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 Hochschule Aachen, is a German public research university located in Aachen, North Rhine-Westphalia, Germany. With more than 47,000 students enrolled in 144 study programs, it is the largest technical university in Germany. In 2018, the university was ranked 31st in the world university rankings in the field of engineering and technology, and 36th world-wide in the category of natural sciences.
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 of the modular group, and also satisfying a growth condition. The theory of modular forms therefore belongs to complex analysis but the main importance of the theory has traditionally been in its connections with number theory. Modular forms appear in other areas, such as algebraic topology, sphere packing, and string theory.
In mathematics, the Leech lattice is an even unimodular lattice Λ24 in 24-dimensional Euclidean space, which is one of the best models for the kissing number problem. It was discovered by John Leech (1967). It may also have been discovered by Ernst Witt in 1940.
In geometry and group theory, a lattice in the real coordinate space is an infinite set of points in this space with the properties that coordinate wise addition or subtraction of two points in the lattice produces another lattice point, that the lattice points are all separated by some minimum distance, and that every point in the space is within some maximum distance of a lattice point. Closure under addition and subtraction means that a lattice must be a subgroup of the additive group of the points in the space, and the requirements of minimum and maximum distance can be summarized by saying that a lattice is a Delone set. More abstractly, a lattice can be described as a free abelian group of dimension which spans the vector space . For any basis of , the subgroup of all linear combinations with integer coefficients of the basis vectors forms a lattice, and every lattice can be formed from a basis in this way. A lattice may be viewed as a regular tiling of a space by a primitive cell.
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 fundamental domain for the lattice be 1.
In mathematics, a Niemeier lattice is one of the 24 positive definite even unimodular lattices of rank 24, which were classified by Hans-Volker Niemeier (1973). Venkov (1978) gave a simplified proof of the classification. Witt (1941) has a sentence mentioning that he found more than 10 such lattices, but gives no further details. One example of a Niemeier lattice is the Leech lattice.
Walter Feit was an Austrian-born American mathematician who worked in finite group theory and representation theory. His contributions provided elementary infrastructure used in algebra, geometry, topology, number theory, and logic. His work helped the development and utilization of sectors like cryptography, chemistry, and physics.
The Gottfried Wilhelm Leibniz Prize, in short Leibniz Prize, is awarded by the German Research Foundation to "exceptional scientists and academics for their outstanding achievements in the field of research". Since 1986, up to ten prizes are awarded annually to individuals or research groups working at a research institution in Germany or at a German research institution abroad. It is considered the most important research award in Germany.
Many branches of mathematics study objects of a given type and prove a classification theorem. A common theme is that the classification results in a number of series of objects and a finite number of exceptions — often with desirable properties — that do not fit into any series. These are known as exceptional objects. In many cases, these exceptional objects play a further and important role in the subject. Furthermore, the exceptional objects in one branch of mathematics often relate to the exceptional objects in others.
Peter Wasserscheid is a German chemist and professor for chemical reaction engineering at the University of Erlangen-Nuremberg. Together with Matthias Beller he won the Gottfried Wilhelm Leibniz Prize in 2006.
Martin Beneke is a German physicist.
Karin Erdmann is a German mathematician specializing in the areas of algebra known as representation theory and homological algebra. She is notable for her work in modular representation theory which has been cited over 1500 times according to the Mathematical Reviews. Her nephew Martin Erdmann is professor for experimental particle physics at the RWTH Aachen University.
Bhama Srinivasan is a mathematician known for her work in the representation theory of finite groups. Her contributions were honored with the 1990 Noether Lecture. She served as President of the Association for Women in Mathematics from 1981 to 1983. She earned her Ph.D. in physics in 1959 with her dissertation Problems on Modular Representations of Finite Groups under J. A. Green at the University of Manchester. She currently is a professor at the University of Illinois at Chicago. She has had five doctoral students. She has co-authored a number of papers with Paul Fong in modular representation theory and Deligne–Lusztig theory.
Irving Reiner was a mathematician at the University of Illinois who worked on representation theory. He solved the problem of finding which abelian groups have a finite number of indecomposable modules. His book with Charles W. Curtis,, was for many years the standard text on representation theory.
Ludwig Staiger is a German mathematician and computer scientist at the Martin Luther University of Halle-Wittenberg.
Maryna Sergiivna Viazovska is a Ukrainian mathematician known for her work in sphere packing. She is full professor and Chair of Number Theory at the Institute of Mathematics of the École Polytechnique Fédérale de Lausanne in Switzerland. She was awarded the Fields Medal in 2022.
Barbara M. Terhal is a theoretical physicist working in quantum information and quantum computing. She is a researcher at the Forschungszentrum Jülich, a Professor in the EEMCS Department at TU Delft, as well as the Research Lead for the Terhal Group at QUTech. Her research concerns many areas in quantum information theory, including entanglement detection, quantum error correction, fault-tolerant quantum computing and quantum memories.
Martin Grohe is a German mathematician and computer scientist known for his research on parameterized complexity, mathematical logic, finite model theory, the logic of graphs, database theory, and descriptive complexity theory. He is a University Professor of Computer Science at RWTH Aachen University, where he holds the Chair for Logic and Theory of Discrete Systems.
Bettina Eick is a German mathematician specializing in computational group theory. She is Professor of Mathematics at the Technische Universität (TU) Braunschweig.
Britta Nestler is a German materials scientist at the Karlsruhe Institute of Technology. Her research involves the development of software to simulate the formation of microstructures in advanced materials for which experimental studies would be too expensive or difficult.
