Christopher D. Hacon

Christopher D. Hacon
Name	Christopher D. Hacon
Birth date	1970
Birth place	Kingston upon Thames, England
Nationality	British
Fields	Algebraic geometry
Workplaces	University of Illinois Urbana–Champaign; University of Utah; University of California, San Diego; University of Cambridge; Imperial College London; Max Planck Institute for Mathematics
Alma mater	University of Cambridge; University of Utah
Doctoral advisor	Robert Lazarsfeld
Known for	Birational geometry; minimal model program; vanishing theorems
Awards	Clay Research Award; AMS Cole Prize; Royal Society Wolfson Research Merit Award; Shaw Prize

Christopher D. Hacon is a mathematician specializing in Algebraic geometry, particularly in birational geometry and the minimal model program. He has held faculty positions at several research universities and has produced influential results on the classification of higher-dimensional algebraic varieties, vanishing theorems, and pluricanonical systems. Hacon's work connects techniques from Complex geometry, Commutative algebra, and singularity theory and has been recognized by major prizes and fellowships.

Early life and education

Hacon was born in Kingston upon Thames and educated at institutions including St John's College, University of Cambridge and the University of Utah. His doctoral studies under Robert Lazarsfeld placed him in a lineage connected to Oscar Zariski, David Mumford, and Alexander Grothendieck through the development of modern algebraic geometry. During his graduate years he interacted with researchers at Harvard University, Princeton University, Massachusetts Institute of Technology, Stanford University, and University of California, Berkeley, attending seminars related to the Minimal model program and Mori theory.

Academic career and positions

Hacon has held appointments at the University of Utah, University of California, San Diego, Imperial College London, University of Cambridge, Max Planck Institute for Mathematics, and the University of Illinois Urbana–Champaign. He has collaborated with mathematicians at the Institute for Advanced Study, Clay Mathematics Institute, Mathematical Sciences Research Institute, Centre de Recerca Matemàtica, and MSRI programs. His visiting positions have included terms at Columbia University, Yale University, New York University, ETH Zurich, Universität Bonn, École Polytechnique, Princeton University, and University of Tokyo.

Research contributions and major results

Hacon's research advanced the classification of higher-dimensional varieties by proving boundedness and birationality results for pluricanonical maps; these connect to work of Shigefumi Mori, Yujiro Kawamata, V. V. Shokurov, and Miles Reid. He proved key cases of effectiveness in the Iitaka conjecture and contributed to the proof of existence of minimal models for varieties of log general type alongside collaborators such as James McKernan, Caucher Birkar, Paolo Cascini, and Vladimir V. Shokurov. His results use techniques from Multiplier ideal sheaf, Vanishing theorem, Kawamata–Viehweg vanishing, Kodaira vanishing, and Hodge theory and exploit connections to Birational geometry and Pluricanonical system. Hacon co-developed methods involving Generic vanishing theory, Seshadri constants, and Adjoint linear systems to control the birational geometry of varieties, influencing subsequent research by Christopher D. Hacon's collaborators and other researchers such as V. Alexeev, Tommaso de Fernex, Christopher Lazda, Burt Totaro, Mark Green, and Robert Lazarsfeld. His collective work intersects with topics investigated by Jean-Pierre Serre, André Weil, Henri Cartan, Alexander Grothendieck, and John Milnor in the broader development of algebraic and complex geometry.

Awards and honors

Hacon's contributions have been recognized by awards including the Clay Research Award, the American Mathematical Society Cole Prize in Algebra, the Royal Society Wolfson Research Merit Award, and the Shaw Prize in Mathematical Sciences. He has been elected a fellow of the American Mathematical Society and a fellow of the Royal Society. He has also received invitations to speak at major gatherings such as the International Congress of Mathematicians, the European Congress of Mathematics, and plenary or invited addresses at the Society for Industrial and Applied Mathematics and national mathematical societies.

Selected publications

- Hacon, C. D.; McKernan, J., "On the existence of minimal models for varieties of log general type", Journal articles and proceedings related to Annals of Mathematics and Inventiones Mathematicae. - Hacon, C. D.; Pardini, R., works on pluricanonical maps and irregular varieties appearing in journals associated with Transactions of the American Mathematical Society and Journal of Differential Geometry. - Hacon, C. D.; Xu, C., research on boundedness and complements in birational geometry published in venues connected to Duke University Press and leading mathematical societies. - Hacon, C. D.; McKernan, J.; Takayama, S., collaborative papers on effective base point freeness and vanishing theorems. These publications appeared in outlets tied to institutions such as American Mathematical Society, Springer-Verlag, Cambridge University Press, and Oxford University Press.

Teaching and mentorship

Hacon has supervised doctoral students and postdoctoral researchers who have gone on to positions at institutions such as Princeton University, Harvard University, University of California, Berkeley, Columbia University, Yale University, Stanford University, Massachusetts Institute of Technology, University of Michigan, University of Chicago, University of Oxford, University of Cambridge, Imperial College London, ETH Zurich, Universität Bonn, and Universidad Complutense de Madrid. He has taught graduate courses on Birational geometry, Complex algebraic geometry, and Singularity theory at departments including Department of Mathematics, University of Utah, Department of Mathematics, University of California, San Diego, and Department of Mathematics, University of Illinois Urbana–Champaign.

Outreach and professional service

Hacon has participated in editorial work for journals associated with the American Mathematical Society, European Mathematical Society, and leading publishers. He has served on program committees and organizing committees for conferences at venues such as the Institute for Advanced Study, Mathematical Sciences Research Institute, International Congress of Mathematicians, European Mathematical Society Congress, Clay Mathematics Institute summer schools, and workshops at the Max Planck Institute for Mathematics. He has engaged with funding and advisory bodies including panels at the Simons Foundation, National Science Foundation, Royal Society, and Engineering and Physical Sciences Research Council.

Category:British mathematicians Category:Algebraic geometers