## Postgraduate Seminars

### Spring 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.

### 18 May 2017

###### 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.