# Institute for Discrete Structures and Symbolic Computation (IDSC)

The IDSC at the University of Stuttgart focuses on algebra and geometry with particular regard to discrete structures and computer-aided methods (symbolic computation).

[Photo: University of Michigan/John Stembridge]

## Welcome to the IDSC website

Our focus in research and teaching is set on algebra and geometry, as well as their application to various problems in computer science, physics or biology. A notable feature is the use of discrete methods and tools from symbolic computation. These involve various areas of pure mathematics, but prove also useful for discrete problems of applied mathematics.

The institute also participates in joint research projects such as as the CRC-TRR 195 "Symbolic tools in Mathematics and their Application“ and is involved in various international software develoment projects such as CHEVIE. Further details can be found on our research pages.

To get an idea of our teaching activities you can also have a look at the presentation of the G.A.G.A. lecture track, or our supervised bachelor and master theses.

**B.Sc.**

- Proofs of Transcendence (Geck)
- Standard generators for finite fields (Geck)
- The Theorem of Riemann-Roch (Witt)
- NTRU-Kryptosystem (Witt)
- Topological data analysis with the Vietoris-Rips complex (Witt)
- The Geometry of Classical Mechanics (Degeratu)
- Sphere packings constructed via binary block codes by means of construction A (Degeratu)
- Mathieu groups (Veniani / Witt)
- Topological Data Analysis with the Vietoris-Rips-Complex (Witt)
- Hyperbolic Spaces (Degeratu)
- Cosmology (Degeratu)
- Rationality questions for characters (Geck)
- On the Glauberman correspondence (Geck)
- Fischer's 3-transposition groups (Geck)
- Quadratic reciprocity (Geck)
- The tropical Grassmannian variety (Witt)
- The Mordell-Weil Theorem on elliptic curves (Witt)
- The collapse of a star and the formation of black holes (Degeratu)
- Traversible Schwarzschild Wormholes (Degeratu)
- Gravitational Waves (Degeratu)
- Constructions of simple Lie algebras (Geck)
- Symmetric groups and their generation (Geck)
- Regular algebraic curves (Witt)
- On the classification of complex surfaces (Witt)
- The Schwarzschild-Metric (Degeratu)
- The theorem of Hasse-Minkowski (Geck)
- Gröbner bases and their applications (Geck)
- The Pfaffian (Geck)
- Factorisation of integers into primes (Geck)
- Elliptic curves and Lenstra's factorisation algorithm (Geck)
- Golay codes (Geck / Iancu)
- Intervals in the Bruhat order (Geck / Iancu)
- Toric Ideals, Gröbner Bases and the Knapsack Problem (Witt)
- Solomon's descent algebra (Geck)
- Representation theory of the symmetric group (Geck / Iancu)
- Invariants and order of a finite reflection group (Geck / Iancu)
- p-adic numbers (Geck / Iancu)
- Mathieu groups (Geck / Iancu)
- The orthogonal group in characteristic 2 (Geck)
- Quotients of algebraic groups (Geck)
- Hilbert's Nullstellensatz (Geck)
- Computation of character tables of finite groups (Geck)

**B.A. **

- Desargues` and Pappus` Theorem in Projective Geometry (Witt)
- The Picard- and Jacobi-Variety of a Riemann surface (Witt)

**M.Sc.**

- Singular value decomposition - theory and applications (Geck)
- Algorithms for Chevalley's Theorem (Geck / Witt)
- Neural Networks and Quiver Varieties (Degeratu)
- Co-Higgs bundles on projective spaces (Witt)
- Elliptic curves and Galois extensions of Q (Witt)
- Protein sequences and tropical geometry (Witt)
- Critical brain hypothesis from a mathematical point of view (Degeratu)
- Toric Co-Higgs bundles and pre-valued vector spaces (Witt)
- The Laws of Black Hole Theromodynamics from a Mathematical Viewpoint (Degeratu)
- Arithmetic of elliptic curves over finite fields (Geck)
- Varieties of commuting matrices (Geck)
- Unipotent classes in algebraic groups (Geck)
- Gravitational Waves in the Presence of Cosmological Constant (Degeratu)
- Maximal subgroups and Wall's conjecture (Geck)
- Canonical bases of quantum groups (Geck)
- Quotients of algebraic varieties (Witt)
- Free Lie algebras and the PBW theorem (Geck)
- Limiting configurations from a hermitian point of view (Witt)
- Hodge Theory on noncompact manifolds (Witt)
- Representations of Chevalley groups (Geck)
- Quantum groups (Geck)
- Blocks of finite groups and the McKay conjecture (Geck)
- Characters and commutators of finite algebra groups (Geck)

**M.Ed.**

- Elliptic curves and Galois extensions of Q (Witt)
- Neural networks and Gröbner bases (Witt)

Further information can be also found on the personal pages of our members.

**Research groups**

The institute currently consists of the research groups

### Contact:

### Brigitta Bauer

Administration office Chair of Algebra

### Rebekka Lutz

Administration office Chair of Differentialgeometry