Lothar Göttsche is a German

Germans

The Germans are a Germanic ethnic group native to Central Europe. The English term Germans has referred to the German-speaking population of the Holy Roman Empire since the Late Middle Ages....

 mathematician

Mathematician

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

, known for his work in algebraic geometry

Algebraic geometry

Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...

. After studying mathematics at the University of Kiel

University of Kiel

The University of Kiel is a university in the city of Kiel, Germany. It was founded in 1665 as the Academia Holsatorum Chiloniensis by Christian Albert, Duke of Holstein-Gottorp and has approximately 23,000 students today...

, he received his Dr. rer. nat. under the direction of Friedrich Hirzebruch

Friedrich Hirzebruch

Friedrich Ernst Peter Hirzebruch is a German mathematician, working in the fields of topology, complex manifolds and algebraic geometry, and a leading figure in his generation.-Life:He was born in Hamm, Westphalia...

 at the University of Bonn

University of Bonn

The University of Bonn is a public research university located in Bonn, Germany. Founded in its present form in 1818, as the linear successor of earlier academic institutions, the University of Bonn is today one of the leading universities in Germany. The University of Bonn offers a large number...

 in 1989. He was invited as speaker to the International Congress of Mathematicians

International Congress of Mathematicians

The International Congress of Mathematicians is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union ....

 in Beijing

Beijing

Beijing , also known as Peking , is the capital of the People's Republic of China and one of the most populous cities in the world, with a population of 19,612,368 as of 2010. The city is the country's political, cultural, and educational center, and home to the headquarters for most of China's...

 in 2002. Göttsche is a research scientist at the International Centre for Theoretical Physics

International Centre for Theoretical Physics

The Abdus Salam International Centre for Theoretical Physics was founded in 1964 by Pakistani scientist and Nobel Laureate Abdus Salam after consulting with Munir Ahmad Khan. It operates under a tripartite agreement among the Italian Government, UNESCO, and International Atomic Energy Agency...

 in Trieste

Trieste

Trieste is a city and seaport in northeastern Italy. It is situated towards the end of a narrow strip of land lying between the Adriatic Sea and Italy's border with Slovenia, which lies almost immediately south and east of the city...

, Italy

Italy

Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...

. He is also editor for Geometry & Topology.

Göttsche received international acclaim with his formula for the generating function

Generating function

In mathematics, a generating function is a formal power series in one indeterminate, whose coefficients encode information about a sequence of numbers an that is indexed by the natural numbers. Generating functions were first introduced by Abraham de Moivre in 1730, in order to solve the general...

 for the Betti numbers of the Hilbert scheme

Hilbert scheme

In algebraic geometry, a branch of mathematics, a Hilbert scheme is a scheme that is the parameter space for the closed subschemes of some projective space , refining the Chow variety. The Hilbert scheme is a disjoint union of projective subschemes corresponding to Hilbert polynomials...

 of points on an algebraic surface

Surface

In mathematics, specifically in topology, a surface is a two-dimensional topological manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R3 — for example, the surface of a ball...

:

If is a smooth surface over an algebraically closed field of characteristic , then the generating function for the motives of the Hilbert schemes of can be expressed in terms of the motivic zeta function by Göttsche's formula


Here is the Hilbert scheme of length subschemes of .

Göttsche is also the author of a celebrated conjecture predicting the number of curve

Curve

In mathematics, a curve is, generally speaking, an object similar to a line but which is not required to be straight...

s in certain linear systems

Linear system of divisors

In algebraic geometry, a linear system of divisors is an algebraic generalization of the geometric notion of a family of curves; the dimension of the linear system corresponds to the number of parameters of the family....

 on algebraic surfaces.