Irish Geometry Conference 2015
Date: Friday, 15 May and Saturday, 16 May
Location: Mary Immaculate College, Limerick, room T115
Details:
on conference homepage
Research Interests
- Algebraic Vector Bundles and Principal Bundles
- Moduli Spaces and Moduli Stacks
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.
Publications
- (with I. Biswas, A. Dhillon) On the essential dimension of coherent sheaves. J. reine angew. Math., ahead of print (July 2015). preprint arXiv:1306.6432
- (with L. Costa, R.M. Miró-Roig, A.H.W. Schmitt) Rational families of instanton bundles on ℙ2n+1. Algebraic Geometry 2 (2014), 229-260. preprint arXiv:1204.5077
- (with I. Biswas, T. Gómez) Torelli Theorem for the Deligne-Hitchin Moduli Space, II.
Documenta Math. 18 (2013), 1177-1189 - (with I. Biswas) A Torelli theorem for moduli spaces of principal bundles over a curve.
Ann. Inst. Fourier 62 (2012), 87-106. preprint arXiv:1003.4061 - (with B. Andreas) New Examples of Stable Bundles on Calabi-Yau Three-Folds.
Int. Math. Res. Not. 2012, doi: 10.1093/imrn/rns132. preprint arXiv:1111.1097 - The Picard group of a coarse moduli space of vector bundles in positive characteristic.
Cent. Eur. J. Math. 10 (2012), 1306-1313. preprint arXiv:1204.4418 - (with B. Andreas) SU(5) Heterotic Standard Model Bundles.
J. High Energy Phys. 2012, Number 4 (2012), 27. preprint arXiv:1111.1099 - (with I. Biswas) Poincaré families of G-bundles on a curve.
Math. Ann. 352 (2012), 133-154. preprint arXiv:1001.2123 - Independent parameters for special instanton bundles on ℙ2n+1.
J. Geom. Phys. 61 (2011), 2321-2330. preprint arXiv:1107.4757 - (with I. Biswas, A. Hogadi, A.H.W. Schmitt) The Brauer group of moduli spaces of vector bundles over a real curve. Proc. Amer. Math. Soc. 139 (2011), 4173-4179. preprint (pdf)
- (with I. Biswas, T. Gómez, A. Hogadi) Einstein-Hermitian connection on twisted Higgs bundles. C. R. Acad. Sci. Paris 348 (2010), 981-983. preprint arXiv:1008.2034
- On moduli stacks of G-bundles over a curve. in: A.H.W. Schmitt (Ed.): Affine Flag Manifolds and Principal Bundles, Birkhäuser Trends in Mathematics (2010), pp. 155-163. preprint (pdf)
- The Moduli Stack of Vector Bundles on a Curve. in: I. Biswas, R. S. Kulkarni, S. Mitra (Eds.): Teichmüller Theory and Moduli Problems, Ramanujan Mathematical Society Lecture Notes Series, Vol. 10 (2010), pp. 387-394. preprint (pdf)
- (with I. Biswas) The Line Bundles on Moduli Stacks of Principal Bundles on a Curve.
Documenta Math. 15 (2010), 35-72. preprint arXiv:0805.2915 - Moduli Stacks of Vector Bundles on Curves and the King-Schofield Rationality Proof.
in: F. Bogomolov, Y. Tschinkel (Eds.): Cohomological and Geometric Approaches to Rationality Problems, Birkhäuser Progr. Math. 282 (2010), pp. 133-148. preprint arXiv:math/0511660 - (with I. Biswas) Poincaré families and automorphisms of principal bundles on a curve.
C. R. Acad. Sci. Paris 347 (2009), 1285-1288 - On Arakelov vector bundles over arithmetic curves. in: I. Kersten, R. Mayer (Eds.): Symmetries in Algebra and Number Theory, Unversitätsverlag Göttingen (2009), pp. 49-58.
- (with I. Biswas, T. Gómez, M. Logares)
Torelli Theorem for the Deligne-Hitchin Moduli Space.
Comm. Math. Phys. 290 (2009), 357-369. preprint arXiv:0901.0021 - (with I. Biswas, G. Hein) On semistable vector bundles over curves.
C. R. Acad. Sci. Paris 346 (2008), 981-984 - (with I. Biswas) Some moduli stacks of symplectic bundles on a curve are rational.
Adv. Math. 219 (2008), 1150-1176. preprint arXiv:math/0604183 - Rationality and Poincaré families for vector bundles with extra structure on a curve.
Int. Math. Res. Not. Vol. 2007, Article ID rnm010. preprint arXiv:math/0511656 - (with M. Spitzweck) Homological algebra with locally compact abelian groups.
Adv. Math. 212 (2007), 504-524. preprint arXiv:math/0510345 - (with U. Stuhler) Moduli Schemes of Generically Simple Azumaya Modules.
Documenta Math. 10 (2005), 369-389. preprint arXiv:math/0411094 - Kreisteilung nach Mihailescu. in: Y. Tschinkel (Ed.): Mathematisches Institut, Universität Göttingen: Seminars 2003/2004, Universitätsdrucke Göttingen (2004), pp. 117-125.
- The Boden-Hu conjecture holds precisely up to rank 8.
Math. Ann. 330 (2004), 729-746. preprint arXiv:math/0310160 - Stability of Arakelov Bundles and Tensor Products without Global Sections.
Documenta Math. 8 (2003), 115-123. preprint arXiv:math/0304017 - (with J. Jahnel, U. Stuhler) Generalized vector bundles on curves.
J. reine angew. Math. 495 (1998), 35-60
Preprints
- (with I. Biswas, T. Gómez) Stability of the Poincaré bundle. preprint arXiv:1701.04649
- (with F. Reede) Torsion-free rank one sheaves over del Pezzo orders. preprint arXiv:1603.03324
- (with U. Derenthal) Degeneration of torsors over families of del Pezzo surfaces. preprint arXiv:1601.00685
Habilitation, Ph. D. and Diploma Thesis
- Modulräume von Bündeln - Rationalität, Existenz von Poincaré-Familien und Geradenbündel auf den Modulstacks. Habilitationsschrift, Berlin 2011. Zusammenfassung (pdf) Summary (pdf)
- On vector bundles over algebraic and arithmetic curves.
Dissertation, Bonn 2002. Bonner Mathematische Schriften 351 (2002). pdf - Verallgemeinerte Garben über einer algebraischen Kurve.
Diplomarbeit, Göttingen 1998. Mathematica Gottingensis 14 (1999)
