Florian Breuer

Professor of Mathematics, University of Newcastle, Australia
Extraordinary Professor, Stellenbosch University

Address:

    School of Mathematical and Physical Sciences
    University of Newcastle
    Australia
    Tel: +61 40339609
    email: florian.breuer (at) newcastle.edu.au

mugshot by David Goss

Activities:

As of April 2018 I'm at the University of Newcastle in Australia.
Click here for my Newcastle webpage.

Editorial duties:

A biennial conference series in Arithmetic Geometry has been held in Stellenbosch since 1997.
The next instalment takes place 14-18 January 2018. Click here for more information.
See below for some of the recent conferences in this series:
2005
2007
2009
2011
2013
2015 (held at AIMS)
2017

Photography

Research

I work in Number Theory. More specifically, my main interst lies in Arithmetic Geometry, where I work on Elliptic curves, Drinfeld modules, Drinfeld modular forms and related topics. I also sometimes work on more elementary things, such as Ducci sequences.

Publications

Note: for copyright reasons, some of the following PDF files are not the final, published versions.
  1. Discovery and analysis of gamma doradus type pulsations in the F0 IV star HR 2740 QW pup, Mon. Not. R. Astron. Soc. 292 (1997), 621-630. (4th author, with E. Poretti, C. Koen, P. Martinez, D. de Alwis and H. Haupt) [PDF]
  2. Line profile variations in the spectra of the gamma Dor star HR 2740, In: IAU Symposium 185 "New Eyes to See Inside the Sun and Stars", (F.-L. Deubner, J. Christensen-Dalsgaard, D. Kurtz, eds) Kyoto, Japan, 18-22 August, 1997, p. 387. (5th author, with E. Poretti, L. Mantegazza, C. Koen, P. Martinez, D. De Alwis and H. Haupt). [PDF]
  3. Strategy and complexity of the game of squares. Bull. London. Math. Soc 30 (1998), 274-282. (With Mike Robson) [PDF]
  4. A note on a paper by Glaser and Schöffl. Fibonacci Quart. 36.5 (1998), 463-466. [PDF]
  5. Ducci sequences over abelian groups. Comm. Algebra 27.12 (1999), 5999-6013. [PDF]
  6. Heights of CM points on complex affine curves. Ramanujan J. 5 (2001), 311-317. [PDF]
  7. Distinguished liftings and the André-Oort conjecture. Quaest. Math. 25(3) (2002), 363-380. [PDF]
  8. La conjecture d'André-Oort pour le produit de deux coubres modulaires de Drinfeld. C. R. Math. Acad. Sci. Paris 335 (2002), no. 11, 867--870. [PDF]
  9. Higher Heegner points on elliptic curves over function fields. J. Number Theory 104 (2004), 315-326. [PDF]
  10. Images of isogeny classes on modular elliptic curves. Math. Res. Lett. 11 (2004), 649-651. [PDF]
  11. The André-Oort conjecture for products of Drinfeld modular curves. J. reine angew. Math. 579 (2005), 115-144. [PDF]
  12. Monodromy groups associated to non-isotrivial Drinfeld modules in generic characteristic. In: "Number Fields and Function Fields - Two Parallel Worlds", (G. van der Geer, B. Moonen, R. Schoof, eds.), Progress in Mathematics, 239, p61-69, Birkhäuser Verlag, 2005. (With Richard Pink.) [PDF]
  13. CM points on products of Drinfeld modular curves. Trans. Amer. Math. Soc. 359 (2007), 1351-1374. [PDF]
  14. Ducci sequences and cyclotomic polynomials. Finite Fields Appl. 13 (2007), 293-304. (With Ernest Lötter and Brink van der Merwe.) [PDF]
  15. Ducci sequences in higher dimensions. Integers: Electronic Journal of Combinatorial Number Theory 7 (2007), #A24. [PDF]
  16. The André-Oort conjecture for Drinfeld modular varieties. C. R. Math. Acad. Sci. Paris, Ser. I, 344 (2007), 733-736. [PDF]
  17. Heegner points and the rank of elliptic curves over large extensions of global fields. Canadian J. Math. 60 (2008), no.3, 481-490. (With Bo-Hae Im) [PDF]
  18. Drinfeld modular polynomials in higher rank. J. Number Theory 129 (2009), 59-83. (With Hans-Georg Rück) [PDF]
  19. Torsion bounds for elliptic curves and Drinfeld modules. J. Number Theory 130 (2010), 1241-1250. [PDF]
  20. Ducci sequences and cyclotomic fields. J. Difference Equ. Appl. 16 (2010), no. 7, 847-862. [PDF]
  21. Special subvarieties of Drinfeld modular varieties. J. reine angew. Math. 668 (2012), 35-57. [PDF]
  22. Newton identities for Weierstrass products. Amer. Math. Monthly 119, no. 9 (2012), 796-799. [PDF]
  23. Explicit Drinfeld moduli schemes and Abhyankar's generalized iteration conjecture. J. Number Theory 160 (2016), 432-450. [PDF]
  24. Drinfeld modular polynomials in higher rank II: Kronecker congruences. (With Hans-Georg Rück). J. Number Theory 165 (2016), 1-14. [PDF]
  25. A note on Gekeler's h-function. Arch. Math. 107 (2016), 305-313. [PDF] The final publication is available at Springer via http://dx.doi.org/doi:10.1007/s00013-016-0923-1.
  26. On certain Drinfeld modular forms of higher rank. (with Dirk Basson). J. Théor. Nombres Bordeaux 29 no.3 (2017), 827-843. [PDF]

  27. Drinfeld modular forms of arbitrary rank, Part I : Analytic theory. (With Dirk Basson and Richard Pink). ArXiV:1805.12335
  28. Drinfeld modular forms of arbitrary rank, Part II: Relation with algebraic theory. (With Dirk Basson and Richard Pink). ArXiV:1805.12337
  29. Drinfeld modular forms of arbitrary rank, Part III: Examples. (With Dirk Basson and Richard Pink). ArXiV:1805.12339
  30. Periods of Ducci sequences and odd solutions to a Pellian equation. [PDF]

Academic qualifications

Curriculum Vitae

Graduate Students

Courses Offered

2018

2017

2016

2015

2014

2013

2012

2011

2010

2009

2008

2007

2006

2005

2004


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