Michael Gekhtman

Professor

Education

Ph.D., Ukrainian Academy of Sciences, 1990

Research Groups

Algebra and Algebraic Geometry, Mathematical Physics

Research Area

Integrable Systems, Poisson Geometry, Cluster Algebras, Inverse Problems, Mathematical Physics

Bio

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.

Email: mgekhtma@nd.edu
Phone: 574-631-7131
Fax: 574-631-6579
Office: 128 Hayes-Healy Bldg