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