The Mathematisches Forschungsinstitut Oberwolfach regularly organizes workshops in all fields of Mathematics. Their aim is to offer 45–48 experts, invited by the Institute's Director, the opportunity to present recent research results, especially new methods, and to initiate future research projects. A great number of important papers have been initiated at Oberwolfach due to informal talks and discussions in small groups. Contrary to the typically large conferences all over the world, workshops at Oberwolfach emphasize active research. The Oberwolfach Reports are meant to capture, in an informal manner, the characteristic ideas and discussions of these workshops. As a service to the community, they are now offered by the Institute, at a nominal price, and allow the public to partake in the lively and stimulating atmosphere of these meetings. While the peer-reviewed results will appear elsewhere, the Oberwolfach Reports will keep the reader abreast of current developments and open problems, and serve as an indispensable source of information for the active mathematician.
In [K], a convex-geometric algorithm was introduced for building new analogs of Gelfand–Zetlin polytopes for arbitrary reductive groups. Conjecturally, these polytopes coincide with the Newton–Okounkov polytopes of flag varieties for a geometric valuation. I outline an algorithm (geometric mitosis) for finding collec- tion of faces in these polytopes that represent a given Schubert cycle. For GL_n and Gelfand–Zetlin polytopes, this algorithm reduces to a geometric version of Knutson–Miller mitosis introduced in [KST].