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作者：Tsimerman, Jacob
摘要：We give a proof of the Andre-Oort conjecture for A(g) - the moduli space of principally polarized abelian varieties. In particular, we show that a recently proven averaged version of the Colmez conjecture yields lower bounds for Galois orbits of CM points. The Andre-Oort conjecture then follows from previous work of Pila and the author.
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作者：Adiprasito, Karim; Huh, June; Katz, Eric
摘要：We prove the hard Lefschetz theorem and the Hodge-Riemann relations for a commutative ring associated to an arbitrary matroid M. We use the Hodge-Riemann relations to resolve a conjecture of Heron, Rota, and Welsh that postulates the log-concavity of the coefficients of the characteristic polynomial of M. We furthermore conclude that the f-vector of the independence complex of a matroid forms a log-concave sequence, proving a conjecture of Mason and Welsh for general matroids.
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作者：Andreatta, Fabrizio; Goren, Eyal Z.; Howard, Benjamin; Pera, Keerthi Madapusi
摘要：Let M be the Shimura variety associated with the group of spinor similitudes of a quadratic space over Q of signature (n, 2). We prove a conjecture of Bruinier-Kudla-Yang, relating the arithmetic intersection multiplicities of special divisors and big CM points on M to the central derivatives of certain L-functions. As an application of this result, we prove an averaged version of Colmez's conjecture on the Faltings heights of CM abelian varieties.
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作者：Yuan, Xinyi; Zhang, Shou-Wu
摘要：The Colmez conjecture is a formula expressing the Faltings height of an abelian variety with complex multiplication in terms of some linear combination of logarithmic derivatives of Artin L-functions. The aim of this paper to prove an averaged version of the conjecture, which was also proposed by Colmez.
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作者：Bresch, Didier; Jabin, Pierre-emmanuel
摘要：We prove global existence of appropriate weak solutions for the compressible Navier-Stokes equations for a more general stress tensor than those previously covered by P.-L.Lions and E. Feireisl's theory. More precisely we focus on more general pressure laws that are not thermodynamically stable; we are also able to handle some anisotropy in the viscous stress tensor. To give answers to these two longstanding problems, we revisit the classical compactness theory on the density by obtaining prec...
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作者：Evseev, Anton; Kleshchev, Alexander
摘要：We prove Turner's conjecture, which describes the blocks of the Hecke algebras of the symmetric groups up to derived equivalence as certain explicit Turner double algebras. Turner doubles are Schur-algebra-like 'local' objects, which replace wreath products of Brauer tree algebras in the context of the Broue abelian defect group conjecture for blocks of symmetric groups with non-abelian defect groups. The main tools used in the proof are generalized Schur algebras corresponding to wreath produ...
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作者：Lawson, Tyler
摘要：The dual Steenrod algebra has a canonical subalgebra isomorphic to the homology of the Brown-Peterson spectrum. We will construct a secondary operation in mod-2 homology and show that this canonical subalgebra is not closed under it. This allows us to conclude that the 2-primary Brown- Peterson spectrum does not admit the structure of an E-n-algebra for any n >= 12, answering a question of May in the negative.
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作者：Hillairet, Luc; Judge, Chris
摘要：We consider the Neumann Laplacian acting on square-integrable functions on a triangle in the hyperbolic plane that has one cusp. We show that the generic such triangle has no eigenvalues embedded in its continuous spectrum. To prove this result we study the behavior of the real-analytic eigenvalue branches of a degenerating family of triangles. In particular, we use a careful analysis of spectral projections near the crossings of these eigenvalue branches with the eigenvalue branches of a mode...
