You are invited to a:

** Special Lecture Series by**

**Prof. Darren Crowdy**

**Imperial College London**

**Titles**: “Advances in applied complex analysis: new tools, techniques and applications”

**Abstract**: Complex analysis has always been a powerful tool in the armoury of applied mathematical techniques. This talk will survey several advances made by the speaker and coworkers in recent years that have added to this toolbox. The ideas will be conveyed in three lectures, each of which is self-contained but which have mathematical interconnections.

When several objects, or entities, interact in some ambient medium it is necessary to solve some field equations in a multiply connected domain.

The first lecture presents a novel framework for solving such problems based on use of a so-called “prime function” which makes solving problems in multiply connected domains a natural extension of well-known approaches for the simply connected, or “single entity”, case.

The second lecture takes the modern field of surface engineering as a case study in how the prime function appears naturally in applications.

The final lecture treats the different topic of transform methods and shows how geometry-fitted transform pairs can be written down that generalize the common notions of a Fourier transform and a Mellin transform to much wider classes of solution domain.

**1st lecture**: Monday, December 2, 2019 at 15:30 – **“Solving problems in multiply connected domains”**

**2nd lecture**: Wednesday, December 4, 2019 at 15:30 – **“Quantifying slip on textured surfaces”**

**3rd lecture**: Thursday, December 5, 2019 at 15:30 – **“Geometry-fitted Fourier-Mellin transform pairs”**

All lectures will be in Amado 232.

Light refreshments will be given in the faculty lounge on the 8th floor.