Stokes Phenomenon and Interpolating Functions

<strong>Seminar of the School of Physical Sciences -------------------------------------------------</strong> Title: <strong>Stokes Phenomenon and Interpolating Functions</strong> Speaker: <strong>Dileep Jatkar</strong> (Harish-Chandra Research Institute, Allahabad) <strong>Date: January 20, 2016</strong> <strong>Abstract: </strong>While studying a physical system we often use perturbative methods. Perturbation theory gives us a power series in terms of a small parameter. In some cases, we can get similar expansion when the parameter is very large. For example, low temperature and high temperature expansions of the free energy of the Ising model. To determine physical quantities at some intermediate value of the parameter we can use the method of interpolation. We study a new class of interpolating functions, these functions are designed in such a way that they agree with the perturbative data at the small and large value of the parameter. A large class of good interpolating functions can be designed in this manner. We devise a method of distinguishing between these good interpolating functions by studying their analytic structure.