Contact Information
377 Altgeld Hall, MC-382
1409 W. Green Street
Urbana, IL 61801
Research Areas
Research Interests
Representation theory, Mathematical physics, Algebraic combinatorics
Research Description
1. Combinatorial representation theory of infinite-dimensional algebras: Kac-Moody algebras, quantum affine algebras, Virasoro and W-algebras and their deformations.
2. Mathematical physics: Exactly solvable systems in statistical mechanics, integrable quantum field theories.
Education
Ph.D., Institute for Theoretical Physics, State University of New York at Stony Brook, 1993
BA Physics, Macalester College, 1988
Grants
NSF DMS-1928749: Conference grant for GROW 2019
NSF grant DMS-1802044 Discrete Quantum Integrability, Quantum Q-Systems, and Generalized Macdonald Operators
NSF conference grant DMS-1643027 for IHP trimester "Combinatorics and Interactions"
NSF grant DMS-1404988 Integrable difference equations and characters of affine Lie algebras
NSF grant DMS-1100929 Affine algebra representations and discrete integrability
NSF grant DMS-0802511 Algebraic and combinatorial structures in integrable systems
NSF grant DMS-0500759 Structure of representations of infinite dimensional Lie algebras and conformal field theory
NSF grant DMS-9870550 Representations of Quantum Affine Algebras and Integrable Models
External Links
Honors & Awards
Simons Fellow 2019-2020
International Congress of Mathematicians Seoul 2014, Invited Speaker
Recent Publications
Di Francesco, P., & Kedem, R. (2024). Macdonald Duality and the proof of the Quantum Q-system conjecture. Selecta Mathematica, New Series, 30(2), Article 23. https://doi.org/10.1007/s00029-023-00909-z
Francesco, P. D., & Kedem, R. (2021). Macdonald Operators and Quantum Q-Systems for Classical Types. In Progress in Mathematics (pp. 163-199). (Progress in Mathematics; Vol. 340). Birkhäuser. https://doi.org/10.1007/978-3-030-78148-4_6
Di Francesco, P., & Kedem, R. (2019). (t, q)-Deformed Q-Systems, DAHA and Quantum Toroidal Algebras via Generalized Macdonald Operators. Communications in Mathematical Physics, 369(3), 867-928. https://doi.org/10.1007/s00220-019-03472-x
Di Francesco, P., & Kedem, R. (2018). DIFFERENCE EQUATIONS FOR GRADED CHARACTERS FROM QUANTUM CLUSTER ALGEBRA. Transformation Groups, 23(2), 391-424. https://doi.org/10.1007/s00031-018-9480-y
Di Francesco, P., Kedem, R., & Turmunkh, B. (2017). A path model for Whittaker vectors. Journal of Physics A: Mathematical and Theoretical, 50(25), 255201, 35. Article 255201. https://doi.org/10.1088/1751-8121/aa7151