Puzzles and patterns in the primes - Christian Bagshaw
For thousands of years, mathematicians have been fascinated by prime numbers. As far as our records indicate, it was Euclid who first provided a proof that there are infinitely many primes. This curiosity has continued into the modern age, leading to more nuanced questions. Are there infinitely many primes that end with the digit 7? What about pairs of primes that differ by two - how many of those are there? Can every even number be written as the sum of two primes? This talk will touch on some of these fascinating problems and provide a glimpse into what a number theory PhD student works on all day.
Random networks, random walks and other stories - Catherine Greenhill
We live in a world filled with large, complex networks, such as social networks, contact networks or transport networks. A network consists some objects (e.g. people, cities) and the relationships between them (e.g. friendship, train lines). Researchers who study a particular real-world network often want to compare their network to a family of networks that share similar properties. We can do this using random networks, where the connections are chosen randomly in some way. I will talk about some of my research on random networks, and the (random?) choices that led me here.