応強丗 戝島媊幒(C搹4奒乯

島墘幰丗 彫墥丂塸梇乮憗堫揷戝妛 棟岺妛弍堾乯

戣栚丗 Hadamard variational formula for the Stokes equations and its application to the shape of domains 丂

応強丗 戝島媊幒(C搹4奒乯

島墘幰丗 抦擮丂岹巌乮嬤婨戝妛乯

戣栚丗 晞崋偲晄曄幃偺僛乕僞娭悢偲偦偺儕乕儅儞梊憐丂

応強丗戝島媊幒(C搹4奒乯

島墘幰丗 壨旛 峗巌乮壀嶳戝妛戝妛堾帺慠壢妛尋媶壢乯

戣栚丂丗Long time behavior of non-symmetric random walks on crystal lattices

応強丗戝島媊幒(C搹4奒乯

島墘幰丗晲揷丂岲巎乮榓壧嶳導棫堛壢戝妛乯

戣栚丂丗惓昗悢偵摿桳側戙悢懡條懱丂

応強丗戝島媊幒(C搹4奒乯

島墘幰丗峳愳丂抦岾乮嫗搒戝妛悢棟夝愅尋媶強乯

戣栚丂丗W戙悢偺桳棟惈丂

Abstract:
偙傟傑偱擇師尦偺嫟宆応棟榑偼悢妛偵偝傑偞傑側傾僀僨傾傪梌偊偰偒偨丅 乮椺偊偽桳棟揑側嫟宆応棟榑傪梡偄偰寢傃栚偺晛曊検傪宯摑揑偵峔惉偱偒傞偙偲 偑抦傜傟偰偄傞丅乯 偲偙傠偑桳棟揑側嫟宆応棟榑偺怴偟偄椺傪峔惉傪偡傞偙偲偼戝曄擄偟偄栤戣偱偁傝丄 傛偔抦傜傟偰偄傞傾僼傿儞儕乕娐傗Virasiro戙悢側偳偺柍尷師尦儕乕娐偲奿巕偵晅悘偡傞傕偺埲奜偵偼 (偦傟偐傜掕傑傞Coset峔惉朄偲婳摴峔惉朄傪彍偄偰乯杮幙揑偵怴偟偄傕偺偼峔惉偝傟偰偙側偐偭偨丅 偙偺傛偆側拞丄80擭戙偵摫擖偝傟偨W戙悢偲偄偆傕偺偵晅悘偡傞嫟宆応棟榑偑怴偟偄桳棟揑側嫟宆応棟榑偺 桳椡側岓曗偱偁傝偮偯偗偨偑丄偦偺暋嶨偝屘徹柧偼偮偄嵟嬤傑偱枹夝寛偵棷傑偭偰偄偨丅 偙偺島墘偱偼島墘幰偵傛傞W戙悢偵晅悘偡傞嫟宆応棟榑偺桳棟惈偺栤戣偺夝寛偵偮偄偰偍榖偟偟偨偄丅

応強丗戝島媊幒(C搹4奒乯

島墘幰丗Prof. Jair Remigio Ju\'arez (Juarez Autonomous University of Tabasco)

戣栚丂丗Seifert manifolds and their coverings branched along fibers丂

Abstract:
This is a joint work with V\'ictor N\'u\~nez. A Seifert manifold M is a (possibly non-orientable) closed 3-manifold $M $ which is a disjoint union of circles (fibers). Seifert manifolds were introduced and classified (under fiber preserving homeomorphism) in six different classes (according to their ``Seifert symbols'') by H. Seifert in 1933. C.Gordon and W. Heil proved that if $\varphi:\tilde{M}\to M$ is a covering of a Seifert manifold $M$ branched along some fibers, then $\tilde{M}$ is a Seifert manifold too. Then a natural question is: What Seifert manifold is $\tilde{M}$? that is, what is the Seifert symbol of $\tilde{M}$? So the plan for this talk is to explore last question, for this reason, we will start studying some basic deffinitions (as Seifert manifold, Seifert symbol, coverings, etc ) and the Seifert's classification for Seifert manifolds. After that, we will introduce the concept of ``imprimitive subgroup of a group'' and will apply this concept to try to compute the Seifert symbol of $\tilde{M}$.

応強丗戝島媊幒(C搹4奒乯

島墘幰丗Prof. Ken Baker 乮Department of Mathematics, University of Miami, Assistant Professor乯

戣栚丂丗Non-unique knot surgery descriptions丂

Abstract:
Every (closed, compact, connected, oriented) 3-manifold admits infinitely many descriptions as surgery on a link in the 3-sphere. However this is not necessarily the case if we restrict ourselves to links of one component, i.e. knots. Aside from more straightforward obstructions such as homology, it is not readily apparent when a manifold even admits a surgery description on a knot. In this talk we'll survey the history of constructions of manifolds with multiple knot surgery descriptions and reexamine its relevance in modern Low Dimensional Topology.

応強丗戝島媊幒(C搹4奒乯

島墘幰丗愳懞丂桭旤乮柤屆壆戝妛戝妛堾丂懡尦悢棟壢妛尋媶壢乯

戣栚丂丗寢傃栚夝徚悢傪恾偐傜昡壙偡傞丂

応強丗戝島媊幒(C搹4奒乯

島墘幰丗惔悈丂棟壚乮峀搰戝妛戝妛堾棟妛尋媶壢丗摿擟彆嫵乯

戣栚丂丗寢傃栚偺幩塭恾偺婛栺搙偵偮偄偰丂

Abstract:
媴柺偵偍偗傞寢傃栚偺幩塭恾乮偁傞偄偼墌廃偺偼傔偙傒乯偼丄乽婛栺乿偲乽壜栺乿 偺傆偨偮偺僞僀僾偵暘偗傜傟傑偡丅杮島墘偱偼丄寢傃栚幩塭恾偑偳傟偖傜偄婛栺 偱偁傞偐傪昞偡乽婛栺搙乿偵偮偄偰偍榖偄偨偟傑偡丅偙傟偼丄敿傂偹傝僗僾儔僀 僗偲偄偆嬊強曄宍傪梡偄偰掕媊偝傟偨傕偺偱偡丅僌儔僼傗僐乕僪恾傪梡偄偰丄婛 栺搙偺條乆側惈幙傪尒偨偁偲偵丄擟堄偺寢傃栚幩塭恾偵偍偄偰婛栺搙偼忢偵俁埲 壓偱偁傞偲偄偆偙偲傪娙扨偵徹柧偟傑偡丅傑偨丄杮尋媶偺偒偭偐偗偲側偭偨僎乕 丒�丄Region Select 傕徯夘偄偨偟傑偡丅

応強丗戝島媊幒(C搹4奒乯

島墘幰丗 忋懞柅戝乮娭惣戝妛乯

戣栚丂丗旘桇傪傕偮奼嶶夁掱偺峔惉偵偮偄偰丂

応強丗戝丒u媊幒(C搹4奒乯

島墘幰丗 墫揷 埨怣乮搶杒妛堾戝妛乯

戣栚丂丗僼儔僋僞儖應搙偲僨僕僞儖榓栤戣

Abstract丗
Mandelbrot 偵傛傞僼儔僋僞儖棟榑偑拲栚偝傟巒傔偨偺偼1980擭戙偱, 偙傟偵巋寖偝傟偰偦傟傑偱悢妛揑偵偼偁傑傝拲栚偝傟側偐偭偨曄側(僼儔 僋僞儖)娭悢傗恾宍偑宯摑揑偵尋媶偝傟傞傛偆偵側偭偰偒偨丏1985擭偵 敤-嶳岥偼崅栘娭悢偲Lebesgue 偺摿堎娭悢傪寢傃偮偗偨岞幃傪摫偄偨. 変乆偼僼儔僋僞儖棟榑偺悢妛揑婎慴偲偄偆娤揰偐傜Lebesgue 偺摿堎娭悢 偑2崁應搙偺暘晍娭悢偱偁傞偙偲偵拝栚偟, 敤-嶳岥偺岞幃偺偄傠偄傠側 堦斒壔傪峴偭偰偒偨.

懠曽, 僨僕僞儖榓栤戣偲偼, 帺慠悢n傪2恑朄偱昞帵偟偨偲偒偵弌偰偔傞 1偺屄悢偵娭偡傞偄傠偄傠側榓偵娭偡傞岞幃傪媮傔傛偆偲偄偆栤戣偱偁傞. 僨僕僞儖榓栤戣偵偮偄偰偼愄偐傜尋媶偝傟偰偍傝, 悢懡偔偺寢壥偑抦傜傟偰偄傞.

堦尒偟偰柍娭學偵尒偊傞2偮偺暘栰偑 Lebesgue 偺摿堎娭悢, 偡側傢偪 2崁應搙傪夘偟偰枾愙偵寢傃偮偔偙偲, 偦偟偰敤-嶳岥偺岞幃偺堦斒壔偑 偄傠偄傠側僨僕僞儖榓栤戣偺榓偵娭偡傞岞幃傪梌偊傞偙偲傪徯夘偡傞.

応強丗戝島媊幒(C搹4奒乯

島墘幰丗 嬥塸巕乮搶嫗岺嬈戝妛 戝妛堾忣曬棟岺妛尋媶壢乯

戣栚丂丗Pseudo-Anosovs with small entropy and the magic 3-manifold

Abstract丗
We consider pseudo-Anosovs which occur as the monodromies on fibers for Dehn fillings of the so called magic manifold. By using these pseudo-Anosovs, we discuss the questions on the minimal dilatation for pseudo-Anosov homeomorphisms (with orientable invariant foliations). This is joint work with Mitsuhiko Takasawa.

応強丗戝島媊幒(C搹4奒乯

島墘幰丗 惵栘岹庽乮搶嫗棟壢戝妛 棟岺妛晹乯

戣栚丂丗Borcherds 偺柍尷愊偵偮偄偰

Abstract丗
Borcherds 柍尷愊偼懡曄悢偺曐宆宍幃偺峔惉朄偺傂偲偮偱偁傞丅 島墘偱偼丄 Borcherds 柍尷愊偵偮偄偰奣梫傪夝愢偡傞偲嫟偵丄 偦偺堦斒壔偵偮偄偰偺尋媶惉壥傪徯夘偡傞丅

応強丗戝島媊幒(C搹4奒乯

島墘幰丗 Reinhard Farwig (Darmstadt University of Technology)

戣栚丂丗The Millennium Problem of the Navier-Stokes Equations

Abstract丗
Since the pioneering work of Jean Leray (1934) it is an open problem whether the instationary Navier-Stokes system, the classical model of viscous, incompressible fluid flow, admits for any initial data in 3D a global in time smooth solution. An equivalent question concerns the possibility of singularities in finite time for strong solutions and also the uniqueness of weak solutions. This issue is one of the seven Millennium Problems formulated in 2000 by Clay Mathematics Institute and still unsolved. The colloquial talk discusses this question both from the mathematical and physical point of view, explains why this problem does not occur in 2D and presents more recent results on regularity of the Navier-Stokes equations.

応強丗戝島媊幒(C搹4奒乯

島墘幰丗 椦丂拠晇乮戝嶃戝妛戝妛堾棟妛尋媶壢丒悢妛愱峌乯

戣栚丂丗旕慄宍Schr\"odinger曽掱幃偺慟嬤夝愅

Abstract丗
旕慄宍Schr\"odinger曽掱幃偺夝偺慟嬤揑怳傞晳偄偵娭偡傞嵟弶偺寢壥偼 Lin-Strauss 1976 偵傛傞傕偺偑嵟弶偩偲巚傢傟傞. 偦偺屻 Ginibre-Velo 1977-78, Cazenave 1978, Strauss 1981, 掔 1987, 彫郪 1991 傜偵傛偭偰尋媶偑妶敪偵峴傢傟崱擔偵帄偭偰偄傞. 偙偙偱偼楌巎揑側帠幚傪弎傋偨屻, 嵟嬤偺恑揥偵偮偄偰奣愢偡傞偙偲偵偡傞.

応強丗戝島媊幒(C搹4奒乯

島墘幰丗 Hermann SOHR (Univ. Paderborn, Prof. emirtus)

戣栚丂丗Recent results on weak and strong solutions of the Navier-Stokes equations

Abstract丗
Our purpose is to develop the optimal initial value condition for the existence of a unique local strong solution of the Navier-Stokes equations in a smooth bounded domain.
This condition is not only sufficient
丂- there are several well-known sufficient conditions in this context
丂- but also necessary, and yields therefore the largest possible class of such strong solutions.
As an application we obtain several extensions of Serrin's regularity condition.
A restricted result also holds for completely general domains.
Furthermore we extend the well-known class of Leray-Hopf weak solutions with zero boundary conditions and zero divergence to a larger class with corresponding nonzero conditions.

応強丗戝島媊幒(C搹4奒乯

島墘幰丗 壨梂婭巕乮University of North Texas & 嫗搒戝妛悢棟夝愅尋媶強乯

戣栚丒@丗偄偨傞偲偙傠旝暘晄壜擻側娭悢偺嵟戝抣丄嵟彫抣偺栤戣丂

Abstract丗
嵟揔壔栤戣偼宱嵪妛丄惗暔妛丄暔棟妛丄岺妛側偳偁傝偲偁傜備傞暘栰偱丄偦偺廳梫惈偼擣幆偝傟偰偄傞丅 側傔傜偐側娭悢偺応崌丄僯儏乕僩儞偺旝暘妛偵傛傝丄嵟戝丄嵟彫偺栤戣傪夝偔偙偲偼梕堈偱偁傞丅 偟偐偟丄偄偨傞偲偙傠旝暘晄壜擻側娭悢偺応崌丄変乆偼偳偆傗偭偰丄偦偺嵟戝抣丄嵟彫抣傪尒偮偗偨傜偄偄偺偐丠
偙偺栤偄偵摎偊傞戞堦曕偲偟偰丄儖儀乕僌摿堎娭悢 乮扨挷憹壛偱丄傎偲傫偳偄偨傞偲偙傠旝學悢偑僛儘偺娭悢乯偺僷儔儊乕僞偵娭偡傞値奒旝暘傪 T_n(x)偲掕媊偟丄峫嶡偡傞丅

応強丗戝島媊幒(C搹4奒乯

島墘幰丗 嶳揷桾巎乮壀嶳戝妛乯

戣栚丂丗僔儏乕傾敓悢偲偲傕偵巐敿悽婭丂

Abstract丗
戝妛堾惗偺崰偵丆嵅摗姴晇愭惗偺KP棟榑偺島媊傪挳偒丆僞僂敓悢偲偟偰偺乽僔儏乕傾敓悢乿偵怗傟偰偐傜俀俆擭埲忋偑夁偓偨丏 偦偟偰巹傕擭傪偲偭偨丏
償傿儔僜儘戙悢偺摿堎儀僋僩儖丆傾僼傿儞儕乕娐偺僂僄僀僩儀僋僩儖摍乆丆僔儏乕傾敓悢偼條乆側応柺偵婄傪偺偧偐偣傞丏 択榖夛偱偼丆廤拞島媊偲廳暋偡傞偐傕偟傟側偄偑丆巹偑幚嵺偵怗偭偨僔儏乕傾敓悢偵偮偄偰丆屄乆丒處v偄弌偲偲傕偵岅傝偨偄丏
尰嵼偼僔儏乕傾敓悢偺儌僕儏儔乕斉偵嫽枴傪帩偭偰偄傞偺偱丆偦偙偵廳揰傪抲偙偆丏 傑偩棟榑偵側偭偰偄側偄弶婜抜奒偺幚尡寢壥偵偮偄偰傕丒�榖偟偟偨偄偲巚偭偰偄傞丏 婥寉偵挳偄偰偄偨偩偒偨偄丏

応強丗戝島媊幒(C搹4奒乯

島墘幰丗嶳嶈棽梇 乮搶杒戝妛乯

戣栚丂丗Higher dimensional class field theory for a product of curves丂丂

Abstract丗
屆揟揑側椶懱榑偲偦偺崅師尦壔偵娭偡傞偙傟傑偱偺尋媶傗栤戣傪夝愢偟偨忋偱丄嬋慄偺愊偵娭偡傞怴偟偄寢壥乮摿偵擇師尦嬊強懱忋偺奐懡條懱偵偮偄偰乯傪徯夘偡傞丅

応強丗戝島媊幒(C搹4奒乯

島墘幰丗埳摗恗堦 乮孎杮戝妛乯

戣栚丂丗儕乕儅儞懡條懱偺嵟彫愓偲娭楢偡傞彅栤戣丂丂

Abstract丗
嵟彫愓偺尋媶偼丆H. Poincar\'{e} 偵傛傞嬋柺偺埵憡偲偺娭楢 偐傜巒傑傝丆偦偺屻挿偔尋媶偝傟懕偗偰偄傑偡丏偙偺島墘偱偼丆堦斒師尦偺懭墌柺偺嵟彫愓偲嫟栶愓偺寛掕乮Jacobi偺掕棟偺堦斒壔乯傗偦偺懠偺懡偔偺嵟彫愓偵娭楢偡傞彅栤戣丆椺偊偽丆嵟墦揰廤崌傗嫍棧娭悢偺椪奅揰偵娭偡傞栤戣丆撌懡柺懱偺揥奐(unfolding)偵娭偡傞栤戣摍乆偵偮偄偰嵟嬤偺敪揥傪徯夘偡傞梊掕偱偡丏

応強丗戝島媊幒(C搹4奒乯

島墘幰丗Maria Gorelik (Weizmann Institute of Science, Israel)

戣栚丂丗Weyl denominator identity for Lie superalgebras丂丂

Abstract丗
The formula
$\prod_{1 \leq 1亙j \leq n} (1-x_i/x_j) = \sum_{\sigma \in S_n}
sgn(\sigma) x_1^{\sigma(1)-1} x_2^{\sigma(2)-2} \dots x_n^{\sigma(n)-n}$
can be interpreted as a the character formula for the trivial sl_n-module. This formula is a particular case of Weyl denominator identity. Macdonald identity is another particular case of Weyl denominator identity.
Weyl denominator identity for Lie superalgebras was conjectured by V. Kac and M. Wakimoto in 1994 and a proof for defect one case was given. In my talk I will review this proof and a proof for other basic Lie superalgebras.

応強丗悢妛戝島媊幒(C搹4奒乯

島墘幰丗棊崌孾擵乮柤屆壆戝乯

戣栚丂丗婙懡條懱偺捈愊忋偺婳摴偺桳尷惈偵偮偄偰丂丂

Abstract丗
偙傟偼惣嶳嫕乮嫗搒戝妛乯偲偺嫟摨尋媶偱偁傞丅婙懡條懱偼孮偑摍幙偵摥偔姰旛側懡條懱偱偁傞丅偙偙偱偼丄婙懡條懱偺偄偔偮偐偺捈愊偵孮偑摥偄偨帪偵婳摴偑桳尷偵側傞偺偼偄偮偐丄偦偟偰婳摴暘夝偼偳偆側傞偐丄偲偄偆栤戣傪懳徧懳乮懳徧嬻娫乯偵娭楢偟偨摿庩側愝掕偱峫偊傞丅丂懳徧懳偑孮懡條懱偐傜棃傞応崌偼mirabolic 晹暘孮偵懳墳偟偨慻崌偣榑側偳偺墳梡偑嬤擭妶敪偱偁傞丅 懳徧丒蝹虖陯噦蛠A偄傑偩媍榑偼巒傑偭偨偽偐傝偱暘偐傜側偄偙偲偑懡偄偑丄懳墳偡傞帠幚偑婜懸偱偒傞偺偱偼側偄偐偲峫偊偰偄傞丅

応強丗戝島媊幒(C搹4奒乯

島墘幰丗Ching Hung Lam (National Cheng Kung University, Taiwan)

戣栚丂丗Some inductive structures of the Moonshine VOA
丂

Abstract丗
Let s, t be 2A involutions of the Monster. It is well-known that s,t will generate a dihedral group of order less than or equal to 12. In this talk, we discuss certain subalgebras of the Moonshine VOA associated to these dihedral groups. We also use these subalgebras to interpret the famous McKay observations on Monster, Babymonster, and the Fischer group.

応強丗戝島媊幒乮C搹4奒乯

島墘幰丗Peter Fiebig (Freiburg 戝妛)

戣栚丂丗Bruhat graphs between representation theory and topology

Abstract:
We show how one can associate to any root system a labelled graph that encodes the intersection cohomology of Schubert varieties as well as the structure of projective objects in various representation theoretic categories. Then we discuss how this can be used to prove various multiplicity conjectures in representation theory.

応強丗戝島媊幒乮C搹係奒 乯

島墘幰丗Michael McQuillan乮University of Glasgow, Scotland乯

戣栚丗Measuring the Unmeasurable

Abstract:
Mathematics may usefully be compared to the Matrix in the film of the same name. In particular, its object is to enslave mathematicians. Some mathematicians have, however, worked extensively to free others from this slavery. Particularly notable in this respect is Alexander Grothendieck. Sadly, there is a common misconception that his wide ranging ideas are something specific to algebraic geometry, rather than a broad set of categorical and functorial principles that encompass all geometry. As an illustration of this, we will apply his ideas to measure theory, so as to measure the un-measurable.
n.b. Watching the film Matrix is essential to a sound understanding of this talk.

応強丗戝島媊幒乮C搹係奒 乯

島墘幰丗拞堜塸堦乮戝嶃嫵堢戝妛乯

戣栚丗丗Hardy spaces with variable exponent

Abstract:
Let $X=(X,d,\mu)$ be a space of homogeneous type. In this talk we define a generalized Hardy space $H^{p(\cdot)}(X)$ with variable exponent and prove that the dual of $H^{p(\cdot)}(X)$ is a generalized Lipschitz space $\Lip_{\alpha(\cdot)}(X)$.