Unfortunately\, multidi mensional complex analysis seems to be way more co mplicated than complex analysis of a single variab le. There exists a number of powerful theorems in it\, but they are organised into several disjoint theories\, and\, generally all of them are far fro m the needs of WH. In this mini-lecture course\, we hope to introduce topics in complex analysis of several variables that we think are important for a generalisation of the WH technique. We will foc us on the similarities and differences between fun ctions of one complex variable and functions of tw o complex variables. Elements of differential form s and homotopy theory will be addressed.

We will start by reviewing some known atte mpts at building a 2D WH and explain why they were not successful. The framework of Fourier transfor ms and analytic functions in 2D will be introduced \, leading us naturally to discuss multidimensiona l integration contours and their possible deformat ions. One of our main focus will be on polar and b ranch singularity sets and how to describe how a m ultidimensional contour bypasses these singulariti es. We will explain how multidimensional integral representation can be used in order to perform an analytical continuation of the unknowns of a 2D fu nctional equation and why we believe it to be impo rtant. Finally\, time permitting\, we will discuss the branching structure of complex integr

LOCATION:Seminar Room 1\, Newton Institute CONTACT:INI IT END:VEVENT END:VCALENDAR