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April 21
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Groups and characters, a farewell symposium for Rob van der
Waall,
Universiteit van Amsterdam, room P.227 of the Euclides
building.
See the UvA
announcement for directions.
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10:30-11:00
| Coffee
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11:00-11:50
| Hendrik Lenstra (Leiden),
Factoring polynomials over solvable closures
Abstract.
One of Rob van der Waall's most celebrated results concerns
solvable extensions of number fields, and it is proved by means
of group theory. The same applies to the result that the present
lecture is devoted to: there is an efficient algorithm for
factoring polynomials over the solvable closure of a number
field. Some care is required in formulating precisely what this
assertion means, because the solvable closure of any number
field is of infinite degree over the field of rational numbers.
The lecture will provide the context, the definitions, the
algorithm, as well as the result from group theory that is
crucial in proving the correctness of the algorithm.
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12:00-12:50
| Gabriele Nebe (Aachen),
Codes and invariant theory
Abstract.
In 1970 on the ICM in Nice, A.M. Gleason presented his famous
theorem that the weight enumerator of a doubly-even self-dual
binary code is an element of the polynomial ring generated by
the weight enumerators of the Hamming code of length 8 and the
Golay code of length 24. The proof uses the fact that
this polynomial ring is the invariant ring of the
complex reflection group G9 of order 192.
In the meantime, many variations of this theorem have been proven.
Together with E. Rains and N. Sloane, we develop a theory that allows
us to prove that, in a quite general situation, the weight
enumerators of codes of a given Type over a not necessary
commutative finite ring span the invariant ring of the associated
Clifford-Weil group. These are finite complex matrix groups
given by explicit generators.
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14:00-18:20
| Afternoon program
To attend the afternoon program and the closing reception
please register by sending an email to
Evelien Wallet at
ewallet@science.uva.nl.
This part of the day will include a lecture of
Bertram Huppert (Mainz) with the title How to shuffle
cards, and lectures by Arjeh Cohen and Rob van der
Waall.
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