Professor Florian Breuer

Professor Florian Breuer

Professor

School of Mathematical and Physical Sciences (Mathematics)

Career Summary

Biography

Research Interests: Florian works in Number Theory, especially in elliptic curves, Drinfeld modules, Drinfeld modular forms and also elementary topics such as Ducci sequences.

Biography: Florian grew up in Stellenbosch, South Africa, where he completed school as well as his undergraduate studies in Mathematics and Theoretical Physics. He then obtained a bursary from the French government to complete his graduate studies in Paris, where he completed his D.E.A. (Masters) at the Université Pierre et Marie Curie (Paris 6) in 1999 and his PhD at the Université Denis Diderot (Paris 7) in 2002, both under supervision of Marc Hindry.

After two postdoctoral fellowships in Taiwan and Germany, he returned to Stellenbosch University in July 2004, and stayed there until April 2018, when he moved to the University of Newcastle. Florian still holds an appointment as extraordinary professor at Stellenbosch University.


Qualifications

  • Doctoral Degree in Mathematics (Equiv PhD), University of Paris - France

Keywords

  • Ducci sequences
  • Number Theory
  • Drinfeld modules
  • Drinfeld modular forms
  • Elliptic curves

Languages

  • German (Mother)
  • English (Fluent)
  • French (Fluent)
  • Afrikaans (Fluent)

Fields of Research

Code Description Percentage
010101 Algebra and Number Theory 100

Professional Experience

UON Appointment

Title Organisation / Department
Professor University of Newcastle
School of Mathematical and Physical Sciences
Australia

Academic appointment

Dates Title Organisation / Department
1/04/2018 - 31/03/2021 Extraordinary Professor Stellenbosch University
Mathematical Sciences
South Africa
1/01/2013 - 31/03/2018 Professor Stellenbosch University
Mathematical Sciences
South Africa
1/10/2007 - 31/12/2012 Associate Professor Stellenbosch University
Mathematical Sciences
South Africa
1/07/2004 - 30/09/2007 Senior Lecturer Stellenbosch University
Mathematical Sciences
South Africa
1/01/2004 - 30/04/2004 Postdoctoral Fellow Max Planck Institute
Max-Planck-Institute for Mathematics
Germany
1/02/2003 - 31/10/2003 Postdoctoral Fellow National Tsing Hua University
National Center for Theoretical Sciences
Taiwan, Province of China

Awards

Prize

Year Award
2008 Meiring-Naude Medal
The Royal Society of South Africa

Scholarship

Year Award
2009 Alexander-von-Humboldt Fellowship for Experienced Researchers
Alexander Von Humboldt Foundation

Teaching

Code Course Role Duration
1210 Mathematical Discovery 1
The University of Newcastle
Professor 1/04/2018 - 30/06/2018
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Publications

For publications that are currently unpublished or in-press, details are shown in italics.


Chapter (1 outputs)

Year Citation Altmetrics Link
2005 Breuer F, Pink R, 'Monodromy groups associated to non-isotrivial Drinfeld modules in generic characteristic', , BIRKHAUSER BOSTON 61-69 (2005)
Citations Scopus - 4Web of Science - 3

Journal article (27 outputs)

Year Citation Altmetrics Link
2017 Basson D, Breuer F, 'On certain Drinfeld modular forms of higher rank', Journal de Théorie des Nombres de Bordeaux, 29 827-843 (2017)
Citations Scopus - 1Web of Science - 1
2016 Breuer F, 'A note on Gekeler's h-function', ARCHIV DER MATHEMATIK, 107 305-313 (2016)
DOI 10.1007/s00013-016-0923-1
Citations Scopus - 1Web of Science - 1
2016 Breuer F, 'Explicit Drinfeld moduli schemes and Abhyankar's Generalized Iteration Conjecture', JOURNAL OF NUMBER THEORY, 160 432-450 (2016)
DOI 10.1016/j.jnt.2015.08.021
Citations Scopus - 1Web of Science - 1
2016 Breuer F, Rueck H-G, 'Drinfeld modular polynomials in higher rank II: Kronecker congruences', JOURNAL OF NUMBER THEORY, 165 1-14 (2016)
DOI 10.1016/j.jnt.2016.01.001
2012 Breuer F, 'Newton Identities for Weierstrass Products', AMERICAN MATHEMATICAL MONTHLY, 119 796-799 (2012)
DOI 10.4169/amer.math.monthly.119.09.796
2012 Breuer F, 'Special subvarieties of Drinfeld modular varieties', JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 668 35-57 (2012)
DOI 10.1515/CRELLE.2011.136
Citations Scopus - 2Web of Science - 2
2010 Breuer F, 'Torsion bounds for elliptic curves and Drinfeld modules', JOURNAL OF NUMBER THEORY, 130 1241-1250 (2010)
DOI 10.1016/j.jnt.2009.11.009
Citations Scopus - 9Web of Science - 9
2010 Breuer F, 'Ducci sequences and cyclotomic fields', JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 16 847-862 (2010)
DOI 10.1080/10236190802566509
Citations Scopus - 4Web of Science - 4
2009 Breuer F, Rueck H-G, 'Drinfeld modular polynomials in higher rank', JOURNAL OF NUMBER THEORY, 129 59-83 (2009)
DOI 10.1016/j.jnt.2008.07.010
Citations Scopus - 3Web of Science - 3
2008 Breuer F, Im B-H, 'Heegner points and the rank of elliptic curves over large extensions of global fields', CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 60 481-490 (2008)
DOI 10.4153/CJM-2008-023-0
Citations Scopus - 2Web of Science - 2
2007 Breuer F, 'Ducci sequences in higher dimensions', Integers: Electronic Journal of Combinatorial Number Theory, 7 A24-A24 (2007)
2007 Breuer F, 'CM points on products of Drinfeld modular curves', TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 359 1351-1374 (2007)
DOI 10.1090/S0002-9947-06-04109-2
Citations Scopus - 2Web of Science - 2
2007 Breuer F, Lotter E, van der Merwe B, 'Ducci-sequences and cyclotomic polynomials', FINITE FIELDS AND THEIR APPLICATIONS, 13 293-304 (2007)
DOI 10.1016/j.ffa.2005.11.003
Citations Scopus - 6Web of Science - 6
2007 Breuer F, 'The Andre-Oort conjecture for Drinfeld modular varieties', COMPTES RENDUS MATHEMATIQUE, 344 733-736 (2007)
DOI 10.1016/j.crma.2007.05.008
2005 Breuer F, 'The Andre-Oort conjecture for products of Drinfeld modular curves', JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 579 115-144 (2005)
Citations Scopus - 5Web of Science - 5
2004 Breuer F, 'Images of isogeny classes on modular elliptic curves', MATHEMATICAL RESEARCH LETTERS, 11 649-651 (2004)
Citations Web of Science - 1
2004 Breuer F, 'Higher Heegner points on elliptic curves over function fields', JOURNAL OF NUMBER THEORY, 104 315-326 (2004)
DOI 10.1016/j.jnt.2003.09.001
Citations Scopus - 7Web of Science - 7
2002 Breuer F, 'La conjecture d¿André¿Oort pour le produit de deux courbes modulaires de Drinfeld', Comptes Rendus Mathematique, 335 867-870 (2002)
2002 Breuer F, 'Distinguished liftings and the andré-oort conjecture', Quaestiones Mathematicae, 25 363-380 (2002)

In this paper we study liftings of affine varieties from finite fields to number fields, such that the lifted varieties contain specified ¿canonical¿ lifts of points. If this cano... [more]

In this paper we study liftings of affine varieties from finite fields to number fields, such that the lifted varieties contain specified ¿canonical¿ lifts of points. If this canonical lifting of points corresponds to the Deuring-Serre-Tate lift of j-invariants of ordinary elliptic curves, then the resulting lifting problem is closely related to the André-Oort conjecture. We explore this connection, prove some results related to the André-Oort conjecture, and then apply these results together with other known special cases of the conjecture to our lifting problems. © 2002, Taylor & Francis Group, LLC. All rights reserved.

DOI 10.2989/16073600209486023
2002 Breuer F, 'The André-Oort conjecture for the product of two Drinfeld modular curves', Comptes Rendus Mathematique, 335 867-870 (2002)

We prove an analogue of the André-Oort conjecture for the product of two Drinfeld modular curves, following S.J. Edixhoven's approach. © 2002 Académie des sciences/Éditions s... [more]

We prove an analogue of the André-Oort conjecture for the product of two Drinfeld modular curves, following S.J. Edixhoven's approach. © 2002 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS.

DOI 10.1016/S1631-073X(02)02589-X
Citations Scopus - 2Web of Science - 2
2001 Breuer F, 'Heights of CM points on complex affine curves', Ramanujan Journal, 5 311-317 (2001)

In this note we show that, assuming the generalized Riemann hypothesis for quadratic imaginary fields, an irreducible algebraic curve in C'' is modular if and only if it... [more]

In this note we show that, assuming the generalized Riemann hypothesis for quadratic imaginary fields, an irreducible algebraic curve in C'' is modular if and only if it contains a CM point of sufficiently large height. This is an effective version of a theorem of Edixhoven.

DOI 10.1023/A:1012982812988
Citations Scopus - 11Web of Science - 9
1999 Breuer F, 'Ducci sequences over abelian groups', COMMUNICATIONS IN ALGEBRA, 27 5999-6013 (1999)
DOI 10.1080/00927879908826804
Citations Scopus - 4Web of Science - 5
1998 Breuer F, 'A note on a paper by Glaser and Schoffl', FIBONACCI QUARTERLY, 36 463-466 (1998)
Citations Scopus - 6Web of Science - 6
1998 Breuer F, Robson JM, 'Strategy and complexity of the game of squares', BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 30 274-282 (1998)
DOI 10.1112/S0024609397004001
1997 Poretti E, Koen C, Martinez P, Breuer F, De Alwis D, Haupt H, 'Discovery and analysis of Gamma Doradus type pulsations in the F0 IV star HR 2740= QW PUP', Monthly Notices of the Royal Astronomical Society, 292 621-630 (1997)
Citations Scopus - 10Web of Science - 13
1997 Poretti E, Koen C, Martinez P, Breuer F, de Alwis D, Haupt H, 'Discovery and analysis of Gamma Doradus type pulsations in the Cloud and the effect of metallicity on pulsation', arXiv preprint astro-ph/9706212, (1997)
1997 Breuer F, 'A NOTE ON A PAPER BY GLASER ANB SCHOFFL (1997)
Show 24 more journal articles

Conference (2 outputs)

Year Citation Altmetrics Link
2012 Breuer F, 'On Abhyankar¿s Generalized Iteration Conjecture', DMV-Jahrestagung 2012 (2012)
1998 Poretti E, Mantegazza L, Koen C, Martinez P, Breuer F, De Alwis D, Haupt H, 'Line Profile Variations in the Spectra of the ¿ Dor Star HR 2740', Symposium-International Astronomical Union, Cambridge University Press (1998)

Other (1 outputs)

Year Citation Altmetrics Link
2013 Breuer F, 'The parallel worlds of number theory', (2013) [O1]

Thesis / Dissertation (1 outputs)

Year Citation Altmetrics Link
2002 Breuer F, Sur la conjecture d¿André-Oort et courbes modulaires de Drinfeld, (2002)
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Research Opportunities

Domestic PhD Scholarship

A PhD scholarship is available for a domestic student to undertake a PhD under my supervision on any topic related to my research interests (e.g. Elliptic curves, Drinfeld modules, Drinfeld modular forms, special points on varieties, Ducci sequences)

Scholarship

School of Mathematical and Physical Sciences

24/05/2018 - 31/12/2018

Contact

Professor Florian Breuer
University of Newcastle
School of Mathematical and Physical Sciences
florian.breuer@newcastle.edu.au

Domestic PhD Scholarship

A PhD scholarship is available for a domestic student to undertake a PhD under my supervision on any topic related to my research interests (e.g. Elliptic curves, Drinfeld modules, Drinfeld modular forms, special points on varieties, Ducci sequences)

Scholarship

School of Mathematical and Physical Sciences

24/05/2018 - 31/12/2018

Contact

Professor Florian Breuer
University of Newcastle
School of Mathematical and Physical Sciences
florian.breuer@newcastle.edu.au

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Professor Florian Breuer

Position

Professor
School of Mathematical and Physical Sciences
Faculty of Science

Focus area

Mathematics

Contact Details

Email florian.breuer@newcastle.edu.au
Phone 0240339609
Link Personal webpage

Office

Room V131
Building Mathematics Building
Location Callaghan
University Drive
Callaghan, NSW 2308
Australia
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