## Postgraduate Seminars

### Summer 2017

These seminars (unless otherwise stated) will take place on **Thursdays at 5pm in Physics A1/3 **** **(Physics Building, Gower Street) on an (almost) weekly basis ** - **see the map for further details. Talks are being given by 2nd and 3rd year Mathematics PhD students for PhD students. They are generally followed by tea and biscuits in the Mathematics Department Staff Room (Room 606, 25 Gordon Street) - see how to find us for further details.

### 11 May 2017

###### Speaker: Antonio Cauchi

**Title: Doughnuts and their arithmetic mystery**

Abstract:

Elliptic curves play a central role in modern number theory for their rich arithmetic properties. For instance, Andrew Wiles' proof of Fermat's Last Theorem relies on a fundamental property that elliptic curves have. In this talk, I will define what elliptic curves are and discuss the Birch and Swinnerton-Dyer conjecture, which describes a beautiful connection between the L-function associated to an elliptic curve and its arithmetic invariants.

### 17 May 2017

This seminar will take place in room 500, 25 Gordon Street.

###### Speaker: Matteo Capoferri

**Title: The algebraic approach to QFT**

Abstract:

Standard Quantum Field Theory (QFT), although outstandingly succeeding in describing the behaviour of matter at short length-scale and high energies, possesses a problematic mathematical status. The Algebraic approach to QFT (AQFT) offers an alternative, mathematically rigorous framework in which to set the theory, allowing, among other remarkable things, for its formulation on curved backgrounds. In my talk, I will try to give an idea of what AQFT consists in and why it is interesting and useful, thanks to the fruitful interplay of algebra, geometry and the analysis of PDEs. As an example, I will show concretely how the theory works for simple case of the Klein-Gordon field. No prior knowledge other than undergraduate maths will be assumed - in particular, no knowledge of quantum physics.

### 1 June 2017

###### Speaker: Sean Jamshidi

**Title: Gravity-capillary waves in nonlinear geometries**

Abstract:

One of the classical problems in fluid mechanics is to ask what waves are created when a uniform flow encounters an obstacle. Much progress has been made in the case where the size of the object is small, but recently it has been shown that a whole variety of new waves are possible when the object is large. In this talk I will give a history of the problem and a simple explanation of one of these new classes of waves. I will then detail some of the challenges that must be overcome in order to numerically verify their existence, and show how these challenges motivate further analysis of the governing equations.