# Projects

The following is a list of research projects and possible PhD subjects for students working in the Graduiertenkolleg.

- Index theory, higher torsion and algebraic K-theory (S. Goette)

- Eta invariants in differential topology (S. Goette)

- Arakelov-Motives (S. Goette, A. Huber-Klawitter)

- Quotient spaces in higher-dimensional algebraic geometry (D. Greb)

- Differential forms on singular spaces: vanishing theorems and Hodge theory (D. Greb, S. Kebekus)

- Special values of Dedekind ζ-functions (A. Huber-Klawitter)
- Periods, torsors and motives (A. Huber-Klawitter)
- Moduli spaces in higher-dimensional algebraic geometry: Variation of Hodge structures and deformation theory (S. Kebekus)
- L
^{2}-cohomology and Morse theory for singular spaces (U. Ludwig) - Noncommutative Hodge theory and Gromov-Witten invariants (E. Scheidegger)
- Deformation theory of matrix factorization and holomorphic vector bundles (E. Scheidegger)
- Koszul duality in representation theory (W. Soergel)
- Formality in modular representation theory (W. Soergel)
- Elliptic genus and the chiral de Rham complex (K. Wendland)
- Deformation theory of conformal field theories (K. Wendland)
- Affine Brown-Gersten property and h-principles (M. Wendt)
- Spherical fibrations in A
^{1}-homotopy (M. Wendt)