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The Life and Work of Caucher Birkar, the Migrant Mathematician

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The Life and Work of Caucher Birkar, the Migrant Mathematician The life and work of Caucher Birkar, the migrant mathematician Diletta Martinelli Universiteit van Amsterdam Nationale Wiskunde Dagen, February 1, 2020 Maths makes the news, 1 August 2018 Internation Congress of Mathematichians, Rio de Janerio. Maths makes the news, 2 August 2018 Official announcement He is Kurdish! 1979: Iranian Revolution. 1980-1988: Iraq-Iran war. Short Bio of Caucher Birkar 1978: Born in Marivan, Iran. 1979: Iranian Revolution. 1980-1988: Iraq-Iran war. Short Bio of Caucher Birkar 1978: Born in Marivan, Iran. He is Kurdish! 1980-1988: Iraq-Iran war. Short Bio of Caucher Birkar 1978: Born in Marivan, Iran. He is Kurdish! 1979: Iranian Revolution. Short Bio of Caucher Birkar 1978: Born in Marivan, Iran. He is Kurdish! 1979: Iranian Revolution. 1980-1988: Iraq-Iran war. Short bio of Cauher Birkar "My brother Haidar started teaching me more advanced mathematics, which was not part of middle school education. He taught me to learn maths for the fun of it rather than passing exams. He is probably the person that had the most influence on my education." Birkar's family. 2000: He travels to England for a mathematics competition and asks political asylum. The British government places him in Nottingham where he enrolls at the University. He changes his name to Caucher Birkar, the migrant mathematician in Kurdish. 2002: He meets Vyacheslav Shokurov and starts working in birational geometry. 2010: He proves a major result in collaboration with Cascini, Hacon and McKernan [BCHM], he becomes professor at Cambridge and a maths superstar. Short bio of Caucher Birkar He attends the University in Tehran; He changes his name to Caucher Birkar, the migrant mathematician in Kurdish. 2002: He meets Vyacheslav Shokurov and starts working in birational geometry. 2010: He proves a major result in collaboration with Cascini, Hacon and McKernan [BCHM], he becomes professor at Cambridge and a maths superstar. Short bio of Caucher Birkar He attends the University in Tehran; 2000: He travels to England for a mathematics competition and asks political asylum. The British government places him in Nottingham where he enrolls at the University. 2002: He meets Vyacheslav Shokurov and starts working in birational geometry. 2010: He proves a major result in collaboration with Cascini, Hacon and McKernan [BCHM], he becomes professor at Cambridge and a maths superstar. Short bio of Caucher Birkar He attends the University in Tehran; 2000: He travels to England for a mathematics competition and asks political asylum. The British government places him in Nottingham where he enrolls at the University. He changes his name to Caucher Birkar, the migrant mathematician in Kurdish. 2010: He proves a major result in collaboration with Cascini, Hacon and McKernan [BCHM], he becomes professor at Cambridge and a maths superstar. Short bio of Caucher Birkar He attends the University in Tehran; 2000: He travels to England for a mathematics competition and asks political asylum. The British government places him in Nottingham where he enrolls at the University. He changes his name to Caucher Birkar, the migrant mathematician in Kurdish. 2002: He meets Vyacheslav Shokurov and starts working in birational geometry. Short bio of Caucher Birkar He attends the University in Tehran; 2000: He travels to England for a mathematics competition and asks political asylum. The British government places him in Nottingham where he enrolls at the University. He changes his name to Caucher Birkar, the migrant mathematician in Kurdish. 2002: He meets Vyacheslav Shokurov and starts working in birational geometry. 2010: He proves a major result in collaboration with Cascini, Hacon and McKernan [BCHM], he becomes professor at Cambridge and a maths superstar. Algebraic ) He uses algebraic tools. Birkar is an Algebraic Geometer Geometer ) He thinks about geometric objects. Birkar is an Algebraic Geometer Geometer ) He thinks about geometric objects. Algebraic ) He uses algebraic tools. The Circle x2 + y2 = 1 The Circle x2 + y2 = 1 The Circle x2 + y2 = 1 Polynomials are everywhere Simple functions. They model many naturally-occurring processes across science. They approximate smooth functions. Sydney Harbour Bridge We call the space of solutions of polynomial equations algebraic varieties. The zoo of polynomials X12 = 243S12 − 22Q12 = 0 where 2 2 2 2 6 Q12 = (x + y + z + w ) p − − − S12 = 33 (5)(s2;3 +s3;4 +s4;2)+ + + + 19(s2;3 + s3;4 + +s4;2) + 10s2;3;4 − 14s1;0 + 2s1;1 − 6s1;2 2 − 352s5;1 + 336l5 l1 + 48l2l3l4 4 4 4 4 l1 = x + y + z + w 2 2 2 2 l2 = x y + z w 2 2 2 2 l3 = x z + y w 2 2 2 2 l4 = x w + y z l5 = xyzw ::: The dodecic surface. It was discovered by Alessandra Sarti in 2008. Classification Caucher Birkar: \We want to bring order to an infinitude of equations." Comparing varieties I Cylinder vs Hyperboloid Isomorphism We say that two varieties are isomorphic if there are morphisms f : X ! Y and h : Y ! X that are inverse of each other. Example: The cylinder and the hyperboloid are isomorphic. The hyperboloid and the cone are NOT isomorphic. Comparing varieties II Hyperboloid vs Cone Comparing varieties II Hyperboloid vs Cone The hyperboloid and the cone are NOT isomorphic. Singularities are evil! Singular vs Smooth Going from the hyperboloid to the cone we created a singularity, i.e. a point where all the partial derivatives vanish. Singular vs Smooth Going from the hyperboloid to the cone we created a singularity, i.e. a point where all the partial derivatives vanish. Singularities are evil! . small modifications e want to allow W 1.2. them happen to be real. could be a 37 dimensionalnot geometric sound object so embedded remarkable in to a 59-dimensional you, ambi- imagine that your the original singular variety polynomial map which takes the cylinder analytic functions, rather thanunderstand polynomial via functions. Fubini’s theorem.the integrability There of is certain also functions,coordinates. a since version integrability As of for monomialsof we (real coordinates, is will or easy the complex) see, function to looks this like has a monomial tremendous implications for computing variable shouldcause of naturally the fundamentalgeometry be theorem are of interpreted more algebra: straightforwardtheorem the in is as zeros the true of complex forthree-space, a case. both polynomial but real The in in and is one complex the essentially varieties, course be- but we the will basicsthemselves of focus singular! algebraic on complexan varieties. 11-dimensional Hironaka’s subvarietyent with space, hundreds and of its components, singular locus all could of be which unimaginably are complicated—perhaps Hironaka’s remarkable theorem says that such a resolution can 2K for space. Pulling this function back under the map invertible everywhere except at the vertex. “monomialized”—after a relatively simpleevery and analytic understandable analytic functionstrong change (in resolution, any or number embedded resolution) of is real equally or impressive. complex It states variables) that can be Returning to the example above, consider the function This cylinder is a In our example, we considered a real variety so we could draw a picture in every Analytic. variety, no matter how twisted, pinched or folded it may be. If this does The analytic interpretation of Hironaka’s theorem (also called resolution of singularities We want them all into the same class! ( Indeed, as you should check yourself, the map x, y, z A R E N ) E 7! . ⇡ S onto M ( I xz, yz, z complex T H the cone in such a way, that it is ⇡ for the cone: there is a simple z above produces the function 1 a 1 )doesthetrick! z numbers, even if some of 2 a 2 ...z x n a 2 n always + in local analytic y 2 − be found, z 2 on 3- 1.2. them happen to be real. could be a 37 dimensionalnot geometric sound object so embedded remarkable in to a 59-dimensional you, ambi- imagine that your the original singular variety polynomial map which takes the cylinder analytic functions, rather thanunderstand polynomial via functions. Fubini’s theorem.the integrability There of is certain also functions,coordinates. a since version integrability As of for monomialsof we (real coordinates, is will or easy the complex) see, function to looks this like has a monomial tremendous implications for computing variable shouldcause of naturally the fundamentalgeometry be theorem are of interpreted more algebra: straightforwardtheorem the in is as zeros the true of complex forthree-space, a case. both polynomial but real The in in and is one complex the essentially varieties, course be- but we the will basicsthemselves of focus singular! algebraic on complexan varieties. 11-dimensional Hironaka’s subvarietyent with space, hundreds and of its components, singular locus all could of be which unimaginably are complicated—perhaps Hironaka’s remarkable theorem says that such a resolution can 2K for space. Pulling this function back under the map invertible everywhere except at the vertex. “monomialized”—after a relatively simpleevery and analytic understandable analytic functionstrong change (in resolution, any or number embedded resolution) of is real equally or impressive. complex It states variables) that can be Returning to the example above, consider the function This cylinder is a In our example, we considered a real variety so we could draw a picture in every Analytic. variety, no matter how twisted, pinched or folded it may be. If this does The analytic interpretation of Hironaka’s theorem (also called small modifications resolution of singularities e want to allow W We want them all into the same class! ( Indeed, as you should check yourself, the map x, y, z A R E N ) E 7! . ⇡ S onto M ( I xz, yz, z complex T H the cone in such a way, that it is ⇡ for the cone: there is a simple z above produces the function 1 a 1 )doesthetrick! z numbers, even if some of 2 a 2 ...z x n a 2 n always + in local analytic y 2 − be found, z 2 on 3- From the cylinder to the cone: the black loop collapses into the singularity.
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