Iva Halacheva works in representation theory and low-dimensional topology, and the interplay of emerging geometric, combinatorial, and categorical structures within.
Topics of her research include
- quantum groups and crystals, and the associated braid and cactus group actions
- Rickard complexes and perverse equivalences on categorifications
- dualities between Lie and diagram algebras
- Schubert calculus
- topological perspective on the Kashiwara-Vergne conjecture