Math.Koll. am 20.6.07/Prof. Kuba

Tue Jun 12 14:35:26 CEST 2007

Mathematisches Kolloquium

EINLADUNG

zu einem

VORTRAG

von

Prof. Gerald Kuba (Universitaet fuer Bodenkultur Wien)

mit dem Thema: ''Counting fields of complex numbers''

Abstract:
For a field K let   (K) be the total number of subfields of K and   (K) the
maximal number of mutually non-isomorphic subfields of K. Trivially,  (K)
(K)     (K) for every field K, where
  (K) is the cardinal number of the power set of K. In the talk we shall
verify the following table, where A   C is the field of all algebraic
numbers and c = 2 0 .
K  (K)   (K)  (K)
Q 1 1 c
Q(i) 2 2 c
Q( ) 3 3 c
Q(i;   ) 8 10 c
Q( ) 2  0 c
A, A R c c c
C, R 2c 2c 2c

Moreover, on the one hand we shall construct 2c mutually non-isomorphic
subfields K of C with [C : K] = 2 in an unexpected easy way. (We avoid
transfinite induction and we do not need the two excessive assumptions 2  0
=  1 and 2  1 =  2 .) On the other hand we shall produce 2c mutually
non-isomorphic proper subfields L of R of smallest possible codimension,
which means that
[R : L] =  0 in view of a famous result due to Artin.

Zeit: Mittwoch, 20. Juni 2007, 15.45 Uhr (Kaffeejause), anschlieszend 16.15
Uhr Vortrag

Ort: Fakultaet fuer Mathematik der Universitaet Wien, Nordbergstr. 15,
Seminarraum C 2.09

Harald Rindler
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Microsoft Formel-Editor 3.0
Type: application/x-microsoft-ole-object
Size: 3584 bytes
Desc: not available
Url : http://www.mat.univie.ac.at/pipermail/mathkoll/attachments/20070612/0a8ca270/MicrosoftFormel-Editor3-0023.bin
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Microsoft Formel-Editor 3.0
Type: application/x-microsoft-ole-object
Size: 3584 bytes
Desc: not available
Url : http://www.mat.univie.ac.at/pipermail/mathkoll/attachments/20070612/0a8ca270/MicrosoftFormel-Editor3-0024.bin
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Microsoft Formel-Editor 3.0
Type: application/x-microsoft-ole-object
Size: 3584 bytes
Desc: not available
Url : http://www.mat.univie.ac.at/pipermail/mathkoll/attachments/20070612/0a8ca270/MicrosoftFormel-Editor3-0025.bin
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Microsoft Formel-Editor 3.0
Type: application/x-microsoft-ole-object
Size: 3584 bytes
Desc: not available
Url : http://www.mat.univie.ac.at/pipermail/mathkoll/attachments/20070612/0a8ca270/MicrosoftFormel-Editor3-0026.bin
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Microsoft Formel-Editor 3.0
Type: application/x-microsoft-ole-object
Size: 3584 bytes
Desc: not available
Url : http://www.mat.univie.ac.at/pipermail/mathkoll/attachments/20070612/0a8ca270/MicrosoftFormel-Editor3-0027.bin
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Microsoft Formel-Editor 3.0
Type: application/x-microsoft-ole-object
Size: 3584 bytes
Desc: not available
Url : http://www.mat.univie.ac.at/pipermail/mathkoll/attachments/20070612/0a8ca270/MicrosoftFormel-Editor3-0028.bin
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Microsoft Formel-Editor 3.0
Type: application/x-microsoft-ole-object
Size: 3584 bytes
Desc: not available
Url : http://www.mat.univie.ac.at/pipermail/mathkoll/attachments/20070612/0a8ca270/MicrosoftFormel-Editor3-0029.bin
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Microsoft Formel-Editor 3.0
Type: application/x-microsoft-ole-object
Size: 3584 bytes
Desc: not available
Url : http://www.mat.univie.ac.at/pipermail/mathkoll/attachments/20070612/0a8ca270/MicrosoftFormel-Editor3-0030.bin
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Microsoft Formel-Editor 3.0
Type: application/x-microsoft-ole-object
Size: 3584 bytes
Desc: not available
Url : http://www.mat.univie.ac.at/pipermail/mathkoll/attachments/20070612/0a8ca270/MicrosoftFormel-Editor3-0031.bin
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Microsoft Formel-Editor 3.0
Type: application/x-microsoft-ole-object
Size: 3584 bytes
Desc: not available
Url : http://www.mat.univie.ac.at/pipermail/mathkoll/attachments/20070612/0a8ca270/MicrosoftFormel-Editor3-0032.bin
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Microsoft Formel-Editor 3.0
Type: application/x-microsoft-ole-object
Size: 3584 bytes
Desc: not available
Url : http://www.mat.univie.ac.at/pipermail/mathkoll/attachments/20070612/0a8ca270/MicrosoftFormel-Editor3-0033.bin
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Microsoft Formel-Editor 3.0
Type: application/x-microsoft-ole-object
Size: 3584 bytes
Desc: not available
Url : http://www.mat.univie.ac.at/pipermail/mathkoll/attachments/20070612/0a8ca270/MicrosoftFormel-Editor3-0034.bin
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Microsoft Formel-Editor 3.0
Type: application/x-microsoft-ole-object
Size: 3584 bytes
Desc: not available
Url : http://www.mat.univie.ac.at/pipermail/mathkoll/attachments/20070612/0a8ca270/MicrosoftFormel-Editor3-0035.bin
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Microsoft Formel-Editor 3.0
Type: application/x-microsoft-ole-object
Size: 4096 bytes
Desc: not available
Url : http://www.mat.univie.ac.at/pipermail/mathkoll/attachments/20070612/0a8ca270/MicrosoftFormel-Editor3-0036.bin
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Microsoft Formel-Editor 3.0
Type: application/x-microsoft-ole-object
Size: 4096 bytes
Desc: not available
Url : http://www.mat.univie.ac.at/pipermail/mathkoll/attachments/20070612/0a8ca270/MicrosoftFormel-Editor3-0037.bin
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Microsoft Formel-Editor 3.0
Type: application/x-microsoft-ole-object
Size: 3584 bytes
Desc: not available
Url : http://www.mat.univie.ac.at/pipermail/mathkoll/attachments/20070612/0a8ca270/MicrosoftFormel-Editor3-0038.bin
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Microsoft Formel-Editor 3.0
Type: application/x-microsoft-ole-object
Size: 3584 bytes
Desc: not available
Url : http://www.mat.univie.ac.at/pipermail/mathkoll/attachments/20070612/0a8ca270/MicrosoftFormel-Editor3-0039.bin
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Microsoft Formel-Editor 3.0
Type: application/x-microsoft-ole-object
Size: 3584 bytes
Desc: not available
Url : http://www.mat.univie.ac.at/pipermail/mathkoll/attachments/20070612/0a8ca270/MicrosoftFormel-Editor3-0040.bin
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Microsoft Formel-Editor 3.0
Type: application/x-microsoft-ole-object
Size: 3584 bytes
Desc: not available
Url : http://www.mat.univie.ac.at/pipermail/mathkoll/attachments/20070612/0a8ca270/MicrosoftFormel-Editor3-0041.bin
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Microsoft Formel-Editor 3.0
Type: application/x-microsoft-ole-object
Size: 3584 bytes
Desc: not available
Url : http://www.mat.univie.ac.at/pipermail/mathkoll/attachments/20070612/0a8ca270/MicrosoftFormel-Editor3-0042.bin
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Microsoft Formel-Editor 3.0
Type: application/x-microsoft-ole-object
Size: 3584 bytes
Desc: not available
Url : http://www.mat.univie.ac.at/pipermail/mathkoll/attachments/20070612/0a8ca270/MicrosoftFormel-Editor3-0043.bin
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Microsoft Formel-Editor 3.0
Type: application/x-microsoft-ole-object
Size: 3584 bytes
Desc: not available
Url : http://www.mat.univie.ac.at/pipermail/mathkoll/attachments/20070612/0a8ca270/MicrosoftFormel-Editor3-0044.bin
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Microsoft Formel-Editor 3.0
Type: application/x-microsoft-ole-object
Size: 3584 bytes
Desc: not available
Url : http://www.mat.univie.ac.at/pipermail/mathkoll/attachments/20070612/0a8ca270/MicrosoftFormel-Editor3-0045.bin