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作者：Haskins, Mark; Kapouleas, Nikolaos
作者单位：Imperial College London; Brown University
摘要：For every odd natural number g = 2d + 1 we prove the existence of a countably infinite family of special Lagrangian cones in C-3 over a closed Riemann surface of genus g, using a geometric PDE gluing method.
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作者：Lazarsfeld, Robert; Lee, Kyungyong
作者单位：University of Michigan System; University of Michigan
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作者：Osin, Denis V.
作者单位：City University of New York (CUNY) System; City College of New York (CUNY)
摘要：In this paper a group theoretic version of Dehn surgery is studied. Starting with an arbitrary relatively hyperbolic group G we define a peripheral filling procedure, which produces quotients of G by imitating the effect of the Dehn filling of a complete finite volume hyperbolic 3-manifold M on the fundamental group pi(1)(M). The main result of the paper is an algebraic counterpart of Thurston's hyperbolic Dehn surgery theorem. We also show that peripheral subgroups of G 'almost' have the Cong...
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作者：Marian, Alina; Oprea, Dragos
作者单位：Yale University; Stanford University
摘要：We prove that the strange duality conjecture of Beauville-Donagi-Tu holds for all curves. We establish first a more extended level-rank duality, interesting in its own right, from which the standard level-rank duality follows by restriction.
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作者：Gubler, Walter
作者单位：Dortmund University of Technology
摘要：Generalizing the construction from tropical algebraic geometry, we associate to every ( irreducible d-dimensional) closed analytic subvariety of G(m)(n) m a tropical variety in R-n with respect to a complete non-archimedean place. By methods of analytic and formal geometry, we prove that the tropical variety is a totally concave locally finite union of d-dimensional polytopes. For an algebraic morphism f : X'. A to a totally degenerate abelian variety A, we give a bound for the dimension of f(...
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作者：Kassabov, Martin
作者单位：Cornell University
摘要：We study the representations of non- commutative universal lattices and use them to compute lower bounds of the tau- constant for the commutative universal lattices G(d),(k) = SLd( Z[ x(1),..., x(k)]), for d >= 3 with respect to several generating sets. As an application we show that the Cayley graphs of the finite groups SL3k( F-p) can be made expanders with a suitable choice of generators. This provides the first example of expander families of groups of Lie type, where the rank is not bound...
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作者：Muro, Fernando; Schwede, Stefan; Strickland, Neil
作者单位：University of Barcelona; University of Bonn; University of Sheffield
摘要：We exhibit examples of triangulated categories which are neither the stable category of a Frobenius category nor a full triangulated subcategory of the homotopy category of a stable model category. Even more drastically, our examples do not admit any non-trivial exact functors to or from these algebraic respectively topological triangulated categories.
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作者：Arakawa, Tomoyuki
作者单位：Nara Womens University
摘要：We study the representation theory of the W- algebra W-k((g) over bar) associated with a simple Lie algebra (g) over bar at level k. We show that the - reduction functor is exact and sends an irreducible module to zero or an irreducible module at any level k epsilon C. Moreover, we show that the character of each irreducible highest weight representation ofW(k)((g) over bar) is completely determined by that of the corresponding irreducible highest weight representation of affine Lie algebra g ...
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作者：Alexeev, Valery; Hacon, Christopher; Kawamata, Yujiro
作者单位：University System of Georgia; University of Georgia; Utah System of Higher Education; University of Utah; University of Tokyo
摘要：We prove that any sequence of 4-dimensional log flips that begins with a klt pair (X,D) such that -(K-X +D) is numerically equivalent to an effective divisor, terminates. This implies termination of flips that begin with a log Fano pair and termination of flips in a relative birational setting. We also prove termination of directed flips with big K-X +D. As a consequence, we prove existence of minimal models of 4-dimensional dlt pairs of general type, existence of 5-dimensional log flips, and ...
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作者：Kerr, Matt; Lewis, James D.
作者单位：University of Chicago; University of Alberta
