Ekaterina Amerik

 

 


 

Graduated from mathematical department of Moscow State University in 1992, went for graduate studies to the University of Leiden (the Netherlands), worked under the guidance of prof. A. Van de Ven. Ph. D obtained in spring 1997, title: «On the geometry of smooth hypersurfaces in projective space». Postdoc at Grenoble University (France) in 1997-1999. From september 1999, assistant professor at the University Paris-IX (Orsay, France); «habilitation» (a post-PhD degree existing in several european countries) obtained in 2007. From 2011 on, works at the mathemaical department of the Higher School of Economics, first as an assistant professor, then as a professor.




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Nov 28th 2016

A very beautiful classical theory on field extensions of a certain type (Galois extensions) initiated by Galois in the 19th century. Explains, in particular, why it is not possible to solve an equation of degree 5 or more in the same way as we solve quadratic or cubic equations. You will learn to compute Galois groups and (before that) study the properties of various field extensions. We first shall survey the basic notions and properties of field extensions: algebraic, transcendental, finite field extensions, degree of an extension, algebraic closure, decomposition field of a polynomial. Then we shall do a bit of commutative algebra (finite algebras over a field, base change via tensor product) and apply this to study the notion of separability in some detail.

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