From: Greg Kuperberg Subject: This week Date: Fri, 17 Jul 1998 11:10:48 -0700 (PDT) Once again my regular announcement to sci.math.research may be of some interest to readers of toplist. And here are some extra comments: Given the way that Mark is announcing new papers here, some people may not see the scale of xxx or the promising (if slow) development of the AT category. You may want to subscribe independently to math.AT by sending this one-line message to math@xxx.lanl.gov: -------------- To: math@xxx.lanl.gov Subject: subscribe add AT -------------- Also, I should mention that xxx has very good version control. xxx has whipped physicists in some already competitive areas into a frenzy so that they write papers as quickly as they can and post them immediately. These people only worry about revisions much later or not at all. On the other hand, it may be wiser to use the archive more conservatively (as most mathematicians might come to use it), since it is better not to repeatedly distract the vast xxx readership with incremental revisions of the same thing. Greg Subject: This week in the xxx mathematics archive (13 Jul - 17 Jul) Here are this week's titles in the xxx mathematics archive. You are invited to browse the corresponding e-prints at the Front for the xxx Mathematics Archive: http://front.math.ucdavis.edu/ and to contribute papers following the instructions at: http://front.math.ucdavis.edu/submissions.html This week I'd like to highlight a paper by Alexander Givental, "The mirror formula for quintic threefolds", math.AG/9807070. Givental has made some major progress on mirror symmetry, a set of hard and deep conjectures in algebraic geometry that are motivated by string theory. Among other things, mirror symmetry relates the number of rational curves in a Calabi-Yau 3-fold to the solutions of certain PDEs on a hypothetical dual 3-fold called a mirror pair. Here a Calabi-Yau 3-fold is a complex manifold (with three complex dimensions) that satisfies a special condition analogous to but more exotic than orientability for ordinary real manifolds. A rational curve is a Riemann sphere (which is called a curve because it has one complex dimension) embedded in a complex analytic way. In string theory such a curve (or some other Riemann surface) -- is swept out by a string as it evolves in spacetime, and the Calabi-Yau 3-fold is the topology and geometry of six hypothetical dimensions in which the universe is very small, leaving the four other macroscopic dimensions that we directly experience. My ulterior motive for mentioning Givental's paper is not the math (which certainly does not need me to advertise it), but the bibliography. Of the 21 references, 9 are explicitly listed as papers in the xxx mathematics archive or hep-th, one of the xxx physics archives, and 7 more are in either math or hep-th, leaving only 5 that are not available via the new technology that is xxx. It's bibliographies like this that give a glimpse of the real promise of xxx. Of course review services and journals and award committees and all that are still important; I certainly believe in evaluating mathematics for the sake of posterity. But while these other institutions are still thinking about papers that have been submitted to them, most mathematicians can decide for themselves which recent papers in their area are worth reading and worth citing. xxx closes the loop so that a paper can go from one mathematician's fingertips to another's bibliography (with a citation that you can actually use to get the paper) in a few weeks or even days. For the record here are the 16 xxx e-prints in Givental's bibliography: hep-th/9110048 alg-geom/9701016 alg-geom/9712011 alg-geom/9710022 math.AG/9803053 alg-geom/9407005 alg-geom/9506023 alg-geom/9607001 hep-th/9412236 math.AG/9803026 alg-geom/9712008 math.AG/9806133 math.AG/9805097 hep-th/9405035 alg-geom/9603021 alg-geom/9602007 All of these except for the first one (which was contributed when xxx was all hep-th and no math) can be accessed directly by prepending http://front.math.ucdavis.edu/; for example http://front.math.ucdavis.edu/math.AG/9805097 and all of them are available at xxx directly in a similar fashion: http://xxx.lanl.gov/abs/hep-th/9110048 The same goes for the papers listed below. Titles in the xxx mathematics archive (13 Jul - 17 Jul) ------------------------------------------------------- AG: Algebraic Geometry ---------------------- math.AG/9807082 Marco Andreatta, Gianluca Occhetta Ample vector bundles with sections vanishing on special varieties math.AG/9807081 Miles Reid Eulogy for Andrew Wiles math.AG/9807070 Alexander B. Givental The mirror formula for quintic threefolds math.AG/9807069 A. A'Campo-Neuen On Generalized $h$--Vectors of Rational Polytopes with a Symmetry of Prime Order math.AG/9807066 Joaquim Roe On the existence of plane curves with prescribed multiple points math.AG/9807061 Peter Magyar, Jerzy Weyman, Andrei Zelevinsky Symplectic multiple flag varieties of finite type math.AG/9807060 St\'ephane Druel Contact structures on algebraic 5-dimensional manifolds AP: Analysis of PDEs -------------------- math.AP/9807078 Steve Shkoller Geometry and curvature of diffeomorphism groups with $H^1$ metric and mean hydrodynamics AT: Algebraic Topology ---------------------- math.AT/9807071 J. Daniel Christensen Ideals in Triangulated Categories: Phantoms, Ghosts and Skeleta math.AT/9807053 M. A. Guest, A. Kozlowski, K. Yamaguchi Spaces of polynomials with roots of bounded multiplicity CA: Classical Analysis ---------------------- math.CA/9807089 Harri Ojanen Orthonormal Compactly Supported Wavelets with Optimal Sobolev Regularity math.CA/9807085 Harri Ojanen Weighted Norm Estimates and Representation Formulas for Rough Singular Integrals CO: Combinatorics ----------------- math.CO/9807079 Sergey Fomin, Andrei Zelevinsky Recognizing Schubert cells math.CO/9807074 Doron Zeilberger A Heterosexual Mehler Formula for the Straight Hermite Polynomials (A La Foata) math.CO/9807068 Christian Krattenthaler Another involution principle-free bijective proof of Stanley's hook-content formula DG: Differential Geometry ------------------------- math.DG/9807087 Maks A. Akivis, Vladislav V. Goldberg On conformal invariance of isotropic geodesics math.DG/9807086 Jerrold E. Marsden, Steve Shkoller Multisymplectic geometry, covariant Hamiltonians, and water waves math.DG/9807083 B.G.Konopelchenko, U.Pinkall Projective generalizations of Lelieuvre's formula math.DG/9807080 Jerrold E. Marsden, George W. Patrick, Steve Shkoller Multisymplectic geometry, variational integrators, and nonlinear PDEs math.DG/9807073 Stefan Berceanu Coherent states, line bundles and divisors math.DG/9807072 Stefan Berceanu Coherent states and geometry math.DG/9807067 A.Vdovina, E.Selivanova Regular minimal nets on surfaces of constant negative curvature math.DG/9807065 Askar Dzhumadil'daev Cohomologies and deformations of right-symmetric algebras math.DG/9807055 Matthew Gursky, Claude LeBrun On Einstein Manifolds of Positive Sectional Curvature math.DG/9807050 Jarolim Bures, Vladimir Soucek Eigenvalues of conformally invariant operators on spheres FA: Functional Analysis ----------------------- math.FA/9807063 Anatoly N. Kochubei Fractional Differentiation Operator over an Infinite Extension of a Local Field math.FA/9807062 Anatoly N. Kochubei Analysis and Probability over Infinite Extensions of a Local Field GT: Geometric Topology ---------------------- math.GT/9807088 John D. McCarthy On the asphericity of a symplectic M3 x S1 math.GT/9807076 A. Stoimenow Some minimal degree Vassiliev invariants not realizable by the Homfly and Kauffman polynomial MP: Mathematical Physics ------------------------ math-ph/9807017 L. A. Ferreira, J. F. Gomes, A. V. Razumov, M. V. Saveliev, A. H . Zimerman Riccati-type equations, generalised WZNW equations, and multidimensional Toda systems math-ph/9807016 R. Coquereaux, G.E. Schieber Action of a finite quantum group on the algebra of complex NxN matrices gr-qc/9806110 Yakov Itin Gravity on a parallelizable manifold. Exact solutions math-ph/9807015 M. Robert Showalter ........ University of Wisconsin, Madison A Modified Equation for Neural Conductance and Resonance hep-th/9807042 J. Gegenberg, G. Kunstatter The Geometrodynamics of Sine-Gordon Solitons math-ph/9807014 G.Giachetta, L.Mangiarotti, G.Sardanashvily Nonholonomic Constraints in Time-Dependent Mechanics math-ph/9807013 Jesus San-Martin, Oscar Sotolongo-Costa Chaos and Non-Archimedean metric in the Bernoulli map math-ph/9807012 R. Coquereaux, A. O. Garcia, R. Trinchero Differential calculus and connections on a quantum plane at a cubic root of unity chao-dyn/9807004 A. Soffer, M.I. Weinstein Nonautonomous Hamiltonians chao-dyn/9807003 A. Soffer, M.I. Weinstein Resonances, Radiation Damping and Instability in Hamiltonian Nonlinear Wave Equations quant-ph/9807025 T. V. Kuliy, V. M. Tkachuk Quasi-Exactly Solvable Potentials with Three Known Eigenstates math-ph/9807008 M.X Shao, Z.Y Zhu Classical Geometric Interaction- picture-like Description NT: Number Theory ----------------- math.NT/9807075 Anatoly N. Kochubei $F_q$-Linear Calculus over Function Fields OA: Operator Algebras --------------------- math.OA/9807084 Marc A. Rieffel Metrics on states from actions of compact groups math.OA/9807054 C. Pop Representable bimodules over C*-algebras QA: Quantum Algebra ------------------- math.QA/9807077 Haisheng Li Some finiteness properties of regular vertex operator algebras math.QA/9807059 Jack Morava Schur Q-functions and a Kontsevich-Witten genus math.QA/9807058 Jack Morava Quantum generalized cohomology math.QA/9807052 Tomasz Brzezinski, Shahn Majid Line bundles on quantum spheres math.QA/9807051 N. Aizawa Drinfeld twist for two-parametric deformation of gl(2) and sl(1/2) hep-th/9712243 A.V.Bratchikov $g/u(1)^d$ parafermions from constrained WZNW theories hep-th/9807074 P. Di Francesco New Integrable Lattice Models From Fuss-Catalan Algebras RT: Representation Theory ------------------------- math.RT/9807057 Peter A. Linnell Von Neumann algebras and linear independence of translates SP: Spectral Theory ------------------- math.SP/9807064 B. Helffer, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, M. P. Ow en Nodal sets for the groundstate of the Schroedinger operator with zero magnetic field in a non simply connected domain math.SP/9807056 Azamat M. Akhtyamov On a new inverse spectral problem