Research Interests

• Complex Algebraic Geometry and Homological Algebra
• Homological Mirror Symmetry
• Quantum Cohomology, Gromov-Witten Invariants
• Classification of complex manifolds
• Twistor spaces

Postragduate Studies at Mary Immaculate College

It is possible to pursue postgraduate research in Mathematics for an MA or PhD thesis under my supervision at Mary Immaculate College. If you are interested, feel free to contact me in order to discuss suitable research areas or any other question which arises.
Further information is available via Postgraduate Studies in Mathematics.

Current Postgraduate Students at MIC

• Lisa Kierans
• Davina Fogarty

Former Postgraduate Students

• Ciara Daly (M.A., 2007)
  Thesis: Stability Concepts in Algebraic Geometry
• Bijan Afshordel (Dipl.-Math., 2002, University Kaiserslautern)
  Thesis: On Fukaya's Category over Elliptic Curves
• Sergey Mozgovoy (Dipl.-Math., 2002, University Kaiserslautern)
  Thesis: Some Observations on Homological Mirror Symmetry in Dimension One

 

---

 

Selected Publications

1. I. Burban, B. Kreussler

   Vector bundles on families of irreducible cubics and applications,
   In: Complex Geometry in Osaka, In honour of Professor Akira Fujiki on the occasion of his 60th birthday, Lecture Note Series in Mathematics Vol. 9, Osaka University (June 2008) 200-216.

2. I. Burban, B. Kreussler

   Vector bundles on degenerations of elliptic curves and Yang-Baxter equations, 99 pages,
   preprint (2007) arXiv:0708.1685 [math.AG]

3. B. Kreussler

   Elliptic Curves — an Introduction,
   Irish Math. Soc. Bulletin, 60 (2007) 39-43

4. B. Kreussler

   Solving Cubic Equations in Two Variables,
   Irish Math. Soc. Bulletin, 60 (2007) 45-66

5. I. Burban, B. Kreussler

   Derived categories of irreducible projective curves of arithmetic genus one, Compositio Mathematica, 142 (2006) 1231-1262,
   preprint version arXiv:math.AG/0503496

6. I. Burban, B. Kreussler

   On a relative Fourier-Mukai transform on genus one fibrations, manuscripta mathematica 120 (2006) 283-306,
   preprint version arXiv:math.AG/0410349

7. I. Burban, B. Kreussler

   Fourier-Mukai transforms and semi-stable sheaves on nodal Weierstrass cubics, J. Reine Angew. Math. 584 (2005) 45-82,
   preprint version arXiv:math.AG/0401437

8. B. Kreussler

   Homological Mirror Symmetry in Dimension One, Emma Previato (ed.) Advances in Algebraic Geometry Motivated by Physics: AMS Special Session Enumerative Geometry in Physics, April 1-2, 2000, University of Massachusetts, Lowell, Massachusetts, Providence, RI: American Mathematical Society. Contemporary Mathematics 276 (2001) 179-198

9. B. Kreussler

   Another Description of Certain Quartic Double Solids, Mathematische Nachrichten 212 (2000) 91-100

10. B. Kreussler

    Twistor Spaces With a Pencil of Fundamental Divisors, Doc.Math.J.DMV 4 (1999) 127-166

11. F. Campana, B. Kreussler

    Existence of twistor spaces of algebraic dimension two over the connected sum of four complex projective planes, Proceedings of the AMS 127 (1999) 2633-2642

12. F. Campana, B. Kreussler

    A conic bundle description of Moishezon twistor spaces without effective divisors of degree one, Mathematische Zeitschrift 229 (1998) 137-162

13. B. Kreussler

    On the algebraic dimension of twistor spaces over the connected sum of four complex projective planes, Geometriae Dedicata 71 (1998) 263-285

14. B. Kreussler

    Moishezon twistor spaces without effective divisors of degree one, Journal of Algebraic Geometry 6 (1997) 379-390

---

The information found on personal pages should not be considered official material from Mary Immaculate College and the College does not accept any responsibility for its accuracy or otherwise.