More about the programme
Developing a geometric counterpart to the commutative algebra, often worded in terms of deformations or quantizations of algebras, requires an abstract foundation allowing the desired generality of its applicability, but should also allow concrete calculations, either in the algebras or in (co)homology groups, reflecting real geometric aspects. The fundamental multidisciplinarity of the mathematics involved is obvious: category theory,algebraic geometry, topology and knot theory, homological methods, Lie theory, representation theory, differential geometry, rings of differential operators..., with applications in physics, statistical physics or even Robotics (mobile robots). International and multidisciplinary cooperation is absolutely necessary for the development of this subject. On the European Scale a concerted action integrating workshops, exchange visits, study centers and schools, research in pairs, grants for researchers, etc... integrating cooperation of top specialists with a training aspect for young researchers in Europe, allows for interaction at all research levels in many directions.
Scientific Objectives
At the level of foundations, four items
- Developing the basic language of noncommutative geometry dealing with geometric properties of quantum groups, quantum spaces, deformations of classical algebras, Hopf algebras and quasi-Hopf algebras, the structutre theory of generalized gauge algebras and the Witten algebras appearing in SU2-gauge theory.
- Expressing the link between geometrical properties and category theoretical constructions at a deeper level, developing higher homological methods etc... in terms of derived categories, braidings and braided categories.
- Developing the algebraic geometry of associative algebras further e.g. extending a scheme theory on the generalized Zariski topology by furthering the study of quasicoherent sheaves, microlocal theory theory and quantum-sections, sheaf cohomology theories and concrete calculation techniques, Chern classes, generalizations of Riemann-Roch theory in the noncommunitative case, intersection theory on noncommutative varieties and singularity theory.
- Exploring the hybrid regions between C*-algebra theory and noncommutative differential geometry and the forementioned noncommutative geometry from the point of view of associative algebras or categorical techniques.
At the level of applications, four items are underlined:
- Applications of noncommutative geometry to the representation theory of algebras (and quantized algebras, quantum groups) and associated quivers.
- Applying techniques of noncommutative geometry rings of differential operators and the theory of pure or holonomic modules, to algebraic Lie representations and the orbit method.
- Describing classes of low dimensional examples. Study of particular cases, e.g. application of noncommutative geometry to algebras satisfying polynomial identities and in particular to quantum groups at roots of unity.
- Application of noncommutative (differential) geometry to physics e.g. the renormalization problem and related Hopf algebras. Reformulating classical phenomena and methods in physics e.g. Feynman diagrams, bozonization etc... from the point of view of noncommutative geometry.
Announcement
European Priority Programme
NONCOMMUTATIVE GEOMETRY
NOG-Workshop of the International Algebra Congress
in memory of Z. I. Borevich
University of St. Petersburg, September 17th – 23rd, 2002
Speakers at Workshop
S. Adian
A. Bak
C. De Concini
L. De Martino
M. Hazewinkel
T. Lenagan
Li Shanzi
Y. Manin
V. Mazurov
A. Mikhalev
B. Plotkin
A. Premet
C. Procesi
Y. Seger
A. Shalev
T. Springer
C. Tamburini
F. Van Oystaeyen
E. Vinberg
J. Wilson
Information about the meeting can be obtained from :
Nicolai Vavilov Email
There is limited support available for young post-docs from countries linked to the European Science Foundation. Interested participants may contact F. Van Oystaeyen Email or N. Vavilov Email
International Advanced Master Degree
Noncommutative Geometry
October 2003 - July 2004
Y
University of Antwerp
2020 Antwerp, Belgium
Supported by the European Science Foundation Scientific Programme Noncommutative Geometry (NOG)
Scope: The programme is a full year programme of courses and seminars leading to a certificate at the advanced master level. A large international team of active researchers in the field will contribute to the programme. In the project sessions the self-activity of participants will be stimulated; detailed "problem scenarios" will be proposed to the students, to be worked out alone or in team.
1st Semester (2003-2004)
Introductory Courses
These courses are in principle outside the programme, students with insufficient background in these areas may choose to participate in some of t
| hours | credits | |
| Algebraic Geometry | 30 | 0 |
| Category Theory and Homological Algebra | 30 | 0 |
Basic courses
| hours | credits | |
| Introduction to Noncommutative Algebra | 60 | 6 |
| Quantum Algebras | 30 | 3 |
| Projects in Noncommutative Algebra | 30 | 3 |
| ||
| Noncommutative Geometry | 30 | 3 |
| ||
| Geometric Invariant Theory | 30 | 3 |
| Projects in Noncommutative Geometry | 30 | 3 |
| ||
| Quantum Groups and Hopf Algebras | 30 | 3 |
Topical Mini-courses and Seminars
A series of compact courses offered by guest lecturers with additional seminars and project-sessions : students get 1 credit per 8 h. course
2nd Semester (2003-2004)
Basic Courses
| hours | credits | |
| Ring Theory | 30 | 3 |
| Projects in Ring Theory | 30 | 3 |
| ||
| Noncommutative Schemes | 30 | 3 |
| Projects in Scheme Theory | 30 | 3 |
| Derived Categories | 15 | 2 |
| ||
| M. Kontsevich Course (May 2004) | 3 | |
Specialized Mini-courses
Continuation of the series started in the 1st semester. These courses typically consist of 8 hours of lectures, some of which are extended by project-sessions.
A partial list of topics includes:
- Braidings and quantum groups
- (Quantum) eveloping algebras
- Quiver varieties
- Quantum matrices
- Noncommutative valuations
- Finite dimensional algebras
- A8 -structures
- Noncommutative topology
There is 1 credit per 8 hours (course or project session)
Full Programme
In order to obtain the diploma of International Advanced Master recognized by the University of Antwerp and with the support of the European Science Foundation, it is necessary to receive the following credits :
1. All basic courses (26 credits)
2. A set of mini-courses, freely chosen from the programme offered, yielding at least 6 c redits
3. Participation in the project sessions associated to the basic courses (12 courses)
4. The composition of a Master Thesis. This thesis may be a summary of work performed in the project-sessions (minimal version) but can also be a personal study of a topic fitting in the programme. The weight of the thesis is 16 credits, bringing the total weight of the master programme to 60 credits.
Lecturers:
J. Alev (Reims), R. Bocklandt (Antwerp), S. Caenepeel (Brussels), P. Fiebig (Chicago), E. Jespers (Brussels), B. Keller (Paris VI), M. Kontsevich (IHES), L. Le Bruyn (Antwerp), T. Lenagan (Edinburgh), S. Majid (London), M. Reinecke (Wuppertal), C. Ringel (Bielefeld), A. Schofield (Bristol), S. Skryabin (Hamburg), M. Van den Bergh (Diepenbeek), F. Van Oystaeyen (Antwerp)
Admission and Registration
The advanced master degree is equivalent to the fifth year of education in the bachelor-master model. Graduates, i.e. students having passed the normal 4 years of education in mathematics or students at the master level or pre-doctoral students are eligible for admission. The master class is restricted to at most 20 students, the selection procedure is done by a local committee.
Registration is necessary before October 12th, 2003. In view of the availability of rooms near the campus early registration is advisable. Registration is free for students in a SOCRATES cooperation (for European students such an agreement can easily be set up) or for students obtaining NOG-support. For other students there is a registration fee € 500.
Contacts:
Prof. Dr. F. Van Oystaeyen
Dept. of Mathematics & Comp. Sci.
University of Antwerpen
Middelheimlaan 1
2020 Antwerp, Belgium
Tel. +32/3/218.08.92
Fax. +32/3/218.07.77
E-mail secretary :
Mrs. P. De Clopper
International Bureau (SOCRATES)
Academic Planning, Bld. D
University of Antwerp
Universiteitsplein 1
2610 Wilrijk/Antwerp, Belgium
Tel. +32/3/820.21.34
E-mail :
