Contact Information
Research Areas
Biography
2024– Professor Emeritus, University of Illinois
2012–2024 Professor, Department of Mathematics, University of Illinois
2006–2012 Associate Professor, Department of Mathematics, University of Illinois
2001–2006 Assistant Professor, Department of Mathematics, University of Illinois.
1997–2001 Assistant Professor, Department of Mathematics, University of Massachusetts, Amherst
1996–1997 Postdoc & Lecturer Mathematics, University of California Berkeley.
1995–1996 Postdoctoral Research Fellow, Mathematics, University of Melbourne.
1993–1995 JSPS Postdoctoral Research Fellow, Research Institute for Mathematical Sciences, Kyoto University.
Research Interests
Representation theory; Mathematical physics; Lattice integrable systems; Quantum universal enveloping algebras;
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
1993 Ph.D. Physics, Stony Brook. Supervisor: Barry M. McCoy
1988 B.A. Physics, Macalester College, St. Paul
Grants
• 2024: PI: NSF Conference grant DMS-2425253 for the workshop “Discrete integrable systems: Difference equations, cluster algebras and probabilistic models” workshop, at ICTS, Bangalore, India.
• 2023–2028 PI: Simons Collaborative grant for Mathematicians
• 2020-2025 co-PI on NSF grant DMS-1937241 RTG: Research in Combinatorics
• 2019–2020 Simons Fellow in Mathematics
• 2019: co-PI on NSF DMS-1928749 conference grant for the conference GROW 2019 (graduate opportunities for women)
• 2018–2021 National Science Foundation: PI, grant DMS-1802044
• 2017: National Science Foundation Conference grant DMS-1643027, “Combinatorics and Interactions” at the Institut Henri Poincaré, Paris, Spring 2017.
• 2016: Fondation Mathématique Jaques Hadamard, Université Paris-Saclay, Visiting Researcher, IPhT CEA/Saclay, France
• 2015: Fondation Mathématique Jaques Hadamard, Université Paris-Saclay, Visiting Researcher, IPhT CEA/Saclay, France
• 2014–2018: National Science Foundation: PI, grant DMS-1404988
• 2011–2015: National Science Foundation PI grant DMS-1100929
• Centre National de la Recherche Scientifique: International collaborative grant CNRS-PICS 2011-2013 (co-PI)
• 2008–2012: National Science Foundation PI grant DMS-0802511
• 2005–2008: National Science Foundation PI grant DMS-0500759
• 1998–2000: National Science Foundation PI grant DMS-9870550
Awards and Honors
• 2019–2020 Simons Fellow in Mathematics
• 2014–2016 Lois M. Lackner Faculty Scholar, University of Illinois.
• 2014 Invited speaker, International Congress of Mathematicians (ICM 2014), Seoul, South Korea.
Additional Campus Affiliations
Professor Emerita, Mathematics
External Links
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
Di Francesco, P., Kedem, R., Khoroshkin, S., Schrader, G., & Shapiro, A. (2024). Ruijsenaars wavefunctions as modular group matrix coefficients. Letters in Mathematical Physics, 114(6), Article 136. https://doi.org/10.1007/s11005-024-01881-1
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