Publications grouped by projects

My research interests concern the representation theory of quantum groups and infinite-dimensional Lie algebras and their applications, from various perspectives involving algebraic geometry, combinatorics and mathematical physics. Here are the main projects in my research work, with the corresponding publications grouped by projects.

Monoidal categorification of cluster algebras
  • Representations of shifted quantum affine algebras and cluster algebras I. The simply-laced case (with C. Geiss and B. Leclerc) : PDF, Preprint arXiv:2401.04616.
Quantum integrable systems and Baxter Q-operators
  • Extended Baxter relations and QQ-systems for quantum affine algebras (with E. Frenkel) : PDF, Preprint arXiv:2312.13256.
Kazhdan-Lusztig polynomials and quantum Grothendieck rings
  • Isomorphisms among quantum Grothendieck rings and cluster algebras (with R. Fujita, S-J. Oh and H. Oya) : PDF, Preprint arXiv:2304.02562.
Shifted quantum groups associated to Coulomb branches Quiver varieties Oper and Langlands duality for quantum groups Stable maps and R-matrices Kirillov-Reshetikhin modules, crystals and T-systems Geometry of loop groups and quantum groups at roots of unity Toroidal algebras, Drinfeld coproduct and fusion product