal Ministry of Education and Cultural Matters, Vienna
…
07.09.1999
Teaching experience at high schools:
computer science, electrotechnology, mechanical engineering,
projective geometry, applied mathematics, applied physics
…
1996  2013
(5)
Recent research:
Due to my research on the capitulation problem for number fields
I was increasingly attracted by the theory of finite pgroups
and infinite prop groups.
Member and referee of professional societies:

Austrian Mathematical Society (ÖMG)
…
since 1983

American Mathematical Society (AMS)
…
since 1990

Reviewer for
Mathematical Reviews (MR) and
MathSciNet
…
since 1992

Association for Computing Machinery (ACM)
…
since 2003

Referee for
International Journal of Number Theory (IJNT)
…
since 2011

Referee for
AsianEuropean Journal of Mathematics (AEJM)
…
since 2014

Referee for
Journal of Algebra and its Applications (JAA)
…
since 2014
Invited lectures:

The pclass numbers of unramified cyclic extensions
of a number field with pclass group of type (p,p),
Journées de Théorie des Nombres, Algorithmique et Applications,
Université Mohammed Premier, Faculté des Sciences d'Oujda (FSO),
Oujda, Morocco
…
27.09.2010

The structure of the 3class groups of the
four unramified cyclic cubic extensions
of a number field with 3class group of type (3,3),
Journées de Théorie des Nombres, Algorithmique et Applications,
Université Mohammed Premier, FSO,
Oujda, Morocco
…
28.09.2010

Quadratic pring spaces for counting dihedral fields,
Workshop International NTCCCS 2012,
Université Mohammed Premier, FSO,
Oujda, Morocco
…
26.04.2012
Presentations at international conferences:

Multiplicities of discriminants of pring class fields
over quadratic fields with modified pclass rank σ ≥ 2,
15. Austrian Math. Congress and
111. Annual Meeting of the DMV 2001,
University of Vienna,
Vienna, Austria
…
20.09.2001

Classical and modern scope of twostage metabelian 3groups,
8. Austrian Math. Meeting,
Bolzano, Italy
…
22.09.2003

Twostage towers of 3class fields
over quadratic number fields
with triadic irregular discriminant,
17. Austrian Math. Congress and
119. Annual Meeting of the DMV 2009,
University of Technology,
Graz, Austria
…
25.09.2009

The distribution of second pclass groups on coclass graphs,
27ièmes Journées Arithmétiques 2011,
Vilnius University,
Vilnius, Lithuania
…
01.07.2011

Principalization algorithm via class group structure,
Joint CSASC Conference 2011,
Danube University,
Krems, Austria
…
25.09.2011

First faultless disproof of Scholz and Taussky's claim concerning
the 3class field tower of Q((9748)^{1/2}),
Workshop on GolodShafarevich groups and algebras and rank gradient,
Erwin Schrödinger International Institute for Mathematical Physics,
Vienna, Austria
…
24.08.2012

Number fields sharing a common discriminant,
122. Annual Meeting of the DMV 2012,
University of the Saarland, Faculty of Mathematics,
Saarbrücken, Germany
…
18.09.2012

Finite 3groups as viewed from class field theory,
Groups St Andrews 2013,
University of St Andrews,
St Andrews, Fife, Scotland
…
09.08.2013
with coauthor Mike F. Newman

3class field towers of exact length 3,
18th ÖMG Congress 2013 and 123rd Annual DMV Meeting 2013,
University of Innsbruck, Technology Campus,
Innsbruck, Tyrol, Austria
…
24.09.2013
with coauthors Michael R. Bush and Mike F. Newman

Class towers and capitulation over quadratic number fields,
West Coast Number Theory 2013,
Asilomar Conference Grounds,
Pacific Grove, Monterey, California, USA
…
18.12.2013
with coauthors Michael R. Bush and Mike F. Newman
(6)
Skills in computer science and information technology:
Computer algebra systems: Magma, Pari/GP, GAP, Singular;
Typesetting: TeX, LaTeX;
Object Oriented Analysis, OO Design, and OO Programming:
Pascal, Delphi, C, C++, Java, JSP, HTML, XML;
usecase, class and sequence diagrams in UML,
objectrelational mappings of class hierarchies on database schemata,
SQL, PL/SQL.
Professional qualification:
Sun Certified Java Programmer
…
22.08.2003
Exam in object oriented programming in Java
by Sun Microsystems, Inc. (now Oracle)
It turned out to be very useful
to be able to write program scripts for
the Computer Algebra Systems
Pari/GP, GAP, Singular, and Magma
and to write publications with
TeX and LaTeX.
I acquired additional skills in
objectoriented analysis, design, and programming,
and became a
Sun Certified Java Programmer
(now Oracle)
…
22.08.2003
(7)
International Research Project P26008N25:
Since neither algebraic number theory nor pgroup theory
is represented by Austrian universities in an amount comparable with my requirements,
the present stand alone project P26008N25 is intended to
stabilize my wellknown status in the international mathematical community,
to establish an Austrian research centre for a multidisciplinary approach
to problems which demand a high portion of expertise in both, number theory and group theory,
and to strengthen my collaboration with international partners
in the United States, the United Kingdom, Australia, Japan, and Morocco.
Invited lectures:

La Théorie Algorithmique des Nombres,
Corps de Nombres Algébriques et Corps de Classes,
École de Recherche CIMPA UNESCO, Théorie des Nombres et ses Applications,
Université Mohammed Premier, Faculté des Sciences d'Oujda (FSO),
Oujda, Morocco
…
18  29.05.2015

Periodic sequences of pclass tower groups,
1st International Conference on Groups and Algebras (ICGA) 2015, Guang Dong Hotel, Shanghai, China
…
21.07.2015

pCapitulation over number fields with pclass rank two,
2nd International Conference on Groups and Algebras (ICGA) 2016, Youngor Central Hotel, Suzhou, China
…
26.07.2016

Recent progress in determining pclass field towers,
1st International Colloquium of Algebra, Number Theory, Cryptography and Information Security (ANCI) 2016, Taza, Morocco
…
11.11.2016
Presentations at international conferences:

Indexp abelianization data of pclass tower groups,
29ièmes Journées Arithmétiques (JA) 2015, University of Debrecen, Hungary
…
09.07.2015

New number fields with known pclass tower,
22nd Czech and Slovak International Conference on Number Theory (CSICNT) 2015, Hotel Sorea Máj, Liptovský Ján, Slovakia
…
31.08.2015


