Boundedness of varieties of log general type
Abstract: We survey recent results on the boundedness of the moduli functor of stable pairs. The post Boundedness of varieties of log general type appeared first on Clay Mathematics Institute.
View ArticleEnumerative geometry and geometric representation theory
Abstract: This is an introduction to: (1) the enumerative geometry of rational curves in equivariant symplectic resolutions, and (2) its relation to the structures of geometric representation theory....
View ArticleA calculus for the moduli space of curves
Abstract: I survey the recent advances in the study of tautological classes on the moduli spaces of curves. After discussing the Faber-Zagier relations on the moduli spaces of nonsingular curves and...
View ArticleThe Cremona group
Abstract: We survey a few results concerning groups of binational transformations. The emphasis is on the Cremona group in two variables and methods coming from geometric group theory. The post The...
View ArticleSome fundamental groups in arithmetic geometry
Abstract: We report on Deligne’s finiteness theorem for l-adic representations on smooth varieties defined over a finite field, on its crystalline version, and on how the geometric étale fundamental...
View ArticlePatterns in the primes
The post Patterns in the primes appeared first on Clay Mathematics Institute.
View ArticleExpanders — how to find them, and what to find in them
Abstract: A graph G = (V,E) is called an expander if every vertex subset U of size up to |V|/2 has an external neighborhood whose size is comparable to |U|. Expanders have been a subject of intensive...
View ArticleLight rays, singularities, and all that
Professor Edward Witten gave the Clay Lecture at the NZMRI Summer School Mathematical Aspects of General Relativity Abstract: This article is an introduction to causal properties of General...
View ArticleCodes and designs in Johnson graphs with high symmetry
Abstract: The Johnson graph J(v,k) has, as vertices, all k-subsets of a v-set V, with two k-subsets adjacent if and only if they share k − 1 common elements of V. Subsets of vertices of J(v,k) can be...
View ArticleHodge Theory and Moduli
Phillip Griffiths delivered the Clay Lecture at the INI workshop K-theory, Algebraic Cycles and Motivic Homotopy Theory. The post Hodge Theory and Moduli appeared first on Clay Mathematics Institute.
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