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November 2009
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Events in January 2010

Group actions in complex geometry, I and II
13:10 Fri 8 Jan 10 | School Board Room | Prof Frank Kutzschebauch, IGA Lecturer | University of Berne
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Group actions in complex geometry, III and IV
10:10 Fri 15 Jan 10 | School Board Room | Prof Frank Kutzschebauch, IGA Lecturer | University of Berne
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Group actions in complex geometry, V and VI
10:10 Fri 22 Jan 10 | School Board Room | Prof Frank Kutzschebauch, IGA Lecturer | University of Berne
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Group actions in complex geometry, VII and VIII
10:10 Fri 29 Jan 10 | School Board Room | Prof Frank Kutzschebauch, IGA Lecturer | University of Berne
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TBA
13:10 Fri 29 Jan 10 | School Board Room | Prof Franc Forstneric | University of Ljubljana
A solution to the Gromov-Vaserstein problem
15:10 Fri 29 Jan 10 | TBA | Professor Frank Kutzschebauch | University of Berne, Switzerland

Abstract...
Any matrix in $SL_n (\mathbb C)$ can be written as a product of elementary matrices using the Gauss elimination process. If instead of the field of complex numbers, the entries in the matrix are elements of a more general ring, this becomes a delicate question. In particular, rings of complex-valued functions on a space are interesting cases. A deep result of Suslin gives an affirmative answer for the polynomial ring in $m$ variables in case the size $n$ of the matrix is at least 3. In the topological category, the problem was solved by Thurston and Vaserstein. For holomorphic functions on $\mathbb C^m$, the problem was posed by Gromov in the 1980s. We report on a complete solution to Gromov's problem. A main tool is the Oka-Grauert-Gromov h-principle in complex analysis. Our main theorem can be formulated as follows: In the absence of obvious topological obstructions, the Gauss elimination process can be performed in a way that depends holomorphically on the matrix. This is joint work with Bj\"orn Ivarsson.
ANZIAM Conference
00:00 Sun 31 Jan 10 | Queenstown, New Zealand

Abstract...
ANZIAM is a division of the Australian Mathematical Society. It is the professional association for industrial and applied mathematics in Australia and New Zealand. The annual conference of ANZIAM is an established gathering of applied mathematicians, scientists and engineers. In 2010 the venue is Rydges Hotel, Queenstown, New Zealand.

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