3 papers
math.CV2021
Non-commutative amoebas
Grigory Mikhalkin, Mikhail Shkolnikov
The group of isometries of the hyperbolic 3-space is one of the simplest non-commutative complex Lie groups. Its quotient by the maximal compact subgroup naturally maps it back to…
math-ph2019
Sandpile monomorphisms and limits
Moritz Lang, Mikhail Shkolnikov
We introduce a tiling problem between bounded open convex polyforms with directed and uniquely colored edges. If there exists a tiling of the polyform…
cond-mat.quant-gas2018
Quantum groups as hidden symmetries of quantum impurities
Enderalp Yakaboylu, Mikhail Shkolnikov, Mikhail Lemeshko
We present an approach to interacting quantum many-body systems based on the notion of quantum groups, also known as -deformed Lie algebras. In particular, we show that if the s…