Curriculum Vitae - Rinat Kedem

RESEARCH AREAS: Mathematical physics; Infinite dimensional Lie algebras and their deformations, their representations and related combinatorics; Integrable models, statistical mechanics and conformal field theories; Cluster algebras and algebraic combinatorics.
 

PROFESSIONAL APPOINTMENTS:
 
8/12-- Professor 
Department of Mathematics, University of Illinois Urbana-Champaign 
8/06-8/12 Associate Professor 
Department of Mathematics, University of Illinois Urbana-Champaign 
8/01--8/06 Assistant Professor 
Department of Mathematics, University of Illinois Urbana-Champaign 
9/97-8/01 Assistant Professor 
Department of Mathematics, University of Massachusetts, Amherst 
8/96-8/97 Postdoctoral Research Associate/Lecturer
Department of Mathematics, University of California, Berkeley 
9/95-7/96 Research Fellow
Department of Mathematics, University of Melbourne 
8/93-8/95 Postdoctoral Research Fellow 
Research Institute for Mathematical Sciences, Kyoto University 
   

EDUCATION:
 
5/1993 Ph.D., Institute for Theoretical Physics
  State University of New York at Stony Brook
Ph.D. Advisor: Barry McCoy.
5/1988 B.A., Physics, Macalester College, St. Paul, Minnesota.

Honors and awards:

Simons Fellow in Mathematics, 2019-2020.

Plenary speaker, Quantum Theory and Symmetries XI, Montreal 2019.

Institut Henri Poincare CNRS professor, Spring 2017.

Lois Lackner Named Scholar 2014-2016, University of Illinois.

Invited speaker, International Congress of Mathematicians, Seoul 2014.

Plenary speaker, Formal Power Series and Algebraic Combinatorics, Nagoya 2012.

National Science Foundation grant awards principal investigator: 1998, 2005, 2008, 2011, 2014, 2018.

Patricia Harris NSF graduate fellowship 1988--1992.

Publications:

(not updated)
  1. P. Di Francesco, R. Kedem, B. Turmunkh, “Path models for Whittaker vectors” 2014.

  2. R. Kedem, Fermionic spectra in integrable models. Proceedings of the International Congress of Mathematicians 2014.

  3. R. Kedem and P. Vichitkunakorn, T-systems and the pentagram map. Journal of Geometry and Physics (2015), pp. 233-247.

  4. P. Di Francesco and R. Kedem, Quantum cluster algebras and fusion products. International Mathematics Research Notices 2013; doi: 10.1093/imrn/rnt004. Journal link, ArXiv link.

  5. P. Di Francesco and R. Kedem, T-systems with boundaries from network solutions. Electronic Journal of Combinatorics 20(1) P3. (2013). Journal, ArXiv.

  6. P. Di Francesco and R. Kedem, The solution of the quantum A1 T-system for arbitrary boundary conditions. Commun. Math. Phys. 313 (2012) 329–350. JournalArXiv.

  7. P. Di Francesco and R. Kedem, Non-commutative integrability, paths and quasi-determinants. (2010) Adv. Math. 228 (2011) 97–152. Journal, ArXiv

  8. R. Kedem, A pentagon of identities, fusion products and the Kirillov-Reshetikhin conjecture. In New Trends in Quantum Integrable Systems, B. Feigin, M. Jimbo, M. Okado Eds., World Scientific (2011) 173–193.

  9. P. Di Francesco and R. Kedem, Discrete non-commutative integrability: Proof of a conjecture by M. Kontsevich, International Mathematics Research Notices (2010), no. 21, 40424063. doi:10.1093/imrn/rnq024.

  10. P. Di Francesco and R. Kedem, Positivity of the T-system cluster algebra. Elec. J. Combinatorics (2009) 16(1).

  11. P. Di Francesco and R. Kedem, Q-system Cluster Algebras, Paths and Total Positivity. SIGMA 6 (2010), 014.

  12. P. Di Francesco and R. Kedem, Q-systems, Heaps, Paths and Cluster Positivity. Comm. Math. Phys. 293 (2010) 727–802. DOI 10.1007/s00220-009-0947-5 (2009).

  13. Ph. Di Francesco and R. Kedem, Q-systems as cluster algebras II: Cartan matrix of finite type and the polynomial property. Lett. Math. Phys. (2009) 89:183–216.

  14. R. Kedem, Q-systems as cluster algebras. J. Phys. A: Math. Theor. 41 (2008) 194011.

  15. P. Di Francesco, R. Kedem, Proof of the combinatorial Kirillov-Reshetikhin conjecture. Int. Math. Res. Notices 2008 (2008): rnn006-57.

  16. E. Ardonne, R. Kedem, Fusion products of Kirillov-Reshetikhin modules and fermionic multiplicity formulas. math.RT/0602177 (to appear in J. Algebra).

  17. E. Ardonne, R. Kedem, M. Stone, Fusion products, Kostka polynomials, and fermionic characters of su(r+1)k. math-ph/0506071. (J. Phys. A: Math. Gen. 38(2005) 9183--9205).

  18.  E. Ardonne, R. Kedem, M. Stone, Fermionic characters and arbitrary highest-weight integrable affine slr+1 modules (Comm. Math. Phys. 264 (2006) 427--464). math.RT/0504364 [abs, ps, pdf, other].

  19.  E. Ardonne, R. Kedem, M. Stone, Filling the Bose sea:  symmetric quantum Hall edge states and affine characters. J. Phys. A: Math. Gen. 38:617--636,2005. cond-mat/0409369 [abs, ps, pdf, other]

  20. R. Kedem, Fusion products of sl_N symmetric power representations and Kostka polynomials (1/2004, Proceedings of QTS3, World Scientific), in PDF format.


  21. R. Kedem, Fusion products, cohomology of GL(N) flag manifolds, and Kostka polynomials.  IMRN 2004:25 (2004) 1273-1298. PDF file available here.


  22. B. Feigin, M. Jimbo, R. Kedem, S. Loktev, T. Miwa, Spaces of coinvariants and fusion product II. Affine sl_2 character formulas in terms of Kostka polynomials.  Journal of Algebra, Volume 279, Issue 1 , 1 September 2004, Pages 147-179.
    math.QA/0208156 [abstract,source, ps]

  23. B. Feigin, M. Jimbo, R. Kedem, S. Loktev, T. Miwa, Spaces of coinvariants and fusion product I. From equivalence theorem to Kostka polynomials. Duke Math. J.  125 (2004), no. 3, 549--588. math.QA/0205324 [abstract,source, ps]

  24. B. Feigin, R. Kedem, S. Loktev, T. Miwa, E. Mukhin, Combinatorics of the $\widehat{sl}_2$ spaces of coinvariants: Dual functional realization and recursion. Compositio Mathematica 134:193--241, 2002. math.QA/0012190 [abstract,source, ps]

  25. B. Feigin, R. Kedem, S. Loktev, T. Miwa, E. Mukhin, Combinatorics of the $\widehat{sl}_2$ spaces of coinvariants: Loop Heisenberg modules and recursion. Selecta Math. 8: 419--474, 2002.
    math.QA/0009198 [abstract,source, ps]
     
  26. B. Feigin, R. Kedem, S. Loktev, T. Miwa, E. Mukhin, Combinatorics of the $\widehat{sl}_2$ spaces of coinvariants. Transform. Groups 6 (2001), no. 1, 25--52. math-ph/9908003 [abstract,source, ps]
     
  27. R. Kedem, Singular R-matrices and Drinfeld's comultiplication, Lett. Math. Phys. 41 (1997) 149--160. q-alg/9611001 [abstract,source, ps]
     
  28. M. Jimbo, R. Kedem, H. Konno, T. Miwa and J. Petersen, Level-0 structure of level-1 $U_q(\widehat{sl}_2)$ modules and Macdonald Polynomials. Phys. Lett. A 28 5589--5606 (1995).

    29. q-alg/9506016 [abstract,source, ps]
     
  29. M. Jimbo, R. Kedem, H. Konno, T. Miwa and J. Petersen, New level-0 action of $U_q(\widehat{sl}_2)$ on level-1 modules. Proceedings of the 1994 statistical mechanics and quantum field theory workshop, Univ. Southern California. World Scientific, Singapore (1995).

    30. q-alg/9505009 [abstract,source, ps]
     
  30. M. Jimbo, R. Kedem, H. Konno, T. Miwa, and R.A. Weston, Difference equations in spin chains with a boundary. Nucl. Phys. B. B448 429--456 (1995).

    31. hep-th/9502060 [abstract,source, ps]
     
  31. M. Jimbo, R. Kedem, T. Kojima, H. Konno and T. Miwa, XXZ chain with a boundary. Nucl. Phys. B441 437--470 (1995).

    32. hep-th/9411112 [abstract,source, ps]
     
  32. R. Kedem and B. M. McCoy, Quasi-particles in the chiral Potts model. Intl. J. Mod. Phys. B8 3601--3621 (1994).

    33. hep-th/9405089 [abstract,source, ps]
     
  33. O. Foda, K. Iohara, M. Jimbo, R. Kedem, T. Miwa and H. Yan, Notes on highest weight modules of the elliptic algebra ${\cal A}_{q,p}(\widehat{sl}_2)$, Prog. Theor. Phys. Suppl. 118 1--34 (1995).

    34. hep-th/9405058 [abstract,source, ps]
     
  34. O. Foda, K. Iohara, M. Jimbo, R. Kedem, T. Miwa and H. Yan, An elliptic quantum algebra for $\widehat{sl}_2$. Lett. Math. Phys. 32 259--268 (1994).

    35. hep-th/9403094 [abstract,source, ps]
     
  35. S. Dasmahapatra, R. Kedem, B. M. McCoy and E. Melzer, Virasoro characters from Bethe equations for the critical ferromagnetic three-state Potts model. J. Stat. Phys. 74 239 (1994).

    36. hep-th/9304150 [abstract,source, ps]
     
  36. R. Kedem, B. M. McCoy and E. Melzer, The sums of Rogers, Schur and Ramanujan and the Bose-Fermi correspendence in 1+1-dimensional quantum field theory, in Proceedings of the 1994 statistical mechanics and quantum field theory workshop, Univ. Southern California. World Scientific, Singapore (1995).

    37. hep-th/9304056 [abstract,source, ps]
     
  37. S. Dasmahapatra, R. Kedem, T. R. Klassen, B. M. McCoy and E. Melzer, Quasi-particles, conformal field theory and $q$-Series. Int. J. Mod. Phys. B 7 3617 (1993).

    38. hep-th/9303013 [abstract,source, ps]
     
  38. R. Kedem, T. R. Klassen, B. M. McCoy and E. Melzer, Fermionic sum representations for conformal field theory characters. Phys. Lett. B307 68 (1993).

    39. hep-th/9304150 [abstract,source, ps]
     
  39. R. Kedem, T. R. Klassen, B. M. McCoy and E. Melzer, Fermionic quasi-particle representations for characters of ${(G^{(1)})_1\times (G^{(1)})_1 \over (G^{(1)})_2}$. Phys. Lett. B. 304 263 (1993).

    40. hep-th/9301046 [abstract,source, ps]
     
  40. R. Kedem and B. M. McCoy, Construction of modular branching functions from Bethe's equations in the 3-State potts chain. J. Stat. Phys. 71 875 (1993).

    41. hep-th/9210129 [abstract,source, ps]
     
  41. R. Kedem, Thermodynamics of the 3-state Potts spin chain, J. Stat. Phys. 71 903 (1993).

    42. hep-th/9210146 [abstract,source, ps]
     
  42. S. Dasmahapatra, R. Kedem and B. M. McCoy, Spectrum and completeness of the 3-State superintegrable chiral Potts model, Nucl. Phys. B396 506 (1993).

    43. hep-th/9204003 [abstract,source, ps]

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