Lothar Göttsche (born January 21, 1961 in Sonderburg,

Denmark ) , song = ( en, "King Christian stood by the lofty mast") , song_type = National and royal anthem , image_map = EU-Denmark.svg , map_caption = , subdivision_type = Sovereign state , subdivision_name = Danish Realm, Kingdom of Denmark ...

) is a German mathematician, known for his work in

algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

. He is a research scientist at the

International Centre for Theoretical Physics The Abdus Salam International Centre for Theoretical Physics (ICTP) is an international research institute for physical and mathematical sciences that operates under a tripartite agreement between the Italian Government, United Nations Education ...

Trieste Trieste ( , ; sl, Trst ; german: Triest ) is a city and seaport in northeastern Italy. It is the capital city, and largest city, of the autonomous region of Friuli Venezia Giulia, one of two autonomous regions which are not subdivided into provi ...

, Italy. He is also editor for

Geometry & Topology ''Geometry & Topology'' is a peer-refereed, international mathematics research journal devoted to geometry and topology, and their applications. It is currently based at the University of Warwick, United Kingdom, and published by Mathematical Sci ...

Biography

After studying mathematics at the University of Kiel, he received his

Dr. rer. nat. ''Doctor rerum naturalium'' ( for, , Latin, doctor of natural sciences, lit. 'doctor of the things of nature'), abbreviated Dr. rer. nat., is a doctoral academic degree awarded by universities in some European countries (e.g. Germany, Austria and C ...

under the direction of Friedrich Hirzebruch at the

University of Bonn The Rhenish Friedrich Wilhelm University of Bonn (german: Rheinische Friedrich-Wilhelms-Universität Bonn) is a public research university located in Bonn, North Rhine-Westphalia, Germany. It was founded in its present form as the ( en, Rhine U ...

in 1989. Göttsche was invited as speaker to the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

in Beijing in 2002. In 2012 he became a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

Work

Göttsche received international acclaim with his formula for the

generating function In mathematics, a generating function is a way of encoding an infinite sequence of numbers () by treating them as the coefficients of a formal power series. This series is called the generating function of the sequence. Unlike an ordinary seri ...

for the

Betti numbers In algebraic topology, the Betti numbers are used to distinguish topological spaces based on the connectivity of ''n''-dimensional simplicial complexes. For the most reasonable finite-dimensional spaces (such as compact manifolds, finite simplicia ...

of the

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 (or a more general projective scheme), refining the Chow variety. The Hilbert scheme is a d ...

of points on an algebraic surface: :If

S

is a smooth surface over an algebraically closed field of characteristic

0

, then the generating function for the motives of the Hilbert schemes of

S

can be expressed in terms of the

motivic zeta function In algebraic geometry, the motivic zeta function of a smooth algebraic variety X is the formal power series :Z(X,t)=\sum_^\infty ^^n Here X^ is the n-th symmetric power of X, i.e., the quotient of X^n by the action of the symmetric group S_n, and ...

by Göttsche's formula ::

^n=\prod_^\infty Z(S,^t^m)

:Here

S^

is the Hilbert scheme of length

n

subschemes of

S

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

curve In mathematics, a curve (also called a curved line in older texts) is an object similar to a line (geometry), line, but that does not have to be Linearity, straight. Intuitively, a curve may be thought of as the trace left by a moving point (ge ...

s in certain

linear systems In systems theory, a linear system is a mathematical model of a system based on the use of a linear operator. Linear systems typically exhibit features and properties that are much simpler than the nonlinear case. As a mathematical abstraction ...

on algebraic surfaces.

References

External links

Home page of Lothar Göttsche
20th-century German mathematicians Algebraic geometers People from Sønderborg Municipality University of Kiel alumni University of Bonn alumni Fellows of the American Mathematical Society 1961 births Living people 21st-century German mathematicians {{Germany-mathematician-stub