The London School of Geometry and Number Theory (LSGNT) is an EPSRC-funded Centre for Doctoral Training (CDT) and is a joint venture between UCL, King's College London and Imperial College London. It offers a wide range of research projects in different aspects of number theory, geometry and topology. Mathematics research at UCL is flourishing with significant funding from EPSRC, ERC, the Royal Society and industry. The department is a member of the UCL Institute of Origins, Centre for Inverse Problems, and CoMPLEX (Centre of Mathematics and Physics in the Life Sciences and Experimental Biology); it hosts the Clinical Operational Research Unit and has 20 postdoctoral researchers including the Clifford Fellow. The London School of Geometry and Number Theory is run by UCL in partnership with King's College London and Imperial College London. Students benefit from our leading role in the inter-university London Taught Course Centre for PhD Students in the Mathematical Sciences. Recent UCL Mathematics graduates have taken up academic posts at universities such as UCL, Sheffield, Kyoto and California State; others have joined the financial services industry at companies such as Barclays Capital, Schroders, Deloitte, ABN Amro and J P Morgan; and others have become mathematics teachers and computer programmers. Some students have taken summer secondments, with two recent ones at the Department of Business, Innovation and Skills.