The main goal of the conference is to discuss recent progress on SCHUBERT VARIETIES, their appearances in algebraic geometry, representation theory, combinatorics and mathematical physics.
Schubert Calculus is a theory relating geometry with combinatorics that grew from attempts to answer rigorously classical questions in enumerative geometry, such as how many lines in the 3-space intersect 4 lines in general position. The answer to this and more general problems can be reformulated as a calculation in an appropriate intersection ring, such as the cohomology and K-theory ring, and it answers an instance of Hilbert's 15th problem. Schubert Calculus is nowadays a well established theory which is a crucial tool in many investigations in algebraic geometry but also motivates further research in branches of mathematics related to combinatorics and representation theory. Although basics of Schubert calculus are now an important part of proper education of mathematicians of different fields, the theory is still developed very actively and continues to cover new territories which includes applications related to physics. In the last two decades, ideas from physics led to the definition of the quantum versions of the cohomology and K-theory rings, where Schubert calculus is being performed nowadays.
In the last years, there have been three large conferences dedicated to Schubert Calculus: in Osaka (Japan, 2012), IMPANGA 15 (Będlewo, Poland 2015) and Guangzhou (China, 2017). Our intent is to continue this tradition, and showcase the latest advances in the subject, as well as the emerging trends. The workshop is meant to encourage discussions among experts in the field, as well as to attract young Ph.D. students and researchers from nearby areas. There will be around 15 - 20 talks delivered by the world-class experts. We aim at creating a stimulating environment for discussions and possible collaborations among the participants, and to deliver a nice introduction to recent achievements in different branches of Schubert calculus, thus there is a period of time planned for discussions among participants after the afternoon sessions.