# HMI Mini-conference ### [Hamilton Mathematics Institute](http://www.tcd.ie/Hamilton/), [Trinity College Dublin](http://www.maths.tcd.ie/) #### February 9, 2018 #### Speakers: * Leon Takhtajan (Stony Brook) * Nikita Nekrasov (SCGP, Stony Brook) * Yuri Tschinkel (Simons Foundation and Courant Institute, NYU) #### Registration: Registration is free of charge but mandatory. Please email hmiadmin@maths.tcd.ie to register. [Travel information](http://www.maths.tcd.ie/~dmc/travelinfo/), [Hamilton Building](https://www.maths.tcd.ie/about/map.php).

Time Speaker Title Abstract Location
10:30 Leon Takhtajan Local Index Theorem for Orbifold Riemann Surfaces I will review local index theorems in Quillen’s form for the families of Cauchy-Riemann operators on compact, punctured and orbifold Riemann surfaces - quotients of the Lobachevsky plane by the action of Fuchsian groups of the first kind. Synge Lecture Theatre
14:30 Nikita Nekrasov Bootstrapping instantons with antiinstantons In quantizing classical mechanical systems to get (the corrections, non-perturbative in $\hbar$) the eigenvalues of the Hamiltonian one often sums over the classical trajectories as in localization formulas, but also takes into account the contributions of the "instanton -- anti-instanton gas": an ill-defined set of approximate solutions of equations of motion. In the lecture we attempt to alleviate some of the frustrations of this 40+ yrs old approach by making use of honest solutions of equations of motion of the complexified classical mechanical system. The examples will include algebraic integrable systems, from the abstract Hitchin systems to the well-studied anharmonic oscillator. These ideas originate in the Bethe/gauge correspondence. Synge Lecture Theatre
15:45 Yuri Tschinkel Geometry over Nonclosed Fields I will discuss recent advances in the study of rationality and unirationality of algebraic varieties. Synge Lecture Theatre