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Six Questions with: Professor Claire Voisin

Six Questions with: Professor Claire Voisin


Claire Voisin is Director of Research at the Institut de Mathématiques de Jussieu and was a Visiting Fellow on the Moduli Spaces programme in 2011.


When did you become first interested in mathematics and what keeps your interest fresh?

I liked doing maths as a teenager, but I became more interested during my last year before starting a PhD thesis, when I started reading research papers in algebraic geometry. Before this I found it hard to take the discipline seriously when you were asked to solve problems whose solution was already known! That seemed more like a game to me, and only at a later stage did I realise that there was an enormous world of new ideas, concepts and problems to be formulated. Even now, the most important thing for me is asking questions, and of course solving open conjectures. In fact, as I get older I see more and more questions left open by my work and the work of others.


Could you tell us a little about your career path so far and what your current research involves?

I work in complex algebraic geometry, which means algebraic geometry over the complex numbers. For some questions, it is irrelevant whether you are over the complex numbers or over any field of characteristic 0. This is the case for commutative algebra. But the domain I like above all is the study of topology and motives of complex algebraic varieties. In this case it is crucial to be over the complex numbers, because we can consider our variety as a complex manifold (if it is smooth) and then use differential topology to introduce the so-called Hodge structures on its Betti cohomology. They provide rather subtle and rich information on your variety.


What achievements are you most proud of?

Two of my best results are in completely different areas. The first one concerns syzygies of canonical curves. This is not as central in my research as the study of Hodge structures, but I proved the Green conjecture for generic curves (of given not too small gonality), and there were new ideas in the proof, in particular an elementary but crucial reformulation of the problem, which I think I can be proud of [1]. The second one is my construction of compact Kähler manifolds not homotopically equivalent to complex projective manifolds. The purely algebraic role played by polarized Hodge structures in the proof was unexpected [2].


How do you achieve a balance between your work and homelife?

I have five children, who are almost grown-up now. I can't remember the details of how I managed a work and life balance, but the main ingredients were the help of my husband and the excellent childcare system in France. We still have three teenagers at home, and I find I do not have enough time to devote to them, which can be frustrating for them and for me.


What advice would you offer to young women who are just starting their careers in the mathematical sciences?

I believe each one has to follow her own way and find her own path.


Has your visit to the Newton Institute been fruitful?

Yes, this has been excellent in many respects. A lot of reflective time; a very peaceful place, no metro at rush hours etc. This is an excellent place to work and meet people.


References

[1] Green's conjecture for curves of even genus lying on a K3 surface, J.Eur. Math. Soc. 4, (2002) pp.363-404.
[2] On the homotopy types of compact Kähler and complex projective manifolds, Inventiones Math. Volume 157, Number 2, (2004), pp.329-343.


University of Cambridge Research Councils UK
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