index.htmpl
Sebastian Zwicknagl
Mathematisches Institut
Universität Bonn
Endenicher Allee 60
52123 Bonn

Tel +49 228 733136
email sebzwi 'at' math dot uni-bonn dot de


Research Interests:
Cluster Algebras, Lie theory, quantum groups, Poisson geometry, total positivity

In particular: the publications 1) -4) investigate quantizations of symmetric and exterior algebras of modules over quantum groups. Papers 1) and 3) are particularly ointerested in the connection to coboundary categories and crystal commutors,m papers 2) and 4) explore surprising  connections between non-commutative geoemtry, multiplicity-freeness and Classical Invariant Theory, mainly using Poisson geometry.

The Papers 5) and 6) investigate the Poisson and symplectic geometry of cluster algebras, by employing the natural torus actions (5). The subsequent paper 6) then uses these results to investigate open questions about the ring theory of quantum groups,  but it needs to be seriously revised.


Publications:

3)Equivariant Quantizations of Symmetric Algebras
J. Algebra 322 (2009), no . 12, 4247--4282.

2)R-matrix Poisson algebras and their deformations.
Adv . Math . 220 (2009), no . 1, 1--58.

1)Braided Symmetric and Exterior Algebras (with A. Berenstein)
Trans. Amer. Math. Soc. 360 (2008), 3429-3472.


Teaching Summer 2012:

Exercises for  Representation Theory 2

(Every other Thursday from 12-2 in MZ 1.008


Preprints:

6)Poisson Ideals in Cluster Algebras and the Spectra of Quantized Coordinate Rings

5)Toric Poisson Ideals in Cluster Algebras (submitted )

4)Braided Symmetric Algebras of Simple $U_q(sl_2)$-Modules and Their Geometry (submitted )

 

Brief CV:

Dec 2006 PhD, University of Oregon
Jan 2007-Jun 2009 Visiting Assistant Professor, University of California, Riverside
Oct 2009--present Assistent, Universitaet Bonn