Research output per year
Research output per year
Personal profile
Research Interests
Representation theory, Mathematical physics, Algebraic combinatorics
Professional Information
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
Honors & Awards
Simons Fellow 2019-2020
International Congress of Mathematicians Seoul 2014, Invited Speaker
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
Fingerprint
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- 1 Similar Profiles
Research output
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Macdonald Duality and the proof of the Quantum Q-system conjecture
Di Francesco, P. & Kedem, R., Apr 2024, In: Selecta Mathematica, New Series. 30, 2, 23.Research output: Contribution to journal › Article › peer-review
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Macdonald Operators and Quantum Q-Systems for Classical Types
Francesco, P. D. & Kedem, R., 2021, Progress in Mathematics. Birkhäuser, p. 163-199 37 p. (Progress in Mathematics; vol. 340).Research output: Chapter in Book/Report/Conference proceeding › Chapter
Open Access -
(t, q)-Deformed Q-Systems, DAHA and Quantum Toroidal Algebras via Generalized Macdonald Operators
Di Francesco, P. & Kedem, R., Aug 1 2019, In: Communications in Mathematical Physics. 369, 3, p. 867-928 62 p.Research output: Contribution to journal › Article › peer-review
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DIFFERENCE EQUATIONS FOR GRADED CHARACTERS FROM QUANTUM CLUSTER ALGEBRA
Di Francesco, P. & Kedem, R., Jun 1 2018, In: Transformation Groups. 23, 2, p. 391-424 34 p.Research output: Contribution to journal › Article › peer-review
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A path model for Whittaker vectors
Di Francesco, P., Kedem, R. & Turmunkh, B., May 24 2017, In: Journal of Physics A: Mathematical and Theoretical. 50, 25, p. 255201, 35 255201.Research output: Contribution to journal › Article › peer-review