Gabriele Nebe (born 1967) is a

German German(s) may refer to: * Germany (of or related to) ** Germania (historical use) * Germans, citizens of Germany, people of German ancestry, or native speakers of the German language ** For citizens of Germany, see also German nationality law **Ge ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

with contributions in the theory of lattices,

modular form In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the Group action (mathematics), group action of the modular group, and also satisfying a grow ...

spherical design A spherical design, part of combinatorial design theory in mathematics, is a finite set of ''N'' points on the ''d''-dimensional unit n-sphere, ''d''-sphere ''Sd'' such that the average value of any polynomial ''f'' of degree ''t'' or less on the se ...

s, and

error-correcting codes In computing, telecommunication, information theory, and coding theory, an error correction code, sometimes error correcting code, (ECC) is used for controlling errors in data over unreliable or noisy communication channels. The central idea is ...

. With

Neil Sloane __NOTOC__ Neil James Alexander Sloane (born October 10, 1939) is a British-American mathematician. His major contributions are in the fields of combinatorics, error-correcting codes, and sphere packing. Sloane is best known for being the creator ...

, she maintains the Online Catalogue of Lattices.Online Catalogue of Lattices
/ref> She is a professor in the department of mathematics at

RWTH Aachen University RWTH Aachen University (), also known as North Rhine-Westphalia Technical University of Aachen, Rhine-Westphalia Technical University of Aachen, Technical University of Aachen, University of Aachen, or ''Rheinisch-Westfälische Technische Hoch ...

Education

Nebe earned a doctorate ( Dr. rer. nat.) in 1995 from

. Her dissertation, ''Endliche Rationale Matrixgruppen vom Grad 24'' concerned the theory of finite

matrix group In mathematics, a matrix group is a group ''G'' consisting of invertible matrices over a specified field ''K'', with the operation of matrix multiplication. A linear group is a group that is isomorphic to a matrix group (that is, admitting a fa ...

s and was supervised by Wilhelm Plesken.

Research

Nebe is known for using integral representations of finite groups to construct explicit examples of discrete mathematical structures using

computer algebra system A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists. The de ...

s. Her constructions include extremal even

unimodular lattice In geometry and mathematical group theory, a unimodular lattice is an integral lattice of determinant 1 or −1. For a lattice in ''n''-dimensional Euclidean space, this is equivalent to requiring that the volume of any fundamen ...

s in 48, 56, and 72 dimensions and an extremal 3-modular lattice in 64 dimensions. These lattices represent the densest known

sphere packing In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical size, and the space is usually three-dimensional Euclidean space. However, sphere packing p ...

s and the highest known

kissing number In geometry, the kissing number of a mathematical space is defined as the greatest number of non-overlapping unit spheres that can be arranged in that space such that they each touch a common unit sphere. For a given sphere packing (arrangement o ...

s in these dimensions. Her discovery of an extremal unimodular lattice in 72 dimensions settled a long open problem.Roland Quême,

Awards and honours

* 1995 – Friedrich Wilhelm Prize
AcademiaNet
' * 2002 – Merckle Research Prize
University of Ulm
' * 2003 – Research Fellowship –

Radcliffe Institute The Radcliffe Institute for Advanced Study at Harvard University—also known as the Harvard Radcliffe Institute—is a part of Harvard University that fosters interdisciplinary research across the humanities, sciences, social sciences, arts, a ...

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...

References

Living people 1967 births 20th-century German mathematicians 21st-century German mathematicians 20th-century women mathematicians 21st-century women mathematicians {{Germany-mathematician-stub