Professor Konstanze Rietsch
Telephone: +44 020 7848 2225
Office: S4.17, Strand Building, Strand Campus
Title: Professor of Geometry
The EPSRC Centre for Doctoral Training in Geometry and Number Theory
The London School of Geometry and Number Theory
Mag.rer.nat. Vienna, 1993, Austrian citizen.
PhD from MIT, 1998, Supervisor G. Lusztig.
Joined King's in 2002.
Promoted to Professor in 2017.
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
R. Marsh and K. Rietsch The B-model connection and mirror symmetry for Grassmannians, arXiv:1307.1085v2, 88 pages
T. Lam and K. Rietsch, Total positivity, Schubert positivity, and geometric Satake, Journal of Algebra, Volume 460, (2016) pp 284 - 319
C. Pech, K. Rietsch, and L. Williams, On Landau-Ginzburg models for quadrics and flat sections of Dubrovin connections, Advances in Mathematics, Volume 300, Special volume honouring Andrei Zelevinsky, (2016) pp 275-319
S. Majid, K. Rietsch, Lie theory and coverings of finite groups
, Journal of Algebra, Volume 389, (2013) pp 137 - 150
K. Rietsch, A mirror symmetric solution to the quantum Toda lattice, Communications in Mathematical Physics, Volume 309, Number 1, (2012) pp 23 - 49
K. Rietsch, A mirror symmetric construction of qH*_T (G/P)_(q)
, Advances in Mathematics, Volume 217, Issue 6, (2008) pp 2401 - 2442
R. Marsh and K. Rietsch, Parametrizations of flag varieties, Representation Theory, 8, (2004) pp 212 - 242
K. Rietsch, Totally positive Toeplitz matrices and quantum cohomology rings of partial flag varieties, Journal of the American Mathematical Society, 16 (2003), pp 363 - 392
K. Rietsch, Quantum cohomology rings of Grassmannians and total positivity, Duke Mathematical Journal, 113 no. 3 (2001) pp 521 - 551
K. Rietsch, An algebraic cell decomposition of the nonnegative part of a flag variety, Journal of Algebra, 213 (1999) pp 144 -154