Lothar Göttsche (born January 21, 1961, in Sonderburg,

Denmark Denmark is a Nordic countries, Nordic country in Northern Europe. It is the metropole and most populous constituent of the Kingdom of Denmark,, . also known as the Danish Realm, a constitutionally unitary state that includes the Autonomous a ...

) is a German mathematician, known for his work in

algebraic geometry Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...

. He is a research scientist at the

International Centre for Theoretical Physics The Abdus Salam International Centre for Theoretical Physics (ICTP) is a research center for physical and mathematical sciences, located in Trieste, Friuli-Venezia Giulia, Italy. The center operates under a tripartite agreement between the Gov ...

Trieste Trieste ( , ; ) is a city and seaport in northeastern Italy. It is the capital and largest city of the Regions of Italy#Autonomous regions with special statute, autonomous region of Friuli-Venezia Giulia, as well as of the Province of Trieste, ...

, Italy. He is also editor for Geometry & Topology.

Biography

After studying mathematics at the

University of Kiel Kiel University, officially the Christian Albrecht University of Kiel, (, abbreviated CAU, known informally as Christiana Albertina) is a public research university in the city of Kiel, Germany. It was founded in 1665 as the ''Academia Holsator ...

, he received his

Dr. rer. nat. for, la, Doctor rerum naturalium, Doctor of Natural Sciences, paren=left, ), abbreviated Dr. rer. nat., is a doctoral academic degree awarded by universities in some European countries (e.g. Germany, Austria and Czech Republic) to graduates in phy ...

under the direction of Friedrich Hirzebruch at the

University of Bonn The University of Bonn, officially the Rhenish Friedrich Wilhelm University of Bonn (), is a public research university in Bonn, North Rhine-Westphalia, Germany. It was founded in its present form as the () on 18 October 1818 by Frederick Willi ...

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 IMU Abacus Medal (known before ...

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 representation of an infinite sequence of numbers as the coefficients of a formal power series. Generating functions are often expressed in closed form (rather than as a series), by some expression invo ...

for the Betti numbers 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 ...

of points on an algebraic

surface A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is ...

: :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 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, but that does not have to be straight. Intuitively, a curve may be thought of as the trace left by a moving point. This is the definition that ...

s in certain linear systems on algebraic

surfaces A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. Surface or surfaces may also refer to: Mathematics *Surface (mathematics), a generalization of a plane which needs not be flat * Sur ...

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