## Easter Term

**Garden Party**

*11:00–15:00, 17th June, Friday
*Scholar’s Garden

**Cricket Match vs Trinity Maths Society**

*12:00, 23th June, Thursday
*St John’s Playing Fields

## Lent Term

**Annual Dinner **

*19:30, 1st March, Tuesday*(open to St John’s Members only)

**Prof Ivan Smith**as guest speaker. Tickets available on UPay.

**Scarves, Symmetry and Solving Equations **by *Dr Vicky Neale*

*18:00-19:00, 15th February, Tuesday*

Castlereagh Room, St John’s College

**About the speaker:** Vicky Neale is a British mathematician and writer. She is the Whitehead Lecturer at the Mathematical Institute at Oxford and Supernumerary Fellow at Balliol College. Her research specialty is number theory.

**Abstract: **Through knitting, I’ve been exploring the symmetry patterns in scarves. How many different types of scarf pattern are there? In this session, we’ll explore this question, and see how it connects with apparently unrelated areas of maths, such as solving polynomial equations. If you like doodling, you might want coloured pens/pencils and squared paper to hand!

**Diophantine Equations **by *Professor Gerd Faltings*

*18:00-19:00, 10th February, Thursday*

**About the speaker:**Gerd Faltings is a German mathematician whose work in algebraic geometry led to important results in number theory, including helping with the proof of Fermat’s Last Theorem. In 1986 Faltings was awarded a Fields Medal at the International Congress of Mathematicians at Berkeley. He now works at Max Planck Institute for Mathematics, University of Bonn and Princeton University.

**Abstract:** I will give an overview of what is known, explaining tools (heights, good reduction, Galois representations), known results (like Mordell, Roth), and additional avenues of research.

**Local-to-global principles in number theory **by *Professor Tom Fisher*

*18:00-19:00, 25th Jan, Tuesday*

**About the speaker:**Professor Tom Fisher is a Professor of Mathematics at the University of Cambridge. His research interests are in arithmetical algebraic geometry and computational number theory. In particular he works on elliptic curve descent calculations, and the construction of explicit elements in the Tate-Shafarevich group.

**Abstract**: A Diophantine problem is a system of equations (typically polynomials) that we seek to solve in terms of integers or rational numbers. Sometimes it is possible to show there are no solutions by working modulo a prime, or a power of a prime, or by showing there are no real solutions. In such cases we say there is a local obstruction. In the talk I will give some examples and non-examples of situations where the absence of a local obstruction is sufficient to ensure the original (global) problem is soluble.

## Michaelmas Term

**A deconstruction of the Regularity Lemma **by Prof. Niranjan Balachandran

*14:00-15:00, 23rd Nov, Tuesday*

**About the speaker:**Professor Niranjan Balachandran is an Associate Professor of Mathematics at the Indian Institute of Technology, Bombay. His research focuses on Combinatorics, in particular Extremal Combinatorics, Probabilistic methods, and Design theory. Recently, he has become interested in the applications Probabilistic methods in Combinatorics especially in Graph-theoretic applications such as coloring problems. Today’s talk will be about deconstructing Szemeredi’s regularity lemma in graph theory – a result with wide applications in areas such as extremal graph theory, additive combinatorics and theoretical computer science – so that we can imagine being Szemeredi and coming up with this powerful lemma.

**Abstract**: The Regularity lemma of Szemeredi is a landmark result in graph theory with far-reaching consequences ranging from applications in extremal graph theory, additive combinatorics, theoretical computer science, and probability theory to name a few. It is not just a lemma – it is a general motif that sweeps across these landscapes. What we shall see in this talk is a deconstruction of this lemma that is better motivated from the following vantage point: YOU are Szemeredi. How did you come up with such an audacious lemma?!

The deconstruction is not a historic account by any means, for I do not know the workings of as fertile and `irregular’ mind as Szemeredi’s; it is as historically authentic as was Tarantino’s version of how World War II ended.

**Can a computer do your problems sheets? **by *Prof. Kevin Buzzard*

*Tuesday, 9th November 2021, 18:00*

Main Lecture Hall, Old Divinity School, St John’s College

**Stein’s Pardox **by *Prof. Richard Samworth *

*Tuesday, 12th October 2021, 18:00*

Castlereagh Room, Fisher Building, St John’s College

Stein’s paradox is one of the most striking results in Statistics. Although it appears to be a basic problem in mathematical statistics, it turns out to have profound implications for the analysis of modern, high-dimensional data. I will describe both the result and some of its consequences.

**Fresher’s Squash **

*Friday, 8th October 2021*

A warm welcome to all our freshers.