Summer Launch Events
A new summer of research projects is about to start and to officially launch the 2025 programme, we’re hosting the below events on Wednesday 9 July 2025.
Panel Discussion with CMS PhD Students and Early Career Researchers
Date & time: 4:30-5:30pm
Location: Recital Room, Churchill College
The first event will be a panel session with PhD students and other early career researchers who have a sense for where you are in your mathematical career at the moment. We’ll have a discussion about what research is like, its joys, and its challenges. Coming along will give you a glimpse of life as a researcher both in the long run and in the 8 weeks that lie ahead of you.
Drinks Reception
Date & time: 5:30-7:00pm
Location: Jock Colville Lawn, Churchill College
Come along to meet other students who will be undertaking projects this summer and find out what they are working on! Project supervisors are also invited.
Undergraduate Colloquia
The Undergraduate Colloquia are a series of seminars which will feature talks on a variety of different topics within maths and theoretical physics. It is a great chance to meet your fellow summer researchers, and to learn about current research. It is considered an official part of the SRIM programme, so participation is strongly encouraged!
Each seminar will be followed by tea and coffee in the CMS (more exact location TBC).
Professor Po-Ling Loh (Statistical Laboratory, DPMMS), Statistical inference for infectious disease modeling
Date & time: 11am, Tuesday 5 August 2025
Location: Hoyle Lecture Theatre, Institute of Astronomy, Madingley Road, CB3 0HA (access is via the main reception at the: see map)
Abstract:
In many scientific problems of contemporary interest, data are acquired in a very heterogeneous and non-i.i.d. fashion: Edges in a network may give rise to important correlations between node-level observations, which must be taken into account when performing data analysis. In large-scale applications, the structure of the graph may also determine the type of algorithms that may be performed. This talk will briefly overview some research problems involving mathematical analysis of network-structured data. A central question is how to formulate rigorous statistical theory for data collected over (or in the form of) a network. I will focus on the problems of source inference and graph hypothesis testing.
In the first part of the talk, I will discuss algorithms for inferring the source of a disease spreading over a tree-structured network. The infection is assumed to spread via contagion (e.g., transmission over the edges of an underlying network). Given the infection status of individuals at a particular time instance, the goal is to identify a confidence set of nodes that contain the source of the infection with high probability. I will present a method for constructing confidence sets for the source of the infection, with the property that the cardinality of the confidence sets depends only on the error probability and the degree of the nodes in the tree, rather than the size of the infection set. The analysis depends on a careful probabilistic analysis of relative subtree sizes as the infection propagates over the tree, and utilizes the theory of Polya urns.
Next, I will discuss a problem concerning hypothesis testing between graph structures. In this scenario, the goal is to infer the network structure of the underlying graph based on knowledge of which individuals have been infected at a certain time, but not their relative connectivity. However, since the infection information is restricted to a single observation, methods such as graphical model estimation become invalid for inferring the connections between individuals. I will present a hypothesis test based on permutation testing, and describe a sufficient condition for the validity of the hypothesis test based on automorphism groups of the two graphs involved in the hypothesis test.
This is joint work with my former PhD student Justin Khim, now a researcher at Meta.
Dr Jef Laga (Number Theory Group, DPMMS), ADE diagrams and the unity of mathematics
Date & time: 11am, Tuesday 12 August 2025
Location: Hoyle Lecture Theatre, Institute of Astronomy, Madingley Road, CB3 0HA (access is via the main reception at the: see map)
Abstract:
When sitting in maths undergraduate courses it seems like mathematics can be neatly categorised into isolated subjects. In this talk I want to give you some examples of surprising connections between different mathematical subjects and concepts, through the lens of ADE classifications. This talk will use concepts from graph theory, group theory and representation theory, but I will aim to assume as little background as possible.
