These seminars (unless otherwise stated) will take place on Tuesdays at 1pm via Zoom (https://ucl.zoom.us/j/97636994687) on an almost weekly basis.

**Zoom link: https://ucl.zoom.us/j/97636994687**

## 26 April 2022

**Speaker: Hugh Kinnear**

Supervisor: TBC

##### Title: Reliability-based Uncertainty Quantification for Intensive Care Unit Data.

**Abstract:**

Reliability methods and Stochastic models are used to calculate the probability that a structure will avoid sustaining intolerable damage. It is possible to apply these techniques to a broad class of problems including optimisation, Bayesian inference and history matching since in general they sample from, and estimate the size of, small regions in high dimensional spaces. In these contexts, reliability methods intrinsically provide uncertainty quantification and so are they naturally suited to tackling practical clinical problems where point estimates do not suffice. This talk will focus on a novel approach called Branching Subset Simulation that attempts to overcome the ergodic and efficiency issues encountered when adapting reliability methods for use with intensive care unit data.

## 25 Jan 2022

**Speaker: **

Supervisor: Ignacia Fierro

##### Title: TBC

**Abstract:**

Wil

## 08 Feb 2022

**Speaker: Marta Benozzo (LSGNT)**

Supervisor: Prof P Cascini (Imperial College London)

##### Title: Iitaka conjecture

**Abstract:**

Classifying varieties is one of the main problems in geometry. In dimension 1, it is completely solved: curves are classified by their genus. What is the invariant we need to use in higher dimension? The genus of a curve is strictly related to the sections of its canonical bundle (dual of the tangent). Thus, the idea is to look at sections of the canonical bundle also in higher dimension. Using them, it is possible to define a new invariant: the Kodaira dimension. This invariant allows us to identify three main “building blocks” of varieties. What we would like to do next is splitting each variety into its building blocks. This is done by means of fibrations and this is where the Iitaka conjecture comes into play. It predicts a relation between the Kodaira dimension of the source, the fibres and the base of every fibration.

## 15 Feb 2022

**Speaker: Ignacia Fierro Piccardo**

Supervisor: Prof T Betcke

##### Title: An OSRC Preconditioner for the

**Abstract:**

The Electric Field Integral Equation (EFIE) is commonly used to solve high-frequency electromagnetic scattering problems. However, the EFIE being a First Kind Fredholm operator, needs a regulariser in order to use iterative solvers. A regulariser alternative is the exact Magnetic-to-Electric (MtE) operator, which has the disadvantage of being as expensive as solving the EFIE. However, Bouajaji et al. have developed a local surface approximation of the MtE for time-harmonic Maxwell’s equations that can be efficiently evaluated through the solution of sparse linear systems. In this research we demonstrate the preconditioning properties of the approximate MtE operator for the EFIE using a Bempp implementation and show a number of numerical comparisons against other preconditioning techniques like the Calderón Preconditioner.

## 22 Feb 2022

**NO SEMINAR**

## 01 Mar 2022

**Speaker: Luke Debono**

Supervisor: Prof HJ Wilson

##### THIS SEMINAR HAS BEEN CANCELLED.

## 08 Mar 2022

**Speaker: Pascale Voegtli (LSGNT)**

Supervisor: Prof P Cascini (Imperial College London)

##### Title:A Gentle Introduction To K-Stability

**Abstract:**

Initially introduced as a criterion to characterize the existence of a special type of metrics on Fano varieties in differential geometry, K-stability has recently transpired to be a notion that can be reformulated in purely algebraic terms using well established tools from higher dimensional algebraic geometry. In the talk we will introduce some of them and try to hint at how they can beneficently be applied in the construction of a moduli space for Fano varieties, the so called K-moduli space.

## 15 Mar 2022

**Speaker: Hannah Tillmann-Morris (LSGNT)**

Supervisor: Prof T Coates (Imperial College London)

##### Title: Can a computer detect blowups of Fano manifolds?

**Abstract:**

Mirror symmetry gives us a correspondence between Fano manifolds and certain types of Laurent polynomials. This could potentially be used to reduce the classification of Fano manifolds to combinatorial problem. But many aspects of this conjectured correspondence are still unknown. For example, given two Fano manifolds and two corresponding Laurent polynomials, can the information of whether one Fano is a blowup of the other be extracted just from the data of the Laurent polynomials? I will explain how this Fano/Laurent polynomial correspondence arises and how Laurent polynomials can reveal the blowup relationship in some simple examples.

## 22 Mar 2022

**Speaker: Alessio Di Lorenzo**

Supervisor: Dr L Foscolo

##### Title: TBC

**Abstract:**

TBC