Boris Bilich

Goat incognito.

Since October 2023, I am a PhD student cosupervised by Ralf Meyer at Georg-August-Universität Göttingen and Adam Dor-On at University of Haifa. Before starting my PhD, I was a Master student in Georg-August-Universität Göttingen and a Bachelor student at HSE University, Moscow.

I work in the field of operator algebras and noncommutative geometry. My primary research focus right now is interpretation of constructions such as (higher-rank, topological) graph C*-algebras, Leavitt path algebras, and Cuntz-Pimsner algebras as limits of diagrams in suitable bicategories. The limit universal property then can provide a lot of information about these objects.

selected publications

Arveson’s hyperrigidity conjecture is false

Boris Bilich, and Adam Dor-On

2024

Abs arXiv

Arveson’s hyperrigidity conjecture predicts that if the non-commutative Choquet boundary of a separable operator system S is the entire spectrum of its generated C*-algebra B then S is hyperrigid in B. We provide a counterexample to the conjecture with a C*-algebra B of type I generated by a single operator.
Equivariant homotopy classification of graph C*-algebras

Boris Bilich, Adam Dor-On, and Efren Ruiz

2024

Abs arXiv

We show that shift equivalence of essential adjacency matrices coincides with gauge-equivariant homotopy equivalence of their stabilized graph C*-algebras. This provide the first equivalent formulation of shift equivalence of essential matrices in terms of gauge actions on graph C*-algebras. Our proof uses bicategory theory for C*-bimodules developed by Meyer and Sehnem, allowing us to avoid the use of K-theory classification of C*-algebras.