FAKE PROJECTIVE SPACES AND FAKE TORI OLIVIER DEBARRE Abstract. Hirzebruch and Kodaira proved in 1957 that when n is odd, any compact K¨ ahler manifold X which is homeomorphic to Pn is isomorphic to Pn . This holds for a

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• Algebra
• Abstract algebra
• Cohomology theories
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• Homological algebra
• Birational geometry
• Algebraic surfaces
• Cohomology
• Projective variety
• Hodge theory
• tale cohomology
• Kodaira dimension

Universit´e Paris Diderot U.F.R. de Math´ematique hh 8 mars 2011

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Proc. Int. Cong. of Math. – 2018 Rio de Janeiro, Vol–1172) SPATIAL REFINEMENTS AND KHOVANOV HOMOLOGY Robert Lipshitz and Sucharit Sarkar

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• Abstract algebra
• Algebra
• Mathematics
• Homological algebra
• Homology theory
• Functors
• Algebraic topology
• Homotopy theory
• Homology
• Natural transformation
• Singular homology
• Khovanov homology

. (0000) “Polynomial functors from algebras over a set-operad and non-linear Mackey functors,” International Mathematics Research Notices, Vol. 0000, Article ID rnn000, 54 pages. doi:imrn/rnn000 Polynomial fu

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• Algebra
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• Category theory
• Functors
• Adjoint functors
• Equivalence
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• Sheaf
• Operad theory
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• Isomorphism of categories
• Additive category

PERIODS AND MODULI OLIVIER DEBARRE Abstract. This text is an introduction, without proofs and by means of many examples, to some elementary aspects of the theory of period maps, period domains, and their relationship wit

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• Algebraic geometry
• Algebra
• Abstract algebra
• Algebraic curves
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• Moduli theory
• Hodge theory
• Projective variety
• Abelian variety
• Hodge structure
• Divisor
• Moduli space

Proc. Int. Cong. of Math. – 2018 Rio de Janeiro, Vol–1316) REPRESENTATIONS OF GALOIS ALGEBRAS Vyacheslav Futorny

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• Algebra
• Abstract algebra
• Mathematics
• Representation theory of Lie algebras
• Quantum group
• Representation theory
• Valuation ring
• Lie algebra
• Universal enveloping algebra
• Quiver
• Approximately finite-dimensional C*-algebra

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• Abstract algebra
• Algebra
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• Complex manifolds
• Algebraic geometry
• Manifold
• Sheaf
• Differential geometry
• Several complex variables
• Algebraic geometry and analytic geometry

¨ UNEXPECTED ISOMORPHISMS BETWEEN HYPERKAHLER FOURFOLDS OLIVIER DEBARRE Abstract. Using Verbitsky’s Torelli theorem, we show the existence of various isomorphisms between certain hyperk¨

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• Topology
• Algebraic surfaces
• Geometry
• Algebraic geometry
• K3 surface
• Birational geometry
• Divisor
• Quartic surface
• Von Neumann algebra
• Hodge structure

Proc. Int. Cong. of Math. – 2018 Rio de Janeiro, Vol–520) PERIODS, CYCLES, AND L-FUNCTIONS: A RELATIVE TRACE FORMULA APPROACH Wei Zhang (张伟)

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• Abstract algebra
• Algebra
• Mathematics
• Automorphic forms
• Algebraic geometry
• Langlands program
• Representation theory
• Algebraic number theory
• Wei Zhang
• Artin L-function
• Modular form
• Waldspurger formula

FUNCTOR CATEGORIES AND STABLE HOMOLOGY VIA FUNCTOR HOMOLOGY CHRISTINE VESPA Abstract. This text is a preliminary version of material used for a course at the University of Tokyo, January 18-22, 2016. These lectures conce

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• Algebra
• Abstract algebra
• Mathematics
• Homological algebra
• Functors
• Category theory
• Additive categories
• Equivalence
• Exact functor
• Natural transformation
• Adjoint functors
• Hochschild homology