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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：Geck, Meinolf
作者单位：University of Aberdeen
摘要：Let H be the one-parameter Hecke algebra associated to a finite Weyl group W, defined over a ground ring in which bad primes for W are invertible. Using deep properties of the Kazhdan-Lusztig basis of H and Lusztig's a-function, we show that H has a natural cellular structure in the sense of Graham and Lehrer. Thus, we obtain a general theory of Specht modules for Hecke algebras of finite type. Previously, a general cellular structure was only known to exist in types A(n) and B-n .
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作者：Kiselev, A.; Nazarov, F.; Volberg, A.
作者单位：University of Wisconsin System; University of Wisconsin Madison; Michigan State University
摘要：We give an elementary proof of the global well-posedness for the critical 2D dissipative quasi-geostrophic equation. The argument is based on a non-local maximum principle involving appropriate moduli of continuity.
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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：Lee, Yongnam; Park, Jongil
作者单位：Sogang University; Seoul National University (SNU)
摘要：In this paper we construct a simply connected, minimal, complex surface of general type with p(g) = 0 and K-2 = 2 using a rational blow-down surgery and a Q-Gorenstein smoothing theory.
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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：Mustata, Andrei; Mustata, Magdalena Anca
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：We describe the Chow ring with rational coefficients of (M) over bar (0,1)(P-n, d) as the subring of invariants of a ring B*((M) over bar (0,1)(P-n, d); Q), relative to the action of the group of symmetries S-d. We compute B*((M) over bar (0,1)(P-n, d); Q) by following a sequence of intermediate spaces for (M) over bar (0,1)(P-n, d).
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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...
