Oxford

DNA double strand breaks (DSB) are the most deleterious type of DNA damage induced by ionizing radiation and cytotoxic agents used in the treatment of cancer. When DSBs are formed, the cell attempts to repair the DNA damage through activation of a variety of molecular repair pathways. One of the earliest events in response to the presence of DSBs is the phosphorylation of a histone protein, H2AX, to form γH2AX. Many hundreds of copies of γH2AX form, occupying several mega bases of DNA at the site of each DSB. These large collections of γH2AX can be visualized using a fluorescence microscopy technique and are called ‘γH2AX foci’. γH2AX serves as a scaffold to which other DNA damage repair proteins adhere and so facilitates repair. Following re-ligation of the DNA DSB, the γH2AX is dephosphorylated and the foci disappear.

We have developed a contrast agent, 111In-anti-γH2AX-Tat, for nuclear medicine (SPECT) imaging of γH2AX which is based on an anti-γH2AX monoclonal antibody. This agent allows us to image DNA DSB in vitro in cells, and in in vivo model systems of cancer. The ability to track the spatiotemporal distribution of DNA damage in vivo would have many potential clinical applications, including as an early read-out of tumour response or resistance to particular anticancer drugs or radiation therapy.

The imaging tracer principle states that a contrast agent should not interfere with the physiology of the process being imaged. Therefore, we have investigated the influence of the contrast agent itself on the kinetics of DSB formation, repair and on γH2AX foci formation and resolution and now wish to synthesise these data into a coherent kinetic-dynamic model.

Understanding the fatigue of metals under cyclic loads is crucial for some fields in mechanical engineering, such as the design of wheels of high speed trains and aero-plane engines. Experimentally it has been found that metal fatigue induced by cyclic loads is closely related to a ladder shape pattern of dislocations known as a persistent slip band (PSB). In this talk, a quantitative description for the formation of PSBs is proposed from two angles: 1. the motion of a single dislocation analised by using asymptotic expansions and numerical simulations; 2. the collective behaviour of a large number of dislocations analised by using a method of multiple scales.

Translation actions appear all over geometry, so it is not surprising that there are many cases of moduli problems which involve non-reductive group actions, where Mumford’s geometric invariant theory does not apply. One example is that of jets of holomorphic map germs from the complex line to a projective variety, which is a central object in global singularity theory. I will explain how to construct this moduli space using the test curve model of Morin singularities and how this can be generalized to study the quotient of projective varieties by a wide class of non-reductive groups. In particular, this gives information about the invariant ring. This is joint work with Frances Kirwan.

I'll present the work of Gaitsgory arXiv:1108.1741. In it he uses Beilinson-Drinfeld factorization techniques in order to uniformize the moduli stack of G-bundles on a curve. The main difference with the gauge theoretic technique is that the the affine Grassmannian is far from being contractible but the fibers of the map to Bun(G) are contractible.

We shall discuss how the algebra norm can be used to identify structure in groups. No prior familiarity with the area will be assumed.

This is joint work with Uri Onn. We use motivic integration to get the growth rate of the sequence consisting of the number of conjugacy classes in quotients of G(O) by congruence subgroups, where $G$ is suitable algebraic group over the rationals and $O$ the ring of integers of a number field.

The proof uses tools from the work of Nir Avni on representation growth of arithmetic groups and results of Cluckers and Loeser on motivic rationality and motivic specialization.