Poorten Macquarie , W. Hart Illinois , E. Gekeler Saarbrucken , D. Jeon Seoul , C. Kim Seoul , A. Mason Glasgow , F. Pop Pennsylvania , A. Tamagawa Kyoto , S. Mochizuki Kyoto , J. Nekovar Paris , S. Saito Tokyo , W. Raskind Los Angeles , K. Fujiwara Nagoya , L. Hesselholt Nagoya , T. Zink Bielefeld.
ANNALES DE L'INSTITUT FOURIER
Prof Langer organised a workshop on p-adic differential equations in October and a workshop on p-adic integration theory in October Since our staff gave 40 invited addresses to conferences and in external seminars, e. We include two Category B staff in our return. Together with Dr Byott he organized an international workshop on Harmonic Analysis and the Langlands-Conjecture in and attracted famous and world-leading experts Langlands, Henniart in this area to Exeter.
We also include as Category B Prof Vamos who retired in but still plays a very active role within the group. Dr Byott's work is centred on integral Galois module structure and on the use of Hopf algebras to generalise Galois theory. He has been a major contributor to many of the developments in the study of Hopf-Galois structures and the arithmetic applications of Hopf algebras over the past decade, and a number of his results are discussed in detail in a monograph by another of the leaders in this field "Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory", L.
Childs, AMS, In particular, he has given the first examples of local Galois extensions whose valuation rings are well-behaved free over their associated order in a non-classical Hopf-Galois structure even though they are badly behaved in classical Galois theory. This depends on some consequences of the classification of finite simple groups.
More recently, Dr Byott has developed ongoing collaborations with B.
Sodaigui Valenciennes and G. Elder Blacksburg, Virginia. The collaboration with Sodaigui concerns realisable Galois module classes over the integral group ring for nonabelian tame extensions.
- Graph Theory, Proceedings of the Conference on Graph Theory, Cambridge;
- Taming Wild Extensions: Hopf Algebras and Local Galois.
- Analysis and Applications of Artificial Neural Networks.
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A related result, in joint work with C. In a different direction, Dr Byott's collaboration with Elder seeks to generalise classical ramification theory to obtain refined ramification invariants that suffice to determine the absolute Galois module structure of ideals in p-adic fields. This has resulted in two publications so far, with further papers in press. Dr Chapman focuses his research on combinatorial and additive number theory.
He also determined the isomorphism types of these lattices as modules over rings of algebraic integers. Dr Chapman has collaborated with R. Poorten Macquarie and W. Hart Illinois and the Hielbronn Institute. Dr Schweizer works on elliptic curves and elliptic surfaces, on Drinfeld modules, and on classical and Drinfeld modular curves.
Jeon and C. Kim Korea determines which finite groups occur infinitely often as torsion groups of elliptic curves over cubic number fields. This is interesting because despite the work of L. Kim Korea determines which finite groups occur infinitely often as torsion groups of elliptic curves over cubic number fields. This is interesting because despite the work of L. Merel and P. Parent it is not completely known which torsion structures occur at all in this setting.
The main result has recently been used in a paper by B. Dr Schweizer also has an ongoing collaboration with A. It is hoped that the action of these groups on the Drinfeld upper half-plane will allow the construction of algebraic curves in positive characteristic with prescribed or big automorphism groups. Prof Langer has a longstanding collaboration with with T. They have invented a relative construction of the de Rham Witt complex which is crucial to understand crystalline cohomology.
Prof Langer also worked on a completely different topic in arithmetic geometry, namely the central and famous Tate-conjecture for divisors in the theory of algebraic cycles. Here their construction of the relative de Rham Witt complex again plays an important role. Dr Saidi's research is centred on fundamental groups and Galois covers of curves. He also studied cyclic Galois covers of degree p n in equal characteristic. Tamagawa in Kyoto on anabelian geometry of curves over finitely generated fields of positive characteristic.
They obtained some major results on the prime-to-p version of Grothendieck's anabelian conjectures and achieved a far-reaching generalization of previous work by Tamagawa and Mochizuki. Research environment Research structure and staffing policy. The Pure Mathematics group provides a vibrant mathematical culture in which staff exchange and promote their ideas, and also a stimulating environment for our research students and visitors.
Abstracts - Representation Theory and Integrable Systems
We run two weekly seminar series: one featuring outside speakers, and the other given by staff and research students. In addition, there are various other study groups and advanced seminar series organised by staff for colleagues and postgraduate students. Prof Langer organised a one-week workshop on p-adic differential equations in October and another workshop on p-adic integration theory in October with external speakers from Austria, France and Germany.
This intensive workshop is planned to take place annually in Exeter with varying topics. Every member of research staff is attached to the Mathematics Research Institute described previously, and it is the Institute that is responsible for the day-to-day support and organisation of research. The MRI thus has responsibility for allocating research studentships, bidding for research infrastructure funding, monitoring and supporting research students and fellows, arranging research seminars and inviting and hosting research visitors.
Staff and students belonging to the Mathematics Research Institute are physically co-located within the University's Harrison Building, so that they occupy a spatially coherent suite of labs, offices and computer rooms.
This helps to integrate colleagues, particularly new ones, within the research institute structure and to our research culture. All new academic staff are allocated a research mentor, usually professorial, to help them develop their research quickly and effectively. The University operates a 5-year probationary process for all new academic appointments except Chair level , during which appropriate research goals for each appointee are clearly identified.
At the end of a successful probationary period staff automatically progress to Senior Lecturer grade. As already pointed out, this directly benefited Pure Mathematics through the provision of new research office space and new computing facilities, and benefited us indirectly by facilitating a closer interaction with colleagues in Applied Mathematics, Engineering and Computer Science.
Research students, research studentships and PhD-training. The University places a maximum duration of 4-years full-time registration and equivalent part-time for PhD completion submission of thesis. We provide our research students with all the necessary facilities and support to facilitate successful completion of their studies.
The training of our mathematics research students is viewed as being crucially important. Generic skills are also developed via courses provided by the University's Graduate School. Exeter takes graduate training provision very seriously and its 'effective research development programme', specifically developed using Roberts funding, is recognised as one of the best in the country www. Within the School, students undergo a formal monitoring process after three months a short review , at the end of the first year a report, presentation and interview and at the end of subsequent years reports , to ensure continued progress and identify potential obstacles.
All give at least one internal seminar during the first two years, and are expected, and funded by us, to present a paper to at least one international conference.
Access-Grid Network facilities for remote learning and training. As such we now have excellent fully interactive facilities for supporting the remote training of our PhD students. Research income, external funding and grants. A Research Fellow funded by this grant has recently joined the group to collaborate with Prof Langer. Cleft extensions of Hopf algebras , Proc. London Math. Cyclic Hopf orders defined by isogenies of formal groups , Amer. Reine Angew. Tome 87 , pp. Extensions of finite group schemes, and Hopf Galois theory over a complete discrete valuation ring , Math.
On the connected components of moduli spaces of finite flat models to appear in Amer.