Advising Notes A course may fulfill the requirement in more than one of the above content categories but will not reduce the number of total units required for the major.
Life[ edit ] Family and childhood[ edit ] Grothendieck was born in Berlin to anarchist parents. His father, Alexander "Sascha" Schapiro also known as Alexander Tanaroffhad Hassidic roots and had been imprisoned in Russia before moving to Germany inwhile his mother, Johanna "Hanka" Grothendieck, came from a Protestant family in Hamburg and worked as a journalist.
Both had broken away from their early backgrounds in their teens. They left Grothendieck in the care of Wilhelm Heydorn, a Lutheran pastor and teacher  in Hamburg. During this time, his parents took part in the Spanish Civil Waraccording to Winfried Scharlauas non-combatant auxiliaries,  though others state that Sascha fought in the anarchist militia.
Shortly afterwards his father was interned in Le Vernet. Once Alexander managed to escape from the camp, intending to assassinate Hitler. After three years of increasingly independent studies there, he went to continue his studies in Paris in Byhe set this subject aside in order to work in algebraic geometry and homological algebra.
The prospect did not worry him, as long as he could have access to books. He was so completely unknown to this group and to their professors, came from such a deprived and chaotic background, and was, compared to them, so ignorant at the start of his research career, that his fulgurating ascent to sudden stardom is all the more incredible; quite unique in the history of mathematics.
He was, however, able to play a dominant role in mathematics for around a decade, gathering a strong school. Closely linked to these cohomology theories, he originated topos theory as a generalisation of topology relevant also in categorical logic.
He also provided an algebraic definition of fundamental groups of schemes and more generally the main structures of a categorical Galois theory. As a framework for his coherent duality theory he also introduced derived categorieswhich were further developed by Verdier. He gave lectures on category theory in the forests surrounding Hanoi while the city was being bombed, to protest against the Vietnam War.
The Grothendieck Festschrift, published inwas a three-volume collection of research papers to mark his sixtieth birthday in By the late s, he had started to become interested in scientific areas outside mathematics.
The group published a bulletin and was dedicated to antimilitary and ecological issues, and also developed strong criticism of the indiscriminate use of science and technology.
Instimulated by correspondence with Ronald Brown and Tim Porter at Bangor UniversityGrothendieck wrote a page manuscript titled Pursuing Stacksstarting with a letter addressed to Daniel Quillen. This letter and successive parts were distributed from Bangor see External links below.
Within these, in an informal, diary-like manner, Grothendieck explained and developed his ideas on the relationship between algebraic homotopy theory and algebraic geometry and prospects for a noncommutative theory of stacks.
The manuscript, which is being edited for publication by G. Written inthis latter opus of about pages further developed the homotopical ideas begun in Pursuing Stacks.
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