Коллоквиум МЛЗС: E. Lupercio (Cinvestav) и Д.Каледин (МИАН, НИУ ВШЭ)
"Quantum Toric Varieties"
E. Lupercio (Cinvestav)
In this talk I present in more detail the theory of quantum toric varieties developed by Katzarkov, Meersseman, Verjosvsky and myself. I will explain what a quantum fan is and how it correspond to a quantum toric variety. Additionally, I will present the moduli of quantum P^1.
"Brown representability for groupoids"
Д.Каледин (МИАН, НИУ ВШЭ)
Abstract: Brown representability theorem in topology was very important when it appeared 50 years ago, but now is reduced to a bit of a historical curiosity and not used much. Part of the reason is that it only applies to functors from pointed connected CW complexes to abelian groups. We will show how to upgrade the theorem to functors from arbitrary complexes to groupoids. This gives a very simple, concise and purely categorical description of homotopy types and enhanced categories, without any need to choose any specific model and impose any notion of a weak equivalence or a model structure. In particular, in this description, it is easy to put some additional algebraic or geometric structure on the target groupoids and obtain notions th