From: Greg Kuperberg Subject: This week in the xxx mathematics archive Date: Fri, 20 Nov 1998 14:44:53 -0800 (PST) I am forwarding "This week in the xxx mathematics archive" to this list because it has a discussion of how widely read the archive is. Greg ----- Subject: This week in the xxx mathematics archive (16 Nov - 20 Nov) Here are this week's titles in the xxx mathematics archive, available at: http://front.math.ucdavis.edu/ Instructions for contributing articles are available at: http://front.math.ucdavis.edu/submissions.html Last week I was so pleased that the claimed proof of the sphere-packing conjecture was posted that I completely missed another major contribution to the archive around the same time: "Trace formula in noncommutative geometry and the zeros of the Riemann zeta function", by Alain Connes (math.NT/9811068). This article describes an interpreation of the Riemann conjecture in terms of quantum chaos and operator theory. Connes doesn't claim to have proved the conjecture, but he apparently wants to, and he may well have changed the terms of the question. Another groovy article that appeared this week is "Isoperimetric and isodiametric functions of groups", by Mark Sapir, Jean-Camille Birget, and Eliyahu Rips (math.GR/9811105). This paper follows the generally philosophy that a derivation in a finitely presented group which consists of repeated applications of the relations between the generators can simulate a Turing machine. This is a fundamental relation between the structure of infinite groups and complexity theory in computer science. This article discusses the Dehn function (or isoperimetric functions) of an infinite group, i.e., the largest number of relation substitutions that you might need to reduce a word of length n to the trivial word. In particular, the article says, for a judiciously chosen group you might need Theta(n^alpha) relators, where alpha>4 is any real number whose d'th digit can be computed in time O(2^(2^(K*d))) for some K. (The notation Theta(f(n)) denotes any function g(n) such that g(n) = O(f(n)) and f(n) = O(g(n)).) For example there is a finitely presented group whose isoperimetric function is C*n^(sqrt(7+pi+e+3*(Euler's constant))) On the other hand alpha can't be just any number; the d'th digit must be computable in time O(2^(2^(2^(K*d)))). Also last week the xxx staff graciously allowed me to analyze a week of web logs from xxx.lanl.gov. I gathered some statistics on the number of retrievals of the roughly 6550 mathematics papers in the archive from this specific site. Here are some of the results in round figures: o There were about 12,000 paper downloads, or more than 1.8 per paper per week. o There were about 5,000 distinct host-paper pairs, or more than .75 per paper per week. o Over 1300, or 20%, of the papers were retrieved at least once, over 500 by at least two hosts. o Every single one of the 93 papers then visible in November was retrieved at least once. All but eight were retrieved by 5 or more distinct hosts, and all eight of these were more than a week old. Two were retrieved by more than 150 hosts, ten by more than 50. o As a rule of thumb, about 1/3 of the hits at xxx.lanl.gov are article downloads. (This does not count viewing the abstracts.) Finally, all of this data is only for the Los Alamos site and not for any of the 14 other mirror sites of the xxx system. Judging by traffic at the Front, I might expect that the global rates are about twice those for xxx.lanl.gov alone. (Note that the Front directs paper retrievals to all of the mirror sites, and is responsible for maybe 1/5 or 1/4 of the math downloads.) The bottom line is that if you contribute an article to the archive, almost invariably a number of mathematicians will read it. "This week in the xxx mathematics archive" may be freely redistributed with attribution and without modification. Titles in the xxx mathematics archive (16 Nov - 20 Nov) ------------------------------------------------------- AG: Algebraic Geometry ---------------------- math.AG/9811111 Mina Teicher The Fundamental Group of a CP^2 Complement of a Branch Curve as an Extension of a Solvable Group by a Symmetric Group math.AG/9811109 Reinhold Huebl, Amnon Yekutieli Adelic Chern Forms and Applications math.AG/9811101 Tom Bridgeland, Antony Maciocia Fourier-Mukai transforms for quotient varieties math.AG/9811099 Holger P. Kley On the existence of curves in K-trivial threefolds math.AG/9811092 Vladimir Baranovsky Moduli of Sheaves on Surfaces and Action of the Oscillator Algebra math.AG/9811091 Miriam Abdon, Fernando Torres On maximal curves in characteristic two AT: Algebraic Topology ---------------------- math.AT/9811102 Ralph Grieder Geometric Representation Theory and G-Signature CO: Combinatorics ----------------- math.CO/9811117 Aaron Robertson New Lower Bounds for Some Multicolored Ramsey Numbers math.CO/9811108 Doron Zeilberger Proof of a Conjecture of Chan, Robbins, and Yuen math.CO/9811095 Jan Snellman On some partial orders associated to generic initial ideals math.CO/9811086 Jozef H. Przytycki, Adam S. Sikora Polygon dissections and Euler, Fuss, Kirkman and Cayley numbers CV: Complex Variables --------------------- math.CV/9811104 M. S. Baouendi, P. Ebenfelt, Linda Preiss Rothschild Rational dependence of smooth and analytic CR mappings on their jets DG: Differential Geometry ------------------------- math.DG/9811116 Wojciech Wieczorek Immersed spheres and finite type of Donaldson invariants math.DG/9811113 Michael Farber Lusternik-Schnirelman theory for closed 1-forms math.DG/9811098 Charles P. Boyer, Krzysztof Galicki On Sasakian-Einstein Geometry math.DG/9811097 Walter Seaman Higgs Bundles and Holomorphic Forms math.DG/9811089 Vicente Mu\~noz Basic classes for four-manifolds not of simple type math.DG/9811087 Peter Ozsvath, Zoltan Szabo The Symplectic Thom Conjecture DS: Dynamical Systems --------------------- math.DS/9811110 Alexander Fel'shtyn, Hector S\'anchez-Morgado Reidemeister torsion and Integrable Hamiltonian systems GR: Group Theory ---------------- math.GR/9811107 A.Yu. Olshanskii, M. Sapir Length and Area Functions on Groups and Quasi-Isometric Higman Embeddings math.GR/9811106 J.-C.Birget, A.Yu. Olshanskii, E. Rips, M.Sapir Isoperimetric Functions of Groups and Computational Complexity of the Word Problem math.GR/9811105 Mark Sapir, Jean-Camille Birget, Eliyahu Rips Isoperimetric and isodiametric functions of groups GT: Geometric Topology ---------------------- math.GT/9811114 Ian Agol, Darren D. Long, Alan W. Reid The Bianchi groups are subgroup separable on geometrically finite subgroups math.GT/9811093 Terry Fuller Lefschetz fibrations and 3-fold branched covering spaces, II MG: Metric Geometry ------------------- math.MG/9811119 Greg Kuperberg The bottleneck conjecture MP: Mathematical Physics ------------------------ math-ph/9811019 P. Fratzl, O. Penrose, J. L. Lebowitz Modelling of Phase Separation in Alloys with Coherent Elastic Misfit math-ph/9811018 I. V. Krasovsky Asymptotic distribution of zeros of polynomials satisfying difference equations math-ph/9811017 R. Coquereaux, A. O. Garcia, R. Trinchero Geometry of the reduced quantum plane cond-mat/9809145 J. L. Lebowitz, A. Mazel, E. Presutti Liquid-Vapor Phase Transitions for Systems with Finite Range Interactions math-ph/9811016 Bernhard Bodmann, Hajo Leschke, Simone Warzel A rigorous path integral for quantum spin using flat-space Wiener regularization math-ph/9811015 V. Aldaya, J. Guerrero, G. Marmo Higher-Order Quantization on a Lie Group hep-th/9811149 D. Anselmi Quantum Conformal Algebras and Closed Conformal Field Theory hep-th/9811041 A. Gonzalez-Arroyo On Nahm's transformation with twisted boundary conditions math-ph/9811014 Piotr G. Grinevich, Roman G. Novikov, University Nantes, France) Discrete spectrum for n-cell potentials math-ph/9811013 Y. S. Kim Separable Four-dimensional Harmonic Oscillators and Representations of the Poincar\'e Group hep-th/9811108 Jean-Loup Gervais, Mikhail Saveliev Progress in classically solving ten dimensional supersymmetric reduced Yang-Mills theories cond-mat/9712138 Elliott H. Lieb, Jakob Yngvason Ground State Energy of the Low Density Bose Gas quant-ph/9811025 Jens Bolte, Stefan Keppeler A semiclassical approach to the Dirac equation math-ph/9811012 D.J. Rowe, B.C. Sanders, H. de Guise Representations of the Weyl group and Wigner functions for SU(3) math-ph/9811011 E.N. Bukina, V.M. Dubovik The gauge freedoms of enlarged Helmholtz theorem and the Neumann --- Debye potentials; their manifestation in the multipole expansion of conserved current math-ph/9811010 Francisco J. Herranz, Mariano Santander The family of quaternionic quasi-unitary Lie algebras and their central extensions math-ph/9811009 A. R. Its, N. A. Slavnov On the Riemann-Hilbert approach to the asymptotic analysis of the correlation functions of the Quantum Nonlinear Schrodinger equation. Non-free fermionic case math-ph/9811004 C. Bartocci, U. Bruzzo, G. Sanguinetti Categorial mirror symmetry for K3 surfaces hep-th/9811118 Hanno Hammer Tree structures, Entropy, and Action Principles for Neighbourhood Topologies NT: Number Theory ----------------- math.NT/9811112 Greg Martin Denser Egyptian Fractions math.NT/9811096 Lubomir Alexandrov On the nonasymptotic prime number distribution math.NT/9811088 J. Maurice Rojas On the Complexity of Diophantine Geometry in Low Dimensions OA: Operator Algebras --------------------- math.OA/9811094 Ruy Exel, Marcelo Laca The K-theory of Cuntz-Krieger algebras for infinite matrices PR: Probability Theory ---------------------- math.PR/9811103 Vladimir Belitsky, Pablo A. Ferrari Invariant Measures and Convergence for Cellular Automaton 184 and Related Processes QA: Quantum Algebra ------------------- math.QA/9811115 A. I. Molev Yangians and transvector algebras hep-th/9811040 A.V.Bratchikov {Coset conformal field theories with abelian isotropy groups.} hep-th/9811136 Pavol Severa Duality and TFT: A suggestion based on d=2+1 RT: Representation Theory ------------------------- math.RT/9811100 Sergey Fomin, Andrei Zelevinsky Totally nonnegative and oscillatory elements in semisimple groups math.RT/9811090 Manabu Yamaguchi A duality of the twisted group algebra of the symmetric group and a Lie superalgebra SP: Spectral Theory ------------------- math.SP/9811118 Mark S. Joshi, Antonio Sa Barreto Inverse Scattering on Asymptotically Hyperbolic Manifolds