Michael Gekhtman

 

Michael Gekhtman

Professor
 

Ph.D., Ukrainian Academy of Sciences, 1990

Email: Michael.Gekhtman.1@nd.edu
Office: 128 Hayes-Healy Bldg
Phone: (574) 631-7131
Fax: (574) 631-6579

Mailing Address:
255 Hurley Bldg
Notre Dame, IN  46556-4618


Research Interests

Integrable systems,  Poisson geometry, cluster algebras, inverse problems.

Selected Publications

  • M. Gekhtman, M. Shapiro and A. Vainshtein, Drinfeld double of GL(n) and generalized cluster structures, Proc. Lond. Math. Soc. (3) 116 (2018), no. 3, 429–484.
  • M. Gekhtman, M. Shapiro and A. Vainshtein,  Exotic cluster structures on SLn: the Cremmer-Gervais case, Mem. Amer. Math. Soc. 246 (2017), no. 1165.
  • M. Gekhtman, M. Shapiro, A. Vainshtein and S. Tabachnikov, Integrable cluster dynamics of directed networks and pentagram maps, Adv. Math. 300 (2016), 390–450.
  • M. Gekhtman, M. Shapiro and A. Vainshtein, Poisson geometry of directed networks in an annulus, J. Eur.      Math. Soc. (JEMS) 14 (2012), no. 2, 541–570. 
  • M. Gekhtman, M. Shapiro and A. Vainshtein, Generalized Backlund-Darboux transformations for Coxeter-Toda flows from cluster algebra perspective, Acta Math. (2011) 206, 245--310.
  • M. Gekhtman, M. Shapiro and A. Vainshtein, Cluster algebras and Poisson geometry, AMS Surveys and Monographs 167 (2010).
  • M. Gekhtman, M. Bertola and J. Szmiegielsky, The Cauchy two-matrix model, Comm. Math. Phys.  287 (2009), 983—1014.  
  • M. Gekhtman, M. Shapiro and A. Vainshtein, Cluster algebras and and Weil-Petersson forms, Duke Math. J.  127 (2005), 291—311.

If you have access to MathSciNet you can see a complete list of publications.

Please direct questions and comments to: Michael.Gekhtman.1@nd.edu