prof. Maszczyk's seminars at SISSA

[Emanuele Tuillier Illingworth]

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MATHEMATICAL PHYSICS SEMINAR
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Prof. Tomasz Maszczyk
University of Warsaw

 
will hold 2 seminars:


Wed. 12 Nov, 11:00, room C

ON SPLITTING POLYNOMIALS WITH NONCOMMUTATIVE COEFFICIENTS.

Abstract. It is showed that for every splitting of a polynomial with 
noncommutative coefficients into linear factors (X . a_k) with a_k.s 
commuting with coefficients, any cyclic permutation of linear factors 
gives the same result and all a_k are roots of that polynomial. It 
implies that although a_k.s appearing in a splitting of a polynomial 
with commutative coefficients in some noncommutative extension do not 
form a set (in general), they do form a cyclic order consisting of 
roots. Examples of this phenomenon are given.




Thu 13 Nov, 16:00, SISSA lecture room D

DISTRIBUTIVE LATTICES AND COHOMOLOGY.

Abstract. A resolution of the intersection of a finite number of
subgroups of an abelian group by means of their sums is constructed,
provided the lattice generated by these subgroups is distributive.
This is used for detecting singularities of modules over Dedekind 
rings. A generalized Chinese remainder theorem is derived as a 
consequence of the above resolution. The Gelfand-Naimark duality 
between finite closed coverings of compact Hausdorff spaces and the 
generalized Chinese remainder theorem is clarified.