# Seminars and Colloquia

The mathematics colloquium is held twice a term.

During term time seminars are held by the different research groups in the School of Mathematics.

## Events this week:

### Geometry and Mathematical Physics seminar: Lagrangian tori and cluster charts

• Marco Castronovo, Rutgers Universit
• Monday 13 January 2020, 16:30
• Watson (Mathematics) Room 310

I will describe a conjectural correspondence between Lagrangian tori in a real symplectic manifold and algebraic tori in a mirror variety. It is not clear what this mirror should be, but for coadjoint orbits work of Rietsch suggests a relation to Langlands duality. I will then explain how to partially verify this correspondence for Grassmannians. This point of view allows to answer purely dynamical questions about displaceability and abundance of Lagrangians.

### Analysis Seminar: Large sets without Fourier restriction theorems

• Constantin Bilz (Birmingham)
• Tuesday 14 January 2020, 14:00
• WATN-R17 18, Watson Building
• Tea and coffee will be provided after the talk at the common room

It was recently established that Fourier restriction theorems have implications for the structure of Lebesgue sets of Fourier transforms. On the other hand, no methodical study of these sets is available. In this talk, we construct a function that lies in Lp(Rd)for every p>1 and whose Fourier transform has no Lebesgue points in a Cantor set of full Hausdorff dimension. We combine this with recent results in restriction theory to prove a lack of valid relationsbetween the Hausdorff dimension of a set and the range of restriction exponents for measures supported in the set.

### Applied Mathematics Seminar Series: Title to be confirmed

• Veronica Grieneisen, Cardiff University
• Thursday 16 January 2020, 12:00
• Biosciences 301

Abstract not available

### Combinatorics and Probability Seminar: Sampling sufficiency for determining modularity.

• Fiona Skerman (University of Bristol)
• Thursday 16 January 2020, 15:00
• Watson LTC
• Tea, coffee and biscuits will be provided after the talk at the common room

Modularity is used in popular algorithms for community detection. For a given network G, each partition of the vertices has a modularity score, with higher values indicating that the partition better captures community structure in G. The (max) modularity q of the network G is defined to be the maximum over all vertex partitions of the modularity score, and satisfies 0 ≤ q(G) ≤ 1.

We analyse when community structure of an underlying network can be determined from its observed network. In a natural model where we suppose edges in an underlying graph G appear with some probability in our observed graph G’ we describe how high a sampling probability we need to infer the community structure of the underlying network.

Joint work with Colin McDiarmid.

### Algebra Seminar: Bases for primitive permutation groups

• Melissa Lee, Imperial College London
• Thursday 16 January 2020, 16:00
• Lecture Theatre B, Watson Building

Let $G \leq \mathrm{Sym}(\Omega)$ be a primitive permutation group. A base for $G$ is a subset $B \subseteq \Omega$ such that the pointwise stabiliser $G_B=1$. In this talk, after outlining the history and uses of bases, I will describe some recent work towards two prominent problems in the area – namely the solution to Pyber’s conjecture and the classification of primitive groups with base size two.