Dr Konstanze Rietsch
Telephone: +44 020 7848 1443
Office: S4.17, Strand Building, Strand Campus
Title: Co-director CDT
PhD from MIT, 1998, Supervisor G. Lusztig,
Joined King's in 2002.
EPSRC Advanced Research Fellow since September 2006.
Konstanze's research is concerned with algebraic groups mostly over the complex numbers. Her particular interests relate to the geometry of flag varieties, or flag manifolds, which are associated to algebraic groups and play a central role in their representation theory. For example, she has been studying their quantum cohomology rings, which encode enumerative invariants related to rational curves in flag varieties (Gromov-Witten invariants). This research has uncovered a close connection between positivity of the Gromov-Witten invariants and the theory of total positivity for algebraic groups, the latter of which is also related to quantum groups. Her more recent work has been on a Lie theoretic approach to mirror symmetry for flag varieties.
Selection of Publications
Here are some recent papers / preprints :
with Thomas Lam ``Total Positivity, Schubert Positivity, and Geometric Satake'', 23 pages, in preparation
with J Lopez Pena and S Majid ``Lie theory of finite simple groups and the generalised Roth conjecture'', 38 pages, version on arxiv under revision
with L. Williams ``Discrete Morse theory for totally non-negative flag varieties'', 30 pages, Advances in Mathematics, (2009), DOI: 10.1016/j.aim.2009.10.011, math.CO/0810.4314
``A mirror symmetric solution to the quantum Toda lattice'', 25 pages, to appear in CMP, math.RT/0705.3202
with L. Williams ``The totally nonnegative part of G/P is a CW complex'', 14 pages, Transformation Groups, Vol. 13, Special volume in honor of B. Kostant's 80th birthday, (2008), 839-953 math.AG/0802.0889
``A mirror symmetric construction for qH*_T(G/P)_(q)'', Advances in Mathematics, Vol 217, Issue 6, (2008), 2401-2442, math.AG/0511.124