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31/10/2002, 14:00 — 15:00 — Room P3.10, Mathematics Building
Freddy Van Oystaeyen, University of Antwerp

Noncommutative topology and geometry

Trying to discover a unifying theory connecting the noncommutative geometry of schematic algebras to the classical basis for quantum mechanics and the noncommutative geometry in terms of C*-algebras, we develop noncommutative topology both in the analytic sense or in the sense of Grothendieck topology. The relation with the lattice of linear closed subspaces of a Hilbert space H is indicated. Function theory in a quaternion variable viewed as two noncommuting complex variables is developed and leads to noncommutative Riemann manifolds and other examples of noncommutative manifolds.

18/10/2002, 15:00 — 16:00 — Room P4.35, Mathematics Building
, Université Catholique de Louvain

On the rational homotopy type of blow-up of submanifolds

There is a general construction of ''blowing-up'' a manifold W along a submanifold V. This construction has applications both in algebraic geometry and in symplectic topology. In this talk we show that the rational homotopy type of such a blow-up is completely determined by the rational homotopy class of the embdedding and the Chern classes of its normal bundle, at least when dim(W)2dim(V)+4. In fact a computable model of the rational homotopy type of the blow-up W ~ can be explicitely described. This construction gives many examples of non-formal simply-connect symplectic manifolds.

12/07/2002, 11:00 — 12:00 — Room P3.10, Mathematics Building
, University of Kentucky

Hilbert-Samuel coefficients of normal ideals

We study the interplay between the integral closedness - or even the normality - of an m-primary ideal I and conditions on the Hilbert-Samuel coefficients of I. We relate these properties to the Cohen-Macaulayness of the associated graded ring of I.

03/06/2002, 15:00 — 16:00 — Room P3.10, Mathematics Building
George Janelidze, Georgian Academy of Sciences, Tbilisi

Course on Category Theory - Session 7

27/05/2002, 15:00 — 16:00 — Room P3.10, Mathematics Building
George Janelidze, Georgian Academy of Sciences, Tbilisi

Course on Category Theory - Session 6

22/05/2002, 11:00 — 12:00 — Room P3.10, Mathematics Building
Thomas Kahl, Universidade do Minho, Braga

Introduction to Rational Homotopy Theory

The purpose of this talk is to provide an introduction to the main techniques and results of rational homotopy theory. No original results will be presented.
To any simply connected space one can associate two algebraic objects - its Quillen model, which is a differential graded Lie algebra, and its Sullivan model, which is a commutative differential graded algebra. The algebraic models of a space contain all its rational homotopy information and have been used by Y. Félix and S. Halperin to establish a dichotomy in rational homotopy theory: Any simply connected finite CW-complex X is either elliptic, i.e., dim π* (X)Q<, or hyperbolic, i.e., the sequence dim πn (X)Q grows exponentially.

20/05/2002, 15:00 — 16:00 — Room P3.10, Mathematics Building
George Janelidze, Georgian Academy of Sciences, Tbilisi

Course on Category Theory - Session 5

15/05/2002, 11:00 — 12:00 — Room P3.10, Mathematics Building
, University of New Brunswick

Noncommutative Surfaces

13/05/2002, 15:00 — 16:00 — Room P3.10, Mathematics Building
George Janelidze, Georgian Academy of Sciences, Tbilisi

Course on Category Theory - Session 4

06/05/2002, 15:00 — 16:00 — Room P3.10, Mathematics Building
George Janelidze, Georgian Academy of Sciences, Tbilisi

Course on Category Theory - Session 3

29/04/2002, 15:00 — 16:00 — Room P3.10, Mathematics Building
George Janelidze, Georgian Academy of Sciences, Tbilisi

Course on Category Theory - Session 2

24/04/2002, 11:00 — 12:00 — Room P3.10, Mathematics Building
George Janelidze, Georgian Academy of Sciences, Tbilisi

Course on Category Theory - Session 1

17/04/2002, 11:00 — 12:00 — Room P3.10, Mathematics Building
Lucile Vandembroucq, Universidade do Minho, Braga

Embeddings up to homotopy of a CW-complex in a sphere

We say that a finite CW-complex X embeds up to homotopy in a sphere Sn if there exists a subpolyhedron K Sn having the same homotopy type as X. In this talk, I will explain a sufficient condition for the existence of such an embedding in a given codimension that we obtained in the particular case where X is a two-cone (that is, X is the homotopy cofibre of a map between two suspensions). As an application of this result, we will see that there is no rational obstruction to embeddings up to homotopy of a two-cone in codimension 3.
(joint work with P. Lambrechts and D. Stanley)

10/04/2002, 11:00 — 12:00 — Room P3.10, Mathematics Building
, The QueenŽs College, Oxford, United Kingdom

The algebraic structure of bounded symmetric domains

The open unit ball in a complex Banach space A is a bounded complex domain, the holomorphic structure of which leads to the existence of a closed subspace As of A and a triple product {...}:A× As ×AA which is symmetric and bilinear in the outer variables, conjugate linear in the middle variable and, for a, b and d in As and c in A, satisfies the Jordan triple identity,

[D(a,b),D(c,d)]=D({abc},d)-D(c,{dab}),

where D(a,b) is the linear operator on A defined, for a in A and b in As by

D(a,b)e={abe}.

When the bounded domain is symmetric As exhausts A and A is then said to be a JB * -triple. Hence, the study of JB * -triples is equivalent to the study of bounded symmetric domains. A complex vector space satisfying the algebraic properties described above is said to be a Jordan * -triple. An associative algebra A, with involution a a* and triple product

{abc}= 1 2 ( ab* c+ cb* a),

is an example of a Jordan * -triple, as is the family of rectangular complex matrices with the same triple product. The algebraic structure of a Jordan * -triple A may be investigated by studying either its family U(A) of tripotents or its family I(A) of inner ideals, which are subspaces J of A for which the space {JAJ} is contained in J. The family I(A) contains the family ZI(A) of triple ideals J for which the spaces {AAJ} and {AJA} are contained in J. In some sense ZI(A) is the centre of I(A) and it is the consequences of this that form the main theme of the talk.

27/02/2002, 11:00 — 12:00 — Room P3.10, Mathematics Building
Santiago Zarzuela, Universitat de Barcelona

Arrangements of linear varieties, D-modules and local cohomolgy

Let Ak n denote the affine space of dimension n over a field k and X Ak n be an arrangement of linear subvarieties. Set R=k[ x1 ,, xn ] and let IR denote an ideal which defines X. If k is a field of characteristic zero, the local cohomology modules modules HI r (R) are known to have a module structure over the Weyl algebra An (k), and one can therefore consider their characteristic cycles, denoted CC( HI r (R)) in this talk. In either the real or the complex case, we shall determine the Betti numbers of the complement of the arrangement X in terms of the multiplicities of the local cohomology modules HI r (R).
(Joint work with Josep Àlvarez-Montaner and Ricardo García- López)

29/01/2002, 14:00 — 15:00 — Room P3.10, Mathematics Building
, Universidade do Porto

Some semigroup theoretic techniques in topology

16/01/2002, 11:00 — 12:00 — Room P3.10, Mathematics Building
Kasper Andersen, Centre de Recerca Matemàtica, Barcelona

The classification of p-compact groups for odd primes p

A central problem in algebraic topology has been to single out the homotopy theoretical properties which characterize compact Lie groups. The right definition of a p-local version of a compact Lie group came with Dwyer and Wilkerson who introduced the so called p-compact groups and proved that they possess many nice properties. For example a p-compact group has a maximal torus, a maximal torus normalizer and a Weyl group.

For odd primes p, we give a classification of p-compact groups by proving that they are determined by their maximal torus normalizers. In particular the Weyl group data gives a bijection between connected p-compact groups and finite p-adic reflection groups.

A number of corollaries follow easily from this classification, for example we give an affirmative answer to the maximal torus conjecture for finite loop spaces up to [1/2]-localization.

19/12/2001, 11:00 — 12:00 — Room P4.35, Mathematics Building
, Instituto Superior Técnico

An introduction to homotopical algebra (episode 2)

12/12/2001, 11:00 — 12:00 — Room P3.10, Mathematics Building
, Instituto Superior Técnico

An introduction to homotopical algebra (episode 1)

28/11/2001, 11:00 — 12:00 — Room P3.10, Mathematics Building
Teresa Monteiro Fernandes, Universidade de Lisboa, Portugal

Aspectos Geométricos em teoria dos D-Módulos

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Current organizer: Gustavo Granja

CAMGSD FCT