Iva Halacheva

Iva Halacheva is an Assistant Professor in the Department of Mathematics at Northeastern University, specializing in geometric and combinatorial representation theory, quantum algebra, and low-dimensional topology.

Her research bridges representation theory with topological structures through categorical frameworks, with emphasis on Drinfeld associators, Kashiwara-Vergne equations, and their topological interpretations. Halacheva's work connects algebraic geometry with knot theory via diagram algebras and cactus group actions.

• Principal Investigator on NSF grant DMS-2302664 (2023-2026) for research on categorical centers and diagram algebras
• Collaborated with Marcy Robertson and Zsuzsanna Dancso on topological characterization of Kashiwara-Vergne groups
• Developed Mathematica code available through the Knot Atlas
• Organizes GPRT seminar, GASC seminar, and Joint colloquium at Northeastern

Halacheva completed her PhD at the University of Toronto under Dror Bar-Natan and Joel Kamnitzer. She visited the Sydney Mathematical Research Institute in mid-2023 and previously held a postdoctoral position at the University of Melbourne.

Her research has significant implications across Lie theory, harmonic analysis, and quantum topology, with applications to universal finite type invariants in knot theory.