Mathematical interests

I am an algebraic geometer. I have mainly worked on the generalisation on the Miyaoka-Yau inequality to singular surfaces and its applications, on problems in finite characteristic and on enumerative geometry. My Erdős number is 3, as is my father's, my brother's is only 2.

I am also interested in algebraic and computational number theory and tropical mathematics.

Publications

1. (with L. Csirmaz) Solutions to two questions of the 1982 International Mathematical Olympiad (in Hungarian). Középiskolai Matematikai Lapok 34 (1984), 8-11.
2. Chern Classes for Q-sheaves. In J. Kollár et. al., Flips and Abundance for Algebraic Threefolds, volume 211 of Astérisque, chapter 10. Société Mathématique de France, 1992.
3. Inequalities between Chern classes. Ph. D. thesis, University of Cambridge, 1993.
4. Bogomolov instability of higher rank sheaves in characteristic p. Math. Ann. 301 (1995) 529-538.
5. Fano threefolds in characteristic p J. Alg. Geom. 7 (1998) 207-218.
6. (with E. Szabó) On the tacnodes of configurations of conics in the projective plane. Math. Ann. 305 (1996) 693-703.
7. Generalisation of the Bogomolov-Miyaoka-Yau inequality to singular surfaces. Proc. London Math. Soc. (3) 78 (1999) 241-282.
8. Configurations of conics with many tacnodes. Tohoku Math. J. 52 (2000), 555-577.
9. The rationality of configuration spaces of lines in P³. Math. Proc. Cambridge Philos. Soc. 128 2000, 193-196.
10. Lines tangent to 4 unit spheres with coplanar centres (2001) 8 pp.

Some useful mathematical links

• The COW seminar, which I attend.
• The algebraic geometry preprint server.
• The algebraic number theory preprint server.

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