Lothar Göttsche's Homepage

My field of research is algebraic geometry. I am in particular interested in moduli spaces and numerical invariants of moduli spaces or defined via moduli spaces.
This includes Hilbert schemes, moduli spaces of sheaves and vector bundles, Donaldson invariants, moduli spaces of curves and Gromov-Witten invariants, enumerative geometry of curves.

I am an editor of Geometry & Topology, and Rendiconti dell'Istituto di Matematica dell'Universita di Trieste.

My publications on MathSciNet, on the Mathematics ArXiv, and on google scholar.

Curriculum vitae, with complete publication list

Recent and current invitations:

Slides of talks:

Hilbert Schemes of points on surfaces, invited talk ICM Beijing 2002
Instanton counting and Donaldson invariants, WAGP, Lisbon 7.9 2004 to 12.9 2004.
Come fare soldi con le curve ellittiche, talk at open day Miramare, 18.9.04 (switch ghostview to "seascape")
Instanton counting,Donaldson invariants, line bundels on moduli spaces of sheaves on rational surfaces, AMS Summer Institute in Algebraic Geometry, Seattle, USA July 25 - August 12, 2005
Virtual Riemann-Roch and Applications, Principal bundles, stacks and gerbes, Bad Honnef June 2007.
Sections of line bundles on moduli spaces of sheaves on surfaces and strange duality, Vancouver February 2009.
Moduli spaces and Modular forms, Trieste October 2009.
Refined curve counting, August 2011.
Refined curve counting and tropical Geometry, Bernoulli Lecture Lausanne, May 2014.
Refined curve counting and tropical Geometry, SWISSMAP conference, January 2015, Lecture 2, Lecture 3, Lecture 4.
Virtual topological invariants of moduli spaces, Seminar Talk ICTP 2017.
Refined curve counting, Talk Cabo Frio August 2018.
Refined Verlinde formulas for moduli spaces of sheaves on surface, Enumeration and Moduli, Oslo 8.12.2018
Virtual topological invariants of moduli spaces of sheaves on surfaces, Talk IGAP 2019.
Tropical refined curve counting, Talk Oberwolfach 2019.
Vafa-Witten formula and generalizations, Calabi-Yau and Geometry, June 2019.
Lehn and Verlinde formulas for moduli spaces of sheaves on surfaces, ETH algebraic geometry seminar June 2020.
Tropical geometry, Basic notions seminar, ICTP, Trieste 15 Juli 2020.

Introductory notes on Schemes: Part 1. Part 2.

Notes of diploma courses:

Algebraic Geometry
Algebra
Algebraic Topology

Notes from schools:

Hilbert schemes: local properties and Hilbert scheme of points.

Lecture notes volumes of schools at ICTP:

Moduli spaces in Algebraic Geometry.
Vanishing Theorems and Effective Results in Algebraic Geometry.
Topology of High-Dimensional Manifolds.
Intersection Theory and Moduli.