Lothar Göttsche
Coordinator of the Diploma Course in Mathematics, Abdus Salam International Centre for Theoretical Physics(ICTP), Trieste, Italy
2008-present: Coordinator of ICTP's diploma course in mathematics
1999-present: Research Scientist at ICTP
1997-1998: Tenure Track Scientist at ICTP
1996-1997: Postdoctoral Fellow at the Mittag-Leffler-Institut (Stockholm, Sweden)
1995-1996: Postdoctoral Fellow at the University of Pisa (Italy)
1993-1995: Postdoctoral Fellow at the Max-Planck-Institut für Mathematik Bonn (Germany)
1992-present: Ph.D in Mathematics at University of Bonn (Germany), Advisor Friedrich Hirzebruch
1992-1993: Postdoctoral Fellow at the University of Trento (Italy)
Field of study
Algebraic geometry, in particular moduli spaces, and generating functions of their numerical invariants. This includes Hilbert schemes, moduli spaces of sheaves and vector bundles, Donaldson invariants, moduli spaces of curves and Gromov-Witten invariants and enumerative geometry of curves. Modular forms and and relations to theoretical physics.
Lectures
ICTP Postgraduate Diploma Programme, Algebraic Geometry, Trieste, 2019
ICTP School and Workshop on Gauge Theories and Differential Invariants, Virtual topological invariants of moduli spaces of sheaves on surfaces, Trieste, 2019
ICTP Basic Notions Seminars, The Weil Conjectures, Trieste, 2016
IMPA Special Thematic Program on Algebraic Geometry, Rio de Janeiro, 2015
ICTP Diploma Programme in Mathematics, Abstract Algebra, Trieste, 2013
ICTP Diploma Programme in Mathematics, Algebraic Geometry, Trieste, 2012
Selected Publications
Perverse sheaves and the cohomology of Hilbert schemes of smooth algebraic surfaces, with W. Soergel, Math. Ann. 296 (1993), 235–245.
The cohomology ring of the Hilbert scheme of 3 points on a smooth projective variety, with B. Fantechi, J. reine angew. Math. 439(1993), 147–158.
Variation of moduli spaces and Donaldson invariants under change of polarization, with G. Ellingsrud, J. reine angew. Math. 467 (1995), 1–49.
Modular forms and Donaldson invariants for 4-manifolds with b+ =1, Journal of the AMS 9 (1996), 827-843.
A conjectural generating function for numbers of curves on surfaces, Comm. Math. Phys. 196 (1998), 523–533.
Theta functions and Hodge numbers of moduli spaces of sheaves on rational surfaces, Comm. Math. Phys. 206 (1999), 105–136.
B. Fantechi, L. G¨ottsche, Orbifold cohomology for global quotients. Duke Math. J. 117 (2003), no. 2, 197–227.
Appointments and Awards
2012 Fellow of the AMS
2011/2012 Hirzebruch Research Chair at Max-Planck-Institut fur Mathematik, Bonn (Germany)
Since 2010 Editor of Rendiconti dell’Istituto di Matematica dell’Università di Trieste
Since 2009 Member of the Board of ICMS
Since 2008 Member of the Program committee, International Centre for Mathematical Sciences (ICMS), Edinburgh
Since 2007-2011 Member of the Scientific council (Fachbeirat) of the Max-Planck-Institut fur Mathematik Bonn
Since Sept. 2005 Editor of Geometry and Topology