This is a page for my BAP project “A program for constructing solutions to the Yang-Baxter equation and its applications“.

News

• Announcement: Boğaziçi Üniversitesi BAP tarafından desteklenen “Yang-Baxter denkleminin çözümlerini oluşturmak için program ve uygulamaları” projem için araştırmacı arıyorum. Adayın Boğaziçi Üniversitesi’nde yüksek lisans veya doktora öğrenci olması gerekiyor. İlgilenen aday 15 Haziran 2020 tarihinden önce bana CV, motivasyon mektubu ve referans olabilecek bir kişinin (daha fazla da olabilir) ismini gönderebilir.

About the project

The project is devoted to the study of quantum integrability and its applications to theoretical and mathematical physics. Recently, there was observed an interesting relationship between exact results in supersymmetric quiver gauge theories and exactly solvable two-dimensional lattice models in statistical mechanics. In the gauge/YBE correspondence, as it is called, the integrability in statistical models is a direct consequence of supersymmetric infrared duality. Gauge/YBE correspondence relates the Yang-Baxter equation with the equality of partition functions for supersymmetric dual theories. This relationship will be one of our main tools in the study of the Yang-Baxter equation and related problems.

The success of supersymmetric gauge theory computations for integrable models stimulated the study of the relevant underlying mathematical structure. The objective of this project is twofold, on one hand, it is intended as a program for generating solutions to the Yang-Baxter equation, on the other hand along the way we will build relations to several areas of mathematical physics, such as knot theory, Painleve equations, cluster algebras etc.