Schubert calculus refers to the calculus of enumerative geometry, which is the art of counting geometric figures determined by given incidence conditions. For example, how many lines in projective 3-space meet four given lines? This was developed in the 19th century and presented in the classic treatise ”Kälkul der abzählanden Geometrie” by Herman Cäser Hannibal Schubert in 1879. Schubert, Pier...

We study Gröbner degenerations of Schubert varieties inside flag varieties. consider toric induced by matching fields and semi-standard Young tableaux. describe an analogue field ideals for the variety give a complete characterization among them. use combinatorial approach to standard monomial theory show that block diagonal rise degenerations. Our methods results combinatorics permutations ass...

[1] Northern India and its surroundings, home to roughly 600 million people, is probably the most heavily irrigated region in the world. Temporal changes in Earth’s gravity field in this region as recorded by the GRACE satellite mission, reveal a steady, large-scale mass loss that we attribute to excessive extraction of groundwater. Combining the GRACE data with hydrological models to remove na...

We investigate double transitivity of Galois groups in the classical Schubert calculus on Grassmannians. We show that all Schubert problems on Grassmannians of 2and 3-planes have doubly transitive Galois groups, as do all Schubert problems involving only special Schubert conditions. We use these results to give a new proof that Schubert problems on Grassmannians of 2-planes have Galois groups t...

Patientinnen mit einem systemischen Lupus erythematodes (SLE) sind aufgrund der Immunerkrankung sowie chronischen immunsuppressiven Therapie anfällig für Virusinfektionen und Malignome. Ein besonders hohes Risiko besteht im Hinblick auf das durch humane Papillomviren (HPV) verursachte Zervixkarzinom. Wie häufig nehmen die Betroffenen empfohlenen Screeninguntersuchungen wahr? Und wie werden dabe...