This week's Mathematical Sciences Department colloquium is given by Dr. Borislav Gajic, Associate Research Professor of Mathematical Institute SANU.

Rigid-body dynamics serves for centuries as a significant laboratory for development and examination of the most recent theoretical mechanical considerations and their applications.  We will use it to illustrate a modern method of algebro-geometric integration of integrable and close to integrable PDEs and ODEs. The method of finite-gap integration creates a fruitful two-way interaction between some classes of nonlinear equations and the geometry of algebraic curves, the Jacobian and the Prym varieties. We will focus on the four-dimensional systems we have constructed, the Lagrange bitop and the systems of Hess-Appel’rot type, and we will show that the integration in the theta-functions leads to a dynamical version of the Mumford relation on the theta-divisors of the Prym varieties and the Mumford-Dalalyan theory of the double coverings. A current research is devoted to the rigid-body dynamics in an ideal fluid. Related Kirchhoff equations are studied using both algebro-geometric and symbolic-computational techniques.

Coffee will be served in FO 2.610F at  1:00 PM.

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