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21<title>Open Problems In Mathematics And Physics - Home</title></head><body class=""><div id="body"><div id="doc" class=""><div xmlns="" id="hd"><style> 22 blockquote {margin-right:0;padding-right:0} 23 </style><div id="hContent"><div id="headerContent" class="editorWrap"><div id="headerZoneElement" class="editable rte flexContent" rel="itemGuid.sit.hc.001"><h1>Open Problems In Mathematics And Physics</h1></div></div></div><div id="hMisc"><div class="contactInfoContainer" style="width:auto;height:auto"><p class="vcard"></p></div></div></div><div id="wrapper" class="navpos_north"><div xmlns="" id="navigation" class="tglsty_arrow sub_dynamic"><ul id="mainNav" role="navigation"><li class="mainNav active" style="z-index:1"><a href="/home">Home</a></li> </ul></div><div xmlns="" id="bd"><div id="pageName"><div id="pageNameContent" class="editorWrap"><div id="pageNameZoneContent" class="editable rte flexContent" rel="itemGuid.homePage.001"><h2>Home</h2></div></div></div><div id="zWrap"><div id="zA"><div id="zA-widget-layout-wrap" class="widget-layout-wrap " rel=""><div class="modWrap"><p>Â </p><p>Â </p><table border="0" width="979" cellPadding="0" cellSpacing="0"><tbody><tr vAlign="top"><td rowSpan="4" colSpan="55" width="419"><strong><font size="+3">OPEN QUESTIONS</font></strong></td><td height="1" colSpan="7">Â </td><td height="1" colSpan="29">Â </td></tr><tr vAlign="top"><td height="20" colSpan="4">Â </td><td height="20" colSpan="7">Â </td><td height="20" colSpan="12">Â </td><td colSpan="15" width="161">Â </td><td height="20" colSpan="2">Â </td></tr><tr vAlign="top"><td height="23" colSpan="4">Â </td><td height="23" colSpan="7">Â </td><td height="23" colSpan="29">Â </td></tr><tr vAlign="top"><td height="1" colSpan="4">Â </td><td height="1" colSpan="89">Â </td></tr><tr vAlign="top"><td height="44" colSpan="148">Â </td></tr><tr vAlign="top"><td height="38" colSpan="5">Â </td><td colSpan="32" width="240"><strong><font size="+2">GENERAL</font></strong></td><td height="38" colSpan="111">Â </td></tr><tr vAlign="top"><td height="12" colSpan="148">Â </td></tr><tr vAlign="top"><td height="22" colSpan="17">Â </td><td colSpan="27" width="240"><a href="http://en.wikipedia.org/wiki/List_of_unsolved_problems">Lists of unsolved problems</a></td><td height="22" colSpan="104">Â </td></tr><tr vAlign="top"><td height="16" colSpan="148">Â </td></tr><tr vAlign="top"><td height="22" colSpan="16">Â </td><td colSpan="27" width="240"><a href="http://www.sciencemag.org/sciext/125th/">Science magazine 125 big questions</a></td><td height="22" colSpan="105">Â </td></tr><tr vAlign="top"><td height="20" colSpan="148">Â </td></tr><tr vAlign="top"><td height="36" colSpan="6">Â </td><td colSpan="93" width="577"><font size="+2"><strong>MATHEMATICS (PHYSICIST'S PERSPECTIVE)</strong></font></td><td height="36" colSpan="49">Â </td></tr><tr vAlign="top"><td height="10" colSpan="148">Â </td></tr><tr vAlign="top"><td height="4" colSpan="69">Â </td><td rowSpan="9" colSpan="77" width="484"><p>Â </p><p><a href="http://duch.mimuw.edu.pl/~sjack/atiyah.ps">Sir Michael Atiyah's Fields Lecture (.ps)</a><br /><br />Areas long to learn: <a href="http://www.york.ac.uk/depts/maths/physics/qg.html">quantum groups</a>, <a href="http://www.ams.org/new-in-math/mathnews/motivic.html">motivic cohomology</a>, local and micro local analysis of large finite groups<br /><br />Exotic areas: <a href="http://www.ams.org/new-in-math/cover/gowers.html">infinite Banach spaces</a>, large and inaccessible cardinals<br /><br /><strong>Some recent links between mathematics and physics</strong><a href="http://www.cse.iitk.ac.in/primality.pdf"><br /><br /></a><a href="http://www.maths.ex.ac.uk/~mwatkins/zeta/physics.htm">Number theory and physics<br /></a><a href="http://www.ams.org/new-in-math/cover/prime-chaos.html">Conjectured links between the Riemann zeta function and chaotic quantum-mechanical systems<br /></a><a href="http://www.math.columbia.edu/~woit/"><br />Deep and relatively recent ideas in mathematics and physics</a><a href="http://www.ams.org/new-in-math/cover/prime-chaos.html"><br /></a>Standard model and mathematics:<br />Gauge field or connection<br />Dirac operators or fundamental classes in K-theory (<a href="http://www.abelprisen.no/nedlastning/2004/popular_english_2004.pdf">Atiyah-Singer index theorem</a>)<br />String theory and mathematics:<br />Mirror symmetry<br />Conformal field theory<br /><br /><a href="http://math.ucr.edu/home/baez/Octonions/octonions.html">Mathematics behind supersymmetry</a><br />
23<a href="http://www.newton.cam.ac.uk/webseminars/mondays/2000/10/16/dijkgraaf/">Mathematics of M-Theory<br /></a><a href="http://en.wikipedia.org/w/index.php?title=Chern-Simons_theory&redirect=no">Chern-Simons theory<br /></a><a href="http://math.ucr.edu/home/baez/highergauge/"><br />Higher gauge theory<br /><br /></a><a href="http://www2.math.northwestern.edu/langlands/index_moreinfo.htm">Geometric Langlands Program</a></p></td><td height="4" colSpan="2"> </td></tr><tr vAlign="top"><td height="38" colSpan="18"> </td><td colSpan="40" width="347"><strong>Unified theory: </strong><a href="http://mathworld.wolfram.com/LanglandsProgram.html">Langlands Program</a>, <a href="http://insti.physics.sunysb.edu/itp/conf/simonswork3/talks/Witten.pdf">Witten on Langlands</a>,<br /><a href="http://en.wikipedia.org/wiki/Motive_(algebraic_geometry)">Theory of "motives"</a></td><td height="38" colSpan="11"> </td><td height="38" colSpan="2"> </td></tr><tr vAlign="top"><td height="8" colSpan="69"> </td><td height="8" colSpan="2"> </td></tr><tr vAlign="top"><td height="402" colSpan="19"> </td><td colSpan="35" width="305"><a href="http://en.wikipedia.org/wiki/Unsolved_problems_in_mathematics">Lists of unsolved problems</a><br /><br /><a href="http://www.maa.org/mathland/mathtrek_12_8.html">ABC Conjecture</a><br /><br /><a href="http://www.math.harvard.edu/~mazur/preprints/Lang.mem.pdf">Lang Conjecture</a><u><br /></u><a href="http://www.claymath.org/millennium/"><br /></a><a href="http://www.claymath.org/millennium/">Long standing open problems </a><a href="http://www.claymath.org/millennium/">PRICE</a><a href="http://www.claymath.org/prize_problems/index.htm"><br /></a>P versus NP<br />The Hodge Conjecture<br />The Poincaré Conjecture (solved)<br />The Riemann Hypothesis<br />Yang-Mills Existence and Mass Gap<br />Navier-Stokes Existence and Smoothness<br />The Birch and Swinnerton-Dyer Conjecture<br /><br /><a href="http://mathworld.wolfram.com/topics/UnsolvedProblems.html">Mathworld list<br /></a><a href="http://www.ams.org/amsmtgs/mathchall.html">Mathematical challenges of the 21st century</a>including <a href="http://www.math.helsinki.fi/EWM/meetings/moduli.html">moduli spaces</a>and borderland physics<br /><a href="http://www.utm.edu/research/primes/glossary/GoldbachConjecture.html">Goldbach conjecture</a><br /><a href="http://mathworld.wolfram.com/NormalNumber.html">Normality of pi digits in an integer base<br /></a><a href="http://sprott.physics.wisc.edu/pickover/mathq.htm">Unsolved problems and difficult to understand areas</a></td><td height="402" colSpan="15"> </td><td height="402" colSpan="2"> </td></tr><tr vAlign="top"><td height="8" colSpan="69"> </td><td height="8" colSpan="2"> </td></tr><tr vAlign="top"><td height="57" colSpan="18"> </td><td colSpan="39" width="337"><strong>PRICES <br /></strong><a href="http://www.mathunion.org/medals/index.html">Fields Medal and Rolf Nevanlinna Prize<br /></a><a href="http://www.abelprisen.no/en/">Abel Prize</a></td><td height="57" colSpan="12"> </td><td height="57" colSpan="2"> </td></tr><tr vAlign="top"><td height="4" colSpan="69"> </td><td height="4" colSpan="2"> </td></tr><tr vAlign="top"><td height="34" colSpan="7"> </td><td colSpan="28" width="121"><font size="+2" face="TimesRoman"><strong>PHYSICS</strong></font></td><td height="34" colSpan="34"> </td><td height="34" colSpan="2"> </td></tr><tr vAlign="top"><td height="1" colSpan="69"> </td><td height="1" colSpan="2"> </td></tr><tr vAlign="top"><td height="7" colSpan="148"> </td></tr><tr vAlign="top"><td height="14" colSpan="20"> </td><td rowSpan="6" colSpan="36" width="310"><a href="http://physicsweb.org/toc/12/12">Important unsolved problems in physics<br /></a>Quantum gravity <br />Explaining high-Tc superconductors <br />Complete theory of the nucleus <br />Realizing the potential of fusion energy <br />Climate prediction <br />Turbulence <br />Glass physics <br />Solar magnetic field <br />Complexity, catastrophe and physics <br />Consciousness</td><td height="14" colSpan="92"> </td></tr><tr vAlign="top"><td height="34" colSpan="20"> </td><td height="34" colSpan="12"> </td><td colSpan="33" width="140"><a href="http://www.superstringtheory.com/math/index.html">Required mathematics</a></td><td height="34" colSpan="47"> </td></tr><tr vAlign="top"><td height="2" colSpan="20"> </td><td height="2" colSpan="92"> </td></tr><tr vAlign="top"><td height="133" colSpan="20"> </td><td height="133" colSpan="11"> </td><td colSpan="77" width="478">Peter Woit's list<br /><br />Riemannian geometry<br />More general geometry of principal and vector bundles: connection, curvature, etc.<br />Spinor geometry<br />Lie groups and representation theory<br />deRham cohomology</td><td height="133" colSpan="4"> </td></tr><tr vAlign="top"><td height="20" colSpan="20"> </td><td height="20" colSpan="92"> </td></tr><tr vAlign="top"><td height="20" colSpan="20"> </td><td height="20" colSpan="14"> </td><td rowSpan="2" colSpan="24" width="108"><a href="http://math.ucr.edu/home/baez/books.html">Required physics</a></td><td height="20" colSpan="54"> </td></tr><tr vAlign="top"><td height="2" colSpan="70"> </td><td height="2" colSpan="54"> </td></tr><tr vAlign="top"><td height="4" colSpan="148"> </td></tr><tr vAlign="top"><td height="17" colSpan="21"> </td><td rowSpan="2" colSpan="32" width="294"><a href="http://www.iop.org/EJ/toc/0143-0807/20/6">Another list from the European Journal of Physics</a></td><td height="17" colSpan="95"> </td></tr><tr vAlign="top"><td height="17" colSpan="21"> </td><td height="17" colSpan="17"> </td><td rowSpan="3" colSpan="60" width="317"><a href="http://www.amazon.co.uk/exec/obidos/tg/stores/detail/-/books/0224044478/reviews/026-7745631-2155605">Learn it all in one fell swoop</a></td><td height="17" colSpan="18"> </td></tr><tr vAlign="top"><td height="3" colSpan="70"> </td><td height="3" colSpan="18"> </td></tr><tr vAlign="top"><td height="1" colSpan="22"> </td><td rowSpan="3" colSpan="23" width="237"><a href="http://physicstoday.org/pt/vol-54/iss-11/p34.html">Physics Today (NRC)</a></td><td height="1" colSpan="25"> </td><td height="1" colSpan="18"> </td></tr><tr vAlign="top"><td height="17" colSpan="22"> </td><td height="17" colSpan="103"> </td></tr><tr vAlign="top"><td height="5" colSpan="22"> </td><td height="5" colSpan="24"> </td><td rowSpan="3" colSpan="51" width="240"><a href="http://www.phys.uu.nl/~thooft/theorist.html">Learn it all on the web</a></td><td height="5" colSpan="28"> </td></tr><tr vAlign="top"><td height="3" colSpan="69"> </td><td height="3" colSpan="28"> </td></tr><tr vAlign="top"><td height="14" colSpan="22"> </td><td rowSpan="2" colSpan="25" width="240"><a href="http://math.ucr.edu/home/baez/open.questions.html">John Baez's list</a></td><td height="14" colSpan="22"> </td><td height="14" colSpan="28"> </td></tr><tr vAlign="top"><td height="8" colSpan="22"> </td><td height="8" colSpan="101"> </td></tr><tr vAlign="top"><td height="6" colSpan="148"> </td></tr><tr vAlign="top"><td height="22" colSpan="21"> </td><td colSpan="25" width="240"><a href="http://agenda.cern.ch/fullAgenda.php?ida=a05302#2005-01-26">David Gross list</a></td><td height="22" colSpan="102"> </td></tr><tr vAlign="top"><td height="6" colSpan="148"> </td></tr><tr vAlign="top"><td height="22" colSpan="21"> </td><td colSpan="25" width="240"><a href="http://www-conf.slac.stanford.edu/ssi/2004/program.htm">Nature's greatest puzzles at SLAC</a></td><td height="22" colSpan="102"> </td></tr><tr vAlign="top"><td height="5" colSpan="148"> </td></tr><tr vAlign="top"><td height="57" colSpan="21"> </td><td colSpan="20" width="220"><strong>PRICES <br /></strong><a href="http://www.nobel.se/physics/index.html">Nobel Prize for physics<br /></a><a href="http://www.wolffund.org.il/cat.asp?id=25&cat_title=PHYSICS">Wolff</a></td><td height="57" colSpan="107"> </td></tr><tr vAlign="top"><td height="7" colSpan="148"> </td></tr><tr vAlign="top"><td height="31" colSpan="9"> </td><td colSpan="84" width="525"><font size="+2" face="TimesRoman"><strong>COSMOLOGY AND ASTROPHYSICS</strong></font></td><td height="31" colSpan="55"> </td></tr><tr vAlign="top"><td height="7" colSpan="148"> </td></tr><tr vAlign="top"><td height="11" colSpan="23"> </td><td rowSpan="2" colSpan="22" width="236"><a href="http://www.nap.edu/books/0309074061/html/">Eleven key questions about the universe</a></td><td height="11" colSpan="103"> </td></tr><tr vAlign="top"><td height="12" colSpan="23"> </td><td height="12" colSpan="31"> </td><td rowSpan="3" colSpan="14" width="50">Inflation</td><td height="12" colSpan="58"> </td></tr><tr vAlign="top"><td height="9" colSpan="76"> </td><td height="9" colSpan="58"> </td></tr><tr vAlign="top"><td height="1" colSpan="22"> </td><td rowSpan="8" colSpan="43" width="382"><a href="http://www.economist.com/surveys/displaystory.cfm?story_id=922278">Survey Of The Universe</a><a href="http://www.economist.com/surveys/displaystory.cfm?story_id=922278"><br /></a>Linde-Vilenkin, inflation (horizon, flatness, density-fluctuation) Photons, ordinary visible matter, ordinary nonluminous matter, MACHOs, exotic dark matter WIMPs, dark energy, Standard model, supersymmetry, technicolor, string theory, M-theory, Multiverses (eternal inflation, Smolin, ekpyrosis)</td><td height="1" colSpan="11"> </td><td height="1" colSpan="58"> </td></tr><tr vAlign="top"><td height="8" colSpan="22"> </td><td height="8" colSpan="83"> </td></tr><tr vAlign="top"><td height="22" colSpan="22"> </td><td height="22" colSpan="12"> </td><td colSpan="20" width="108">Brane cosmology</td><td height="22" colSpan="51"> </td></tr><tr vAlign="top"><td height="6" colSpan="22"> </td><td height="6" colSpan="83"> </td></tr><tr vAlign="top"><td height="24" colSpan="22"> </td><td height="24" colSpan="37"> </td><td colSpan="22" width="118"><a href="http://xxx.lanl.gov/abs/hep-th/0103239">Ekpyrotic Universe</a></td><td height="24" colSpan="24"> </td></tr><tr vAlign="top"><td height="10" colSpan="22"> </td><td height="10" colSpan="83"> </td></tr><tr vAlign="top"><td height="22" colSpan="22"> </td><td height="22" colSpan="38"> </td><td colSpan="19" width="109"><a href="http://en.wikipedia.org/wiki/Randall-Sundrum_model">Randall-Sudrum</a></td><td height="22" colSpan="26"> </td></tr><tr vAlign="top"><td height="28" colSpan="22"> </td><td height="28" colSpan="83"> </td></tr><tr vAlign="top"><td height="12" colSpan="148"> </td></tr><tr vAlign="top"><td height="22" colSpan="23"> </td><td colSpan="25" width="240"><a href="http://www.newscientist.com/channel/fundamentals/mg19225751.200-the-elephant-and-the-event-horizon.html">Black holes and nonlocality</a></td><td height="22" colSpan="100"> </td></tr><tr vAlign="top"><td height="78" colSpan="148"> </td></tr><tr vAlign="top"><td height="3" colSpan="11"> </td><td rowSpan="5" colSpan="52" width="410"><font size="+2" face="TimesRoman"><strong>QUANTUM GRAVITY</strong></font></td><td height="3" colSpan="85"> </td></tr><tr vAlign="top"><td height="1" colSpan="11"> </td><td height="1" colSpan="53"> </td><td rowSpan="10" colSpan="28" width="255"><a href="http://www.geocities.com/ednitou/Equations.doc">What they look like:<br />Schrodinger's equation<br />Dirac's equation<br />Einstein's equation<br />Superstring action<br />Connes-Chamseddine spectral action<br />Area eigenvalues</a></td><td height="1" colSpan="4"> </td></tr><tr vAlign="top"><td height="18" colSpan="11"> </td><td height="18" colSpan="15"> </td><td rowSpan="4" colSpan="30" width="171"><a href="http://xxx.lanl.gov/abs/gr-qc/0108040">Survey of quantum gravity</a></td><td height="18" colSpan="8"> </td><td height="18" colSpan="4"> </td></tr><tr vAlign="top"><td width="1" align="center" vAlign="middle"><font color="#0066cc"><img border="0" width="1" src="http://www.geocities.com/ednitou/serv" height="1" /></font></td><td width="1" align="center" vAlign="middle"><font color="#0066cc"><img border="0" width="1" src="http://www.geocities.com/ednitou/serv" height="1" /></font></td><td width="1" align="center" vAlign="middle"><font color="#0066cc"><img border="0" width="1" src="http://www.geocities.com/ednitou/serv" height="1" /></font></td><td height="1" colSpan="8"> </td><td height="1" colSpan="15"> </td><td height="1" colSpan="8"> </td><td height="1" colSpan="4"> </td></tr><tr vAlign="top"><td height="12" colSpan="11"> </td><td height="12" colSpan="15"> </td><td height="12" colSpan="8"> </td><td height="12" colSpan="4"> </td></tr><tr vAlign="top"><td height="3" colSpan="78"> </td><td height="3" colSpan="8"> </td><td height="3" colSpan="4"> </td></tr><tr vAlign="top"><td height="15" colSpan="116"> </td><td height="15" colSpan="4"> </td></tr><tr vAlign="top"><td height="58" colSpan="24"> </td><td colSpan="37" width="369">Problem of continuous approaches: parametrization of the dynamical degrees of freedom in a diffeomorphism invariant way</td><td height="58" colSpan="55"> </td><td height="58" colSpan="4"> </td></tr><tr vAlign="top"><td height="16" colSpan="116"> </td><td height="16" colSpan="4"> </td></tr><tr vAlign="top"><td height="3" colSpan="82"> </td><td rowSpan="2" colSpan="10" width="72"><a href="http://bookmark.iop.org/bookpge.htm?ID=628818102-24049-20169067-Y&book=815p"><strong>M-theory</strong></a></td><td height="3" colSpan="24"> </td><td height="3" colSpan="4"> </td></tr><tr vAlign="top"><td height="18" colSpan="25"> </td><td rowSpan="2" colSpan="24" width="240">Problem of infinity of vacua</td><td height="18" colSpan="33"> </td><td height="18" colSpan="24"> </td><td height="18" colSpan="4"> </td></tr><tr vAlign="top"><td height="4" colSpan="25"> </td><td height="4" colSpan="99"> </td></tr><tr vAlign="top"><td height="5" colSpan="148"> </td></tr><tr vAlign="top"><td height="1" colSpan="26"> </td><td rowSpan="3" colSpan="10" width="167"><a href="http://www.physics.ucsb.edu/~giddings/Mquest.html">Top questions in M-theory</a></td><td height="1" colSpan="112"> </td></tr><tr vAlign="top"><td height="22" colSpan="26"> </td><td height="22" colSpan="45"> </td><td colSpan="43" width="240"><a href="http://xxx.lanl.gov/PS_cache/hep-th/pdf/0203/0203101.pdf">Review article</a></td><td height="22" colSpan="24"> </td></tr><tr vAlign="top"><td height="6" colSpan="26"> </td><td height="6" colSpan="112"> </td></tr><tr vAlign="top"><td height="6" colSpan="148"> </td></tr><tr vAlign="top"><td height="1" colSpan="28"> </td><td rowSpan="2" colSpan="22" width="237"><a href="http://insti.physics.sunysb.edu/~siegel/top.html">Top ten string theory questions</a></td><td height="1" colSpan="98"> </td></tr><tr vAlign="top"><td height="22" colSpan="28"> </td><td height="22" colSpan="30"> </td><td colSpan="26" width="160">String theory</td><td height="22" colSpan="42"> </td></tr><tr vAlign="top"><td height="9" colSpan="148"> </td></tr><tr vAlign="top"><td height="3" colSpan="27"> </td><td rowSpan="3" colSpan="44" width="384"><a href="http://feynman.physics.lsa.umich.edu/strings2000/millennium.html">Ten physics problems for the next millenium from the Strings 2000 Conference<br /></a>Are all the (measurable) dimensionless paramters that characterize the physical universe calculable in principle or are some merely determined by historical or quantum mechanical accident and uncalculable?<br />How can quantum gravity help explain the origin of the universe?<br />What is the lifetime of the proton and how do we understand it?<br />Is nature supersymmetric and if so, how is supersymmetry broken?<br />Why does the universe appear to have one time and three space dimensions?<br />Why does the cosmological constant have the value that it has, is it zero and is it really constant?<br />What are the fundamental degrees of freedom of M-theory (the theory whose low-energy limit is eleven-dimensional supergravity and which subsumes the five consistent superstring theories) and does the theory describe nature?<br />What is the resolution of the black hole information paradox?<br />What physics explains the disparity between the gravitational scale and the typical mass scale of the elementary particles?<br />Can we quantitatively understand quark and gluon confinement in quantum chromodynamics and the existence of
23a mass gap?</td><td height="3" colSpan="77">Â </td></tr><tr vAlign="top"><td height="22" colSpan="27">Â </td><td height="22" colSpan="8">Â </td><td colSpan="44" width="240"><a href="http://superstringtheory.com/history/history3.html">Timeline</a></td><td height="22" colSpan="25">Â </td></tr><tr vAlign="top"><td height="422" colSpan="27">Â </td><td height="422" colSpan="77">Â </td></tr><tr vAlign="top"><td height="10" colSpan="148">Â </td></tr><tr vAlign="top"><td height="2" colSpan="101">Â </td><td rowSpan="4" colSpan="27" width="160"><a href="http://www.damtp.cam.ac.uk/user/gr/public/holo/">Holographic principle</a></td><td height="2">Â </td><td rowSpan="2" colSpan="4" width="84"><a href="http://en.wikipedia.org/wiki/AdS/CFT">AdS/CFT</a></td><td height="2" colSpan="15">Â </td></tr><tr vAlign="top"><td height="20" colSpan="74">Â </td><td rowSpan="2" colSpan="22" width="110"><a href="http://en.wikipedia.org/wiki/Supergravity">Supergravity</a></td><td height="20" colSpan="5">Â </td><td height="20">Â </td><td height="20" colSpan="15">Â </td></tr><tr vAlign="top"><td height="2" colSpan="74">Â </td><td height="2" colSpan="5">Â </td><td height="2" colSpan="20">Â </td></tr><tr vAlign="top"><td height="8" colSpan="101">Â </td><td height="8" colSpan="20">Â </td></tr><tr vAlign="top"><td height="7" colSpan="148">Â </td></tr><tr vAlign="top"><td height="4" colSpan="127">Â </td><td rowSpan="4" colSpan="11" width="146"><a href="http://mathworld.wolfram.com/TwistorCorrespondence.html">Twistor correspondence</a></td><td height="4" colSpan="10">Â </td></tr><tr vAlign="top"><td height="2" colSpan="100">Â </td><td rowSpan="4" colSpan="25" width="131"><a href="http://mathworld.wolfram.com/Twistor.html">What are twistors?</a></td><td height="2" colSpan="2">Â </td><td height="2" colSpan="10">Â </td></tr><tr vAlign="top"><td height="19" colSpan="73">Â </td><td colSpan="22" width="109"><a href="http://www.rdegraaf.nl/index.asp?sND_ID=436182">Twistor theory</a></td><td height="19" colSpan="5">Â </td><td height="19" colSpan="2">Â </td><td height="19" colSpan="10">Â </td></tr><tr vAlign="top"><td height="7" colSpan="100">Â </td><td height="7" colSpan="2">Â </td><td height="7" colSpan="10">Â </td></tr><tr vAlign="top"><td height="4" colSpan="100">Â </td><td height="4" colSpan="23">Â </td></tr><tr vAlign="top"><td height="10" colSpan="148">Â </td></tr><tr vAlign="top"><td height="22" colSpan="73">Â </td><td colSpan="48" width="240"><a href="http://arxiv.org/abs/hep-th/0312171">Witten's article</a></td><td height="22" colSpan="27">Â </td></tr><tr vAlign="top"><td height="35" colSpan="148">Â </td></tr><tr vAlign="top"><td height="1" colSpan="29">Â </td><td rowSpan="3" colSpan="41" width="380">Problems: construct a quantum theory of gravity from some basic principles assuming noncommutative geometry (John Madore, ...) or express some sector or limit of an underlying theory in terms of the language of noncommutative geometry</td><td height="1" colSpan="78">Â </td></tr><tr vAlign="top"><td height="29" colSpan="29">Â </td><td height="29" colSpan="4">Â </td><td colSpan="34" width="179"><a href="http://math.ucr.edu/home/baez/week39.html"><strong>Noncommutative geometry</strong></a></td><td height="29" colSpan="40">Â </td></tr><tr vAlign="top"><td height="58" colSpan="29">Â </td><td height="58" colSpan="78">Â </td></tr><tr vAlign="top"><td height="6" colSpan="148">Â </td></tr><tr vAlign="top"><td height="1" colSpan="73">Â </td><td rowSpan="3" colSpan="37" width="184"><a href="http://en.wikipedia.org/wiki/Euclidean_quantum_gravity"><strong>Euclidean quantum gravity</strong></a></td><td height="1" colSpan="38">Â </td></tr><tr vAlign="top"><td height="22" colSpan="73">Â </td><td height="22" colSpan="2">Â </td><td colSpan="27" width="240">Stephen Hawking</td><td height="22" colSpan="9">Â </td></tr><tr vAlign="top"><td height="11" colSpan="73">Â </td><td height="11" colSpan="38">Â </td></tr><tr vAlign="top"><td height="6" colSpan="148">Â </td></tr><tr vAlign="top"><td height="2" colSpan="30">Â </td><td rowSpan="5" colSpan="32" width="358">Problem: show the classical limit of smooth space-time can be recovered</td><td height="2" colSpan="86">Â </td></tr><tr vAlign="top"><td height="19" colSpan="30">Â </td><td height="19" colSpan="12">Â </td><td rowSpan="2" colSpan="31" width="156"><strong>Discrete approaches</strong></td><td height="19" colSpan="43">Â </td></tr><tr vAlign="top"><td height="3" colSpan="30">Â </td><td height="3" colSpan="12">Â </td><td height="3" colSpan="8">Â </td><td rowSpan="2" colSpan="27" width="240"><a href="http://en.wikipedia.org/wiki/Discrete_Lorentzian_quantum_gravity">Lorentzian</a></td><td height="3" colSpan="8">Â </td></tr><tr vAlign="top"><td height="19" colSpan="30">Â </td><td height="19" colSpan="51">Â </td><td height="19" colSpan="8">Â </td></tr><tr vAlign="top"><td height="2" colSpan="30">Â </td><td height="2" colSpan="86">Â </td></tr><tr vAlign="top"><td height="7" colSpan="148">Â </td></tr><tr vAlign="top"><td height="22" colSpan="114">Â </td><td colSpan="27" width="240"><a href="http://en.wikipedia.org/wiki/Regge_calculus">Regge calculus</a></td><td height="22" colSpan="7">Â </td></tr><tr vAlign="top"><td height="5" colSpan="148">Â </td></tr><tr vAlign="top"><td height="22" colSpan="115">Â </td><td colSpan="27" width="240">a variant: <a href="http://arxiv.org/abs/hep-th/0509010">causal dynamical calculations</a></td><td height="22" colSpan="6">Â </td></tr><tr vAlign="top"><td height="5" colSpan="148">Â </td></tr><tr vAlign="top"><td height="21" colSpan="114">Â </td><td rowSpan="2" colSpan="27" width="240">Causal sets (Rafael Sorkin, ...)</td><td height="21" colSpan="7">Â </td></tr><tr vAlign="top"><td height="1" colSpan="32">Â </td><td rowSpan="4" colSpan="28" width="342">Problem: cannot mimic general relativity at large scales</td><td height="1" colSpan="17">Â </td><td rowSpan="2" colSpan="30" width="172"><a href="http://relativity.livingreviews.org/Articles/lrr-1998-1/"><strong>Loop quantum gravity</strong></a></td><td height="1" colSpan="7">Â </td><td height="1" colSpan="7">Â </td></tr><tr vAlign="top"><td height="22" colSpan="32">Â </td><td height="22" colSpan="17">Â </td><td height="22" colSpan="41">Â </td></tr><tr vAlign="top"><td height="8" colSpan="32">Â </td><td height="8" colSpan="88">Â </td></tr><tr vAlign="top"><td height="7" colSpan="32">Â </td><td height="7" colSpan="53">Â </td><td rowSpan="2" colSpan="27" width="240">Hamiltonian or <a href="http://en.wikipedia.org/wiki/Spin_network">spin network</a>approach</td><td height="7" colSpan="8">Â </td></tr><tr vAlign="top"><td height="15" colSpan="113">Â </td><td height="15" colSpan="8">Â </td></tr><tr vAlign="top"><td height="8" colSpan="148">Â </td></tr><tr vAlign="top"><td height="26" colSpan="114">Â </td><td colSpan="33" width="283"><a href="http://xxx.lanl.gov/abs/gr-qc/0106091"><strong>Lagrgangian approach or spin foam models</strong></a></td><td height="26">Â </td></tr><tr vAlign="top"><td height="12" colSpan="148">Â </td></tr><tr vAlign="top"><td height="30" colSpan="77">Â </td><td colSpan="17" width="97">
23<a href="http://theory.ic.ac.uk/staffresearch.html"><strong>Topos theory</strong></a></td><td height="30" colSpan="54">Â </td></tr><tr vAlign="top"><td height="27" colSpan="148">Â </td></tr><tr vAlign="top"><td height="28" colSpan="74">Â </td><td rowSpan="2" colSpan="58" width="369"><strong>Emerging properties (Sakharov induced gravity, ...)</strong></td><td height="28" colSpan="16">Â </td></tr><tr vAlign="top"><td height="6" colSpan="13">Â </td><td rowSpan="2" colSpan="42" width="335"><strong><font size="+2" face="TimesRoman">CONDENSED MATTER</font></strong></td><td height="6" colSpan="19">Â </td><td height="6" colSpan="16">Â </td></tr><tr vAlign="top"><td height="31" colSpan="13">Â </td><td height="31" colSpan="93">Â </td></tr><tr vAlign="top"><td height="15" colSpan="148">Â </td></tr><tr vAlign="top"><td height="32" colSpan="33">Â </td><td colSpan="65" width="501"><a href="http://math.ucr.edu/home/baez/physics/General/open_questions.html">List of open questions including condensed matter problems</a></td><td height="32" colSpan="50">Â </td></tr><tr vAlign="top"><td height="45" colSpan="148">Â </td></tr><tr vAlign="top"><td height="35" colSpan="11">Â </td><td colSpan="126" width="855"><font size="+2" face="TimesRoman"><strong>PARTICLE PHYSICS</strong></font></td><td height="35" colSpan="11">Â </td></tr><tr vAlign="top"><td height="13" colSpan="148">Â </td></tr><tr vAlign="top"><td height="3" colSpan="33">Â </td><td rowSpan="3" colSpan="18" width="228"><strong>Standard model open questions</strong></td><td height="3" colSpan="97">Â </td></tr><tr vAlign="top"><td height="22" colSpan="33">Â </td><td height="22" colSpan="33">Â </td><td colSpan="27" width="181"><strong>Areas of research</strong></td><td height="22" colSpan="37">Â </td></tr><tr vAlign="top"><td height="9" colSpan="33">Â </td><td height="9" colSpan="97">Â </td></tr><tr vAlign="top"><td height="15" colSpan="83">Â </td><td rowSpan="2" colSpan="51" width="380">Technicolour: the unifying symmetry is a scaled-up version of the strong force</td><td height="15" colSpan="14">Â </td></tr><tr vAlign="top"><td height="30" colSpan="34">Â </td><td rowSpan="3" colSpan="36" width="370">Unnaturalness problem: original calculation in which the introduction of the Higgs boson in the standard model gives it and the Z and two W infinite mass </td><td height="30" colSpan="13">Â </td><td height="30" colSpan="14">Â </td></tr><tr vAlign="top"><td height="19" colSpan="34">Â </td><td height="19" colSpan="78">Â </td></tr><tr vAlign="top"><td height="17" colSpan="34">Â </td><td height="17" colSpan="15">Â </td><td rowSpan="3" colSpan="50" width="383">Supersymmetry: for every fermion in the standard model, there is a corresponding supersymmetric boson, and vice versa</td><td height="17" colSpan="13">Â </td></tr><tr vAlign="top"><td height="11" colSpan="85">Â </td><td height="11" colSpan="13">Â </td></tr><tr vAlign="top"><td height="18" colSpan="34">Â </td><td rowSpan="2" colSpan="4" width="181">Failure to account for gravity</td><td height="18" colSpan="47">Â </td><td height="18" colSpan="13">Â </td></tr><tr vAlign="top"><td height="6" colSpan="34">Â </td><td height="6" colSpan="110">Â </td></tr><tr vAlign="top"><td height="9" colSpan="148">Â </td></tr><tr vAlign="top"><td height="1" colSpan="86">Â </td><td rowSpan="2" colSpan="57" width="443"><a href="http://fnth37.fnal.gov/lykken/">Theories of extra dimensions: there are at least five dimensions and a single new particle, a gravitational boson called a graviton</a></td><td height="1" colSpan="5">Â </td></tr><tr vAlign="top"><td height="45" colSpan="31">Â </td><td rowSpan="3" colSpan="44" width="382">Flavour problem: why are they three and only three generations of fermions and why do the particles in each generation have the masses that they do?</td><td height="45" colSpan="11">Â </td><td height="45" colSpan="5">Â </td></tr><tr vAlign="top"><td height="10" colSpan="31">Â </td><td height="10" colSpan="73">Â </td></tr><tr vAlign="top"><td height="4" colSpan="31">Â </td><td height="4" colSpan="11">Â </td><td rowSpan="3" colSpan="39" width="240"><a href="http://en.wikipedia.org/wiki/Neutrino_oscillation">Neutrino oscillation</a></td><td height="4" colSpan="23">Â </td></tr><tr vAlign="top"><td height="11" colSpan="86">Â </td><td height="11" colSpan="23">Â </td></tr><tr vAlign="top"><td height="7" colSpan="32">Â </td><td rowSpan="2" colSpan="41" width="379">Hierarchy problem: why do the different forces operate at such different energies, are they all manifestations of the same underlying phenomenon, and if they are, can they be united mathematically?</td><td height="7" colSpan="13">Â </td><td height="7" colSpan="23">Â </td></tr><tr vAlign="top"><td height="76" colSpan="32">Â </td><td height="76" colSpan="75">Â </td></tr><tr vAlign="top"><td height="16" colSpan="148">Â </td></tr><tr vAlign="top"><td height="36" colSpan="12">Â </td><td colSpan="60" width="429"><strong><font size="+2">COMPLEX AND CHAOTIC SYSTEMS</font></strong></td><td height="36" colSpan="76">Â </td></tr><tr vAlign="top"><td height="4" colSpan="148">Â </td></tr><tr vAlign="top"><td height="125" colSpan="12">Â </td><td colSpan="97" width="615">Non-linear dynamics<br /><br />Evolutionary dynamics<br /><a href="http://mathworld.wolfram.com/CellularAutomaton.html">Cellular automata </a><br />Self-organising systems<br /><a href="http://www.chaos.cornell.edu/exploring_complex_networks3.pdf">Networks</a></td><td height="125" colSpan="39">Â </td></tr><tr vAlign="top"><td height="15" colSpan="148">Â </td></tr><tr vAlign="top"><td height="31" colSpan="14">Â </td><td colSpan="26" width="240"><font size="+2"><strong>PARADOXES</strong></font></td><td height="31" colSpan="108">Â </td></tr><tr vAlign="top"><td height="17" colSpan="148">Â </td></tr><tr vAlign="top"><td height="38" colSpan="15">Â </td><td colSpan="103" width="645"><a href="http://en.wikipedia.org/wiki/Monty_Hall_problem">Monty Hall</a>, <a href="http://en.wikipedia.org/wiki/Elevator_paradox">Gamow-Stern</a>, <a href="http://www.maa.org/mathland/mathtrek_12_24_01.html">Kruskal</a>, <a href="http://en.wikipedia.org/wiki/Aleph-null">Cantor</a>, <a href="http://en.wikipedia.org/wiki/BanachâTarski_paradox">Banach-Tarski<br /></a><a href="http://en.wikipedia.org/wiki/List_of_paradoxes">List of paradoxes</a></td><td height="38" colSpan="30">Â </td></tr><tr vAlign="top"><td height="25" colSpan="148">Â </td></tr><tr vAlign="top"><td height="38" colSpan="10">Â </td><td colSpan="42" width="301"><a href="http://www.santafe.edu/~shalizi/reviews/physics-of-finance/"><font size="+2" color="#0066cc">PHYSICS OF FINANCE</font></a></td><td height="38" colSpan="96">Â </td></tr><tr vAlign="top"><td height="9" colSpan="148">Â </td></tr><tr vAlign="top"><td height="2" colSpan="42">Â </td><td rowSpan="3" colSpan="22" width="158"><a href="http://www.sciencedirect.com/science?_ob=IssueURL&_tockey=#TOC#5940#2001#998999998#221710#FLA#display#Volume_100,_Issue_1,_Pages_1-318_(January_2001)#tagged#Volume#first=100#Issue#first=1#Pages#first=1#last=318#date#(January_2001)#&_auth=y&_acct=C000000593&_version=1&_urlVersion=0&_userid=2735&md5=50b3da08a482419bf07e25c57350d103">
23Future of econometrics</a></td><td height="2" colSpan="84">Â </td></tr><tr vAlign="top"><td height="22" colSpan="11">Â </td><td rowSpan="3" colSpan="28" width="240"><a href="http://www.cxoadvisory.com/blog/external/blog6-15-07/">Open questions in financial econometrics</a><br /></td><td height="22" colSpan="3">Â </td><td height="22" colSpan="24">Â </td><td colSpan="38" width="240"><a href="http://www.palgrave.com/products/Catalogue.aspx?is=1403996652">Evolutionary finance</a></td><td height="22" colSpan="22">Â </td></tr><tr vAlign="top"><td height="8" colSpan="11">Â </td><td height="8" colSpan="3">Â </td><td height="8" colSpan="84">Â </td></tr><tr vAlign="top"><td height="11" colSpan="11">Â </td><td height="11" colSpan="109">Â </td></tr><tr vAlign="top"><td height="2" colSpan="148">Â </td></tr><tr vAlign="top"><td height="19" colSpan="89">Â </td><td colSpan="28" width="180"><a href="http://mathworld.wolfram.com/NonparametricEstimation.html">Nonparametric estimation</a></td><td height="19" colSpan="31">Â </td></tr><tr vAlign="top"><td height="7" colSpan="148">Â </td></tr><tr vAlign="top"><td height="32" colSpan="88">Â </td><td colSpan="57" width="436"><a href="http://forecasting.cwru.edu/IJFcall2003.pdf">Forecasting Economic and Financial Time Series Using Nonlinear Methods</a></td><td height="32" colSpan="3">Â </td></tr><tr vAlign="top"><td height="3" colSpan="148">Â </td></tr><tr vAlign="top"><td height="27" colSpan="87">Â </td><td colSpan="49" width="383"><a href="http://www.occf.ox.ac.uk/">Scientific study of financial data</a></td><td height="27" colSpan="12">Â </td></tr><tr vAlign="top"><td height="20" colSpan="148">Â </td></tr><tr vAlign="top"><td height="32" colSpan="8">Â </td><td colSpan="83" width="496"><a href="http://en.wikipedia.org/wiki/Unsolved_problems_in_biology"><font size="+2" color="#0066cc">UNSOLVED PROBLEMS IN BIOLOGY</font></a></td><td height="32" colSpan="57">Â </td></tr><tr vAlign="top"><td height="20" colSpan="148">Â </td></tr><tr vAlign="top"><td height="42" colSpan="8">Â </td><td colSpan="96" width="597"><a href="http://www.amazon.com/exec/obidos/tg/stores/detail/-/books/0500510504/reviews/qid=1003492171/ref=sr_11_0_1/002-9157009-7656836"><strong><font size="+2" color="#0066cc" face="TimesRoman">SEVENTY OPEN QUESTIONS IN ARCHEOLOGY</font></strong></a></td><td height="42" colSpan="44">Â </td></tr><tr vAlign="top"><td height="10" colSpan="148">Â </td></tr><tr vAlign="top"><td height="36" colSpan="8">Â </td><td colSpan="63" width="436"><a href="http://search.barnesandnoble.com/booksearch/isbnInquiry.asp?isbn=0071357432"><strong><font size="+2" color="#0066cc">NINE UNDECIPHERED LANGUAGES</font></strong></a></td><td height="36" colSpan="77">Â </td></tr></tbody></table><p><!-- text below generated by server. PLEASE REMOVE --></p><p><font color="#0066cc"><img border="0" src="http://visit.geocities.com/visit.gif?&r=http://www.geocities.com/ednitou/&b=Microsoft Internet Explorer 4.0 (compatible; MSIE 7.0; Windows NT 6.0; SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.5.30729; .NET CLR 3.0.30618)&s=1920x1200&o=Win32&c=32&j=true&v=1.2" style="display: none" /></font> <img width="1" src="http://geo.yahoo.com/serv?s=76001084&t=1254587659&f=us-w3" alt="1" height="1" /> </p></div></div></div><div id="zB"><div id="zB-widget-layout-wrap" class="widget-layout-wrap " rel=""><div class="modWrap"></div></div></div><div id="zC"><div id="zC-widget-layout-wrap" class="widget-layout-wrap " rel=""><div class="modWrap"></div></div></div></div></div></div><div xmlns="" id="ft"><div id="fWrapper"><div id="fContent"><div id="footerContent" class="editorWrap"><div id="footerZoneElement" class="editable rte flexContent" rel="itemGuid.sit.fc.001"><p>Copyright 2009 Open Problems In Mathematics And Physics. All rights reserved.</p><p><a target="_top" href="https://www.turbify.com/hosting">Web Hosting by Turbify</a></p></div></div></div><div id="fMisc"><div class="contactInfoContainer" style="width:auto;height:auto"><p class="vcard"></p></div></div><div id="fBadges"></div></div></div></div></div></body>
23<script xmlns="" type="text/javascript"></script>
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23<script xmlns="" type="text/javascript"> 24 YAHOO.namespace('Smb.Asteroids'); 25 var YSA = YAHOO.Smb.Asteroids; 26 27 YSA.Nav = { 28 isNavNorth : false, 29 tmr : null, 30 tmrInterval : 600, 31 prevCloseNode : null, 32 isFirstVisit : true, 33 34 openSub : function(navNode) { 35 $LOG('openSub'); 36 37 // Clear the timer if any, and if the previously opened subnav is still open (timeout expiration) 38 YSA.Nav.clearTimer(); 39 YSA.Nav.closePrevSubMenu(); 40 41 // For horizontal navigation, set the top position of sub-nav as the height of the 'trigger' element. 42 if (YSA.Nav.isNavNorth) { 43 var subNavNode = navNode.getElementsByTagName('ul')[0]; 44 subNavNode.style.top = navNode.offsetHeight + 'px'; 45 } 46 47 $D.addClass(navNode, 'opened'); 48 $D.addClass('admincontrols', 'displayNone'); 49 }, 50 closeSub : function(navNode) { 51 $LOG('closeSub'); 52 YSA.Nav.clearTimer(); 53 YSA.Nav.prevCloseNode = navNode; 54 YSA.Nav.tmr = setTimeout(function() { YSA.Nav.hideSub(navNode); }, YSA.Nav.tmrInterval); 55 }, 56 hideSub : function(navNode) { 57 YSA.Nav.clearTimer(); 58 59 // For key board accessibility, the active sub menu is display:block., not none. So giving -999 to move it off screen in hide mode 60 if (YSA.Nav.isNavNorth && $D.hasClass(navNode, 'active')) { 61 var subNavNode = navNode.getElementsByTagName('ul')[0]; 62 subNavNode.style.top = '-999px'; 63 } 64 $D.removeClass(navNode, 'opened'); 65 $D.removeClass('admincontrols', 'displayNone'); 66 }, 67 closePrevSubMenu : function() { 68 if (YSA.Nav.prevCloseNode) { 69 $LOG('Closing previous sub nav'); 70 YSA.Nav.hideSub(YSA.Nav.prevCloseNode); 71 YSA.Nav.prevCloseNode = null; 72 } 73 }, 74 isSubOpen : function(navNode) { 75 return $D.hasClass(navNode, 'opened'); 76 }, 77 toggleSub : function(navNode) { 78 var NAV = YSA.Nav; 79 if (NAV.isSubOpen(navNode)) { 80 NAV.closeSub(navNode); 81 } else { 82 NAV.openSub(navNode); 83 } 84 }, 85 mouseOverTrigger : function(e) { 86 $LOG('mouseOverTrigger'); 87 YSA.Nav.openSub(this); 88 }, 89 mouseOutTrigger : function(e) { 90 $LOG('mouseOutTrigger'); 91 var target = $E.getTarget(e); 92 var relatedTarget = $E.getRelatedTarget(e); 93 $LOG(target); 94 $LOG(relatedTarget); 95 YSA.Nav.closeSub(this); 96 }, 97 mouseOverMainNav : function(e) { 98 $LOG('mouseOverMainNav'); 99 if (!$D.hasClass(this, 'trigger')) { 100 YSA.Nav.closePrevSubMenu(); 101 } 102 }, 103 toggleClicked : function(e) { 104 $LOG('toggle clicked'); 105 $LOG(e); 106 $E.stopEvent(e); 107 YSA.Nav.toggleSub(this.parentNode); 108 }, 109 clearTimer : function() { 110 $LOG('Clearing Nav Timer'); 111 if (YSA.Nav.tmr) { 112 clearTimeout(YSA.Nav.tmr); 113 } 114 YSA.Nav.tmr = null; 115 }, 116 clearSubNavStyles : function() { 117 /* For horizontal navigation, we set the 'top' of subNav to align it with the bottom of trigger 118 Now if the user chage the template from ribbon, remove this inline style. Else this old inline value will take precedence! */ 119 var subNavNode; 120 var navDiv = $('navigation'); 121 var triggers = $D.getElementsByClassName('trigger', '', navDiv); 122 for (var el in triggers) { 123 if (YAHOO.lang.hasOwnProperty(triggers, el)) { 124 subNavNode = triggers[el].getElementsByTagName('ul')[0]; 125 subNavNode.style.top = ''; 126 } 127 } 128 }, 129 initNavSettings : function() { 130 var wrapperDiv = $('wrapper'); 131 YSA.Nav.isNavNorth = (wrapperDiv && $D.hasClass(wrapperDiv, 'navpos_north')) ? true : false; 132 }, 133 init : function() { 134 // For the first visit, subscribe to the layout(template) change event 135 // When user changes template from the ribbon, we need to re-init this JS, based on the new templates settings. 136 if (YSA.Nav.isFirstVisit) { 137 YSA.Nav.isFirstVisit = false;
138 if (YSA.UiMgr) { 139 YSA.UiMgr.Layout.onChange.eventObj.subscribe( 140 function() { YSA.Nav.init() }); 141 } 142 } else { 143 YSA.Nav.clearSubNavStyles(); 144 } 145 146 YSA.Nav.initNavSettings(); 147 var navDiv = $('navigation'); 148 if (! $D.hasClass(navDiv, 'sub_dynamic')) { 149 return; 150 } 151 YSA.Nav.initNavSettings(); 152 var triggers = $D.getElementsByClassName('trigger', '', navDiv); 153 $E.on(triggers, 'mouseover', this.mouseOverTrigger); 154 $E.on(triggers, 'mouseout', this.mouseOutTrigger); 155 var toggles = $D.getElementsByClassName('toggle', 'a', navDiv); 156 $E.on(toggles, 'click', this.toggleClicked); 157 var triggers = $D.getElementsByClassName('mainNav', '', navDiv); 158 $E.on(triggers, 'mouseover', this.mouseOverMainNav); 159 } 160 }; 161 $E.on(window, 'load', YSA.Nav.init, YSA.Nav, true); 162</script>
162</html>
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