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Caucher Birkar FRS (Kurdish: کۆچەر بیرکار, romanized: Koçer Bîrkar, lit. 'migrant mathematician'; born Fereydoun Derakhshani ( Kurdish : فەرەیدوون درەخشانی ، Persian : فریدون درخشانی ); July 1978) is a Kurdish-British mathematician [ 3 ] (born in Iran) and a professor at Tsinghua University .
The existence of log flips in higher dimensions has been settled by (Caucher Birkar, Paolo Cascini & Christopher D. Hacon et al. 2010). On the other hand, the problem of termination—proving that there can be no infinite sequence of flips—is still open in dimensions greater than 3.
The existence of the more general log flips was established by Vyacheslav Shokurov in dimensions three and four. This was subsequently generalized to higher dimensions by Caucher Birkar, Paolo Cascini, Christopher Hacon, and James McKernan relying on earlier work of Shokurov and Hacon, and McKernan. They also proved several other problems ...
In algebraic geometry, the abundance conjecture is a conjecture in birational geometry, more precisely in the minimal model program, stating that for every projective variety with Kawamata log terminal singularities over a field if the canonical bundle is nef, then is semi-ample.
One of Shokurov's ideas formed a basis for a paper titled 3-fold log flips where the existence of three-dimensional flips (first proved by Shigefumi Mori) was established in a more general log setting. The inductive method and the singularity theory of log pairs developed in the framework of that paper allowed most of the paper's results to be ...
Maryna Sergiivna Viazovska (Ukrainian: Марина Сергіївна Вязовська, [2] pronounced [mɐˈrɪnɐ wjɐˈzɔu̯sʲkɐ]; born 2 December 1984) [3] is a Ukrainian mathematician known for her work in sphere packing.
Akshay Venkatesh was born in Delhi, India, and his family emigrated to Perth in Western Australia when he was two years old. He attended Scotch College.His mother, Svetha, is a computer science professor at Deakin University.
A birational map from X to Y is a rational map f : X ⇢ Y such that there is a rational map Y ⇢ X inverse to f.A birational map induces an isomorphism from a nonempty open subset of X to a nonempty open subset of Y, and vice versa: an isomorphism between nonempty open subsets of X, Y by definition gives a birational map f : X ⇢ Y.