Volodymyr Vynnychenko. Shchodennyk, 1929–1931. [Diary, 1929–1931.]

THE TRIANGULATED HOPF CATEGORY n+SL(2) VOLODYMYR LYUBASHENKO

We discuss an example of a triangulated Hopf category related to SL(2). It is an equivariant derived category equipped with multiplication and comultiplication functors and structure isomorphisms. We prove some coherence equations for structure isomorphisms. In particular, the Hopf category is monoidal.

EFFICIENT ALGORITHMS FOR WILDLAND FIRE SIMULATION by VOLODYMYR Y. KONDRATENKO

In this dissertation, we develop the multiple-source shortest path algorithms and examine their application importance in real world problems, such as wildfire modeling. The theoretical basis and its implementation in the Weather Research Forecasting (WRF) model coupled with the fire spread code SFIRE (WRF-SFIRE model) are described. We present a data assimilation method that gives the fire spr...

TRIANGULATED HOPF CATEGORY n+SL(2) VOLODYMYR LYUBASHENKO

Crane and Frenkel proposed a notion of a Hopf category [2]. It was motivated by Lusztig’s approach to quantum groups – his theory of canonical bases. In particular, Lusztig obtains braided deformations Uqn+ of universal enveloping algebras Un+ for some nilpotent Lie algebras n+ together with canonical bases of these braided Hopf algebras [4, 5, 6]. The elements of the canonical basis are identi...

Ambulance Diary for 1919

First-year student diary.

Rosie Perrett has finished her first year of studies at Liverpool and is awaiting her exam results. In the meantime, EMS placements will give her the chance to consolidate what she has learnt.