Graduate School of Information Sciences, Tohoku University Geometry and Analysis Seminar ENGLISH GSIS RCPAM ACCESS ABOUT THE SEMINAR

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2017Nx

1. 2017N 623ij15:00 -- 16:30, 2Ku
镔 u iꋴwoϊwȁj
^CgFfBbNɑ΂郂[XEtA[zW[

Abstract:
ϕƂĒ莮RpNgl̏̔fBbNɑ΂āA [XEtA[^̃zW[l@B zW[̍\т͔̖̐ɂU镑ɈˑB Q葬傷DQAQIɐU镑Q߂Q̂ꂼ ̏ꍇɃzW[̍\̊TvƂ̌vZ@ЉB pƂāAfBbN̉̑ݒ藝B

2. 2017N 531ij15:00 -- 16:30, 2Ku
Jn q ikww@Ȋwȁj
̈ɂ񑊌ŗLlɂ

Abstract:
vXpfʂ̓Kȉ~^pf̌ŗLl̗̈lXȐۓɑ΂ Ăǂ̂悤ɕω邩Ƃ Courant-Hilbert ̐Iȗdvȉ łDɗ̈钴Ȗʂɑމꍇł锖̈ɂ郉vX pf̌ŗLlɊւẮCSchatzman(1996)_-qc(2016)ȂǂɂėlX ȋEɂďڍׂɌĂ邪Cv̌W敪IȒ萔֐ł ȉ~^pf̔̈ɂŗLlɂĂ͌W̕sA炱 Ŗ炩ɂĂȂD{uł͂̂悤Ȕ̈ɂ񑊌ŗLl ɂčl@CW̕sAёމ̒Ȗʂ̊􉽊wI󂪌ŗLl̑Qߋ ΂Ăǂ̂悤ȉeyڂ̂ɂēꂽʂЉD

2016Nx

3. 2017N 316i؁j15:00 -- 16:30, 2Ku
Fc i{wwj
Finite gap solutions for horizontal minimal surfaces of finite type in 5-sphere

Abstract:

* {u tR~j}bNX/׋ (316-17) Ƃ̋ÂłD

4. 2017N 2 3ij15:00 -- 16:30, 2Ku
Tv iwHj
퐔 0 ̃EBA^Ȗʂ̑

Abstract:
ʂ 3[}l̂ɂċȖʐψƂ̉C EBAĊ֐̗ՊE_ƂȂȖ (EBA^ȖʂƌĂԂƂɂ) ݂̑ɂčlD ̋Ȗʐς͏\̂lCɎ퐔 0 ̋ȖʂD ̍uł́C[}l̂̃XJ[ȗމՊE_ꍇC ̓_ɋÏWEBA^Ȗʂ݂̑ʂ̕[}l̏ł EBA^Ȗʂ̑dݐȂǂɂċc_D ȂC{u A. Malchiodi (SNS Pisa) A. Mondino (Univ. of Warwick) Ƃ̋ɊÂD

5. 2017N 119i؁j15:00 -- 16:30, 2Ku
_ iwwȁj
Ricci \g̊􉽊w

Abstract:
1980N R. S. Hamilton ɂēꂽ Ricci t[͑l̏ Wvʂ̍\ɂđ傫Ȑ, 􉽊wɂvȓ ƂĂ̒nʂmBł G. Perelman ɂ Poincar\'{e} \z S. Brendle y R. Schoen ɂ\ʒ藝̉͋LɐVB Riemann l̏ Ricci \g Einstein l̂̎RȈʉł łȂ, Ricci t[̎ȑɑΉ, ̃t[̓ٓ_f ƂĎRɌdvȌΏۂłBRicci \g͐ŵ݂Ȃ炸 _ AdS/CFT ΉɂĂ̏dvwE, ߔNȌ sĂB{uł Riemann l̏ Ricci \gɏœ_𓖂, ̊{IȐЉ, u҂ʂɂĂbB ̓Iɂ Einstein l̂ɑ΂ Bonnet-Myers ̒藝 Hitchin-Thorpe sȂǂ̊{IȌʂ Ricci \gɑ΂Ăǂ̒xgo邩 bBԂ, ߔN Ricci t[ɑ΂錤̐_@ ƂēꂽX-Ricci \g quasi-Einstein l̂Ȃǂ ʉɑ΂Ăl̍l@݂B

6. 2016N1121ij14:00 -- 15:30, 6Ku
~ iHƑw_j
Onsager\zƂɊւ蓙Av܂܂

Abstract:
SŜ̉^xzĂƂ Euler ̐ϕۑ̔^ʑQ ${\rm Diff}_{\sigma}(M)$ n'' ƂȂBLl $M$ ̑nǂ''B A2l$M$̔^ʑQ͖A Euler ԑ̌ÓTBƂ낪A3ȏゾƂƂɓȂ iQx $\omega = \nabla \times u$ 2̏ꍇ̂݃XJ[ɂȂjB ƂŁAŵ݂Ȃ炸 Navier-Stokes pċLqƍlA Ɋւēv̗͊wIȊϓ_ Kolmogorov 1941NɊ dvȖ@𔭕\ĂBɐGĂ Onsager ͔ŜȂ EulerɊւ\z1949NɏqׂB ̗\zߔNoAł Littlewood-Paley _ uǂ{IvɗpAw҂̂ $e^{i\infty} \Doteq 0$ ̈Ӗ͖炩ɂĂ悤łB WIɂ́A̒ɗp鎎֐ł͑s\Ȃ̂A āȀ󋵂@I

7. 2016N1027i؁j13:30 -- 15:00, 2Ku
D h ikww@Ȋwȁj
nThCbƃvVA
(Ham sandwich and Laplacian)

Abstract:
vVǍŗL֐ɑ΂nThCb 藝pă[Nbhԓ̓ʗ̈̃vVA mC}ŗLlɊւĎ3̏ؖ̊TԂ͈ łbB
1. 萔{̈P
2. 萔{̈P
3. ŗLl̊Ԃ̕Օs

2015Nx

8. 2016N 3 4ij15:30 -- 16:30, 6K u [ύX]
Cristian Enache (Research Group of the project PN-II-ID-PCE-2012-4-0021, IMAR, Romania)
On some recent maximum principles for P-functions and their applications

Abstract:
In this talk we will discuss about some new maximum principles for P-functions and their applications to the study of partial differential equations. More exactly, we will show how one may employ such maximum principles in problems of physical or geometrical interest, in order to get a priori estimates, isoperimetric inequalities, symmetry results, convexity results, the shape of some free boundaries and Liouville type results.

9. 2016N 219ij16:30 -- 17:30, 6K u
Oc itwwȁj
On nonlinear Fermi Golden Rule

Abstract:
In this talk, we study the long time dynamics of small solutions of nonlinear Schrodinger equation. If the Schrodinger operator has more that 2 eigenvalues, there will be a nontrivial nonlinear interaction between the eigenvalues and continuous spectrum. Further, by this interaction, there will be no quasi-periodic solutions. I would like to explain the mechanism of this nonlinear interaction which is called Fermi Golden Rule.

10. 2016N 219ij 15:15 -- 16:15 [ԕύX], 6K u
V ikwȊwȁj
Shape Optimization Problems Considering Hydrodynamics Stability

Abstract:
The author is tackling to construct more versatile shape optimization methods controlling Hydrodynamics stability. So far, together with Prof. H. AZEGAMI, we suggested a pioneering shape optimization method by which the real part of the leading eigenvalues is defined as a cost function, and the critical Reynolds number is increased. However, the only disturbance with a maximum real part is used to evaluate the sensitivity in the method. Therefore, in the case that two and more unstable disturbances are growing up, the method is lack versatility. Wherein, the author suggest a new shape optimization method considering all the unstable disturbances.
In particular, disturbance momentum energy is defined as the cost function, and the stationary Navier-Stokes problem and the time evolution problem for nonlinear disturbances are used as main problems. The shape derivative of the cost function is defined as the Fréchet derivative of the cost function with respect to arbitrary variation of the design variable, which denotes the domain variation, and is evaluated using the Lagrange multiplier method. To obtain a numerical solution, the author uses an iterative algorithm based on the H1 gradient method using the finite element method. To confirm the validity of the solution, a numerical example for two-dimensional Cavity flow is presented.

11. 2016N 219ij 13:30 -- 15:00, 6 K u
y iQwHwȐȊwUj
Opюlʑ̏LagrangeԂ̌덷]ɂ
(Error estimates of the Lagrange interpolation on triangles and tetrahedrons)

Abstract:
Op܂͎lʑ̏LagrangeԂ̌덷]́Al͊wA Lvf@̌덷̗͂_ɂďdvȉۑłB]ALvf@ ̋ȏł́ALvf@Ŕ̉𐸓x悭ߎ邽߂ɂ́A ̈̎Opilʑ́jɎgOpilʑ́j͂Ȃׂuӂ 炵ẮvgׂłƂĂBŋ߂̍u҂̌ ŁA̔F͕KȂƂ킩ĂB
{uł́ALagrangeԂ̌덷]̗jTςAɍŋ߂̍u҂ ̌ʂ񍐂B܂ALagrangeԂ̌덷]ƋȖʂ̖ʐς̒ Ԃɂ֌WɂĂyB

12. 2015N1029i؁j 13:30-- , 2K u
{ ikwwȁj
Spectral convergence under bounded Ricci curvature

Abstract:
Riemann l̗̂񂪂قȋԂ Gromov-Hausdorff ƂC K؂ȋȗ̉̉ŁC֐ɍp郉vVÃXyNg 邱Ƃ킩ĂD {uł͔ɍp郉vVAlDɁCHodge vVAɂĂ $1$-ɂăXyNg̎C $3$ ȏł͂̃XyNg̎͊҂łȂƁC connection vVAɂĂ͑SĂ $k$-ɂăXyNg ̎邱ƂЉD

13. 2015N 9 8i΁j 14:00 -- , 2K u
Colette Anné (Université de Nantes, France)
Signature and the gap in the spectrum of the Hodge Laplacian

Abstract:
Gilles Carron proved that if the complete Riemannian manifold $M$ can be partitioned by a closed oriented hypersurface with non zero signature, then the spectrum of the Hodge Laplacian on $M$ is the all half line $[0, + \infty [.$ We present a result in the reciprocal way: If the closed Riemannian manifold $M$ can be partitioned by a closed oriented hypersurface with zero cohomological group in the middle degree, then one can construct on the corresponding $\Z$-covering a metric such that the spectrum of the Hodge Laplacian has as many gaps as we want.

14. 2015N 728i΁j 10:00 -- 12:00, 6K u
G (ȑw)
Generation of analytic semigroups on $L^p$ by scale-invariant elliptic operators

Abstract:
Paper: http://arxiv.org/abs/1405.5657v1
{uł́C$L^p=L^p(\R^N)$ɂ 2 Kȉ~^pf
$L=|x|^{\alpha}\Delta +c|x|^{\alpha-2}x\cdot\nabla -b|x|^{\alpha-2}$
ɂ͓IQ̐ɂčlD ŁC$N \in \N$, $1 < p < \infty$, $\alpha, c, b \in \R$ ƂD pf L ̓XP[ϊ ɂĒ萔ĕsςłD $\alpha=0$, $c=0$ ̏ꍇCL inverse square potential $|x|^{-2}$ Schrödinger pfłC̐s $\alpha \neq 0$ ̏ꍇ͊gUW $|x|^{\alpha}$ Ɍ_Ƌԉ ِ̂ŁCƂ b=c=0 łĂ L ̍pfƂĂ̐ eՂɂ͓ȂD {uł́CN, p ƍpf L ̃p[^$\alpha, c, b \in \R$ Ɋւ L ɂ͓IQ̐̕Kv\ꂽ̂ŁAɂĉD
{úCTgwGiorgio Metafune搶CChiara Spina搶C ȑw̉o搶Ƃ̋ɊÂD

15. 2015N 727ij16:00 -- 18:00, 2K u
o (ȑw)
Spectral theory of linear m-sectorial operators in Banach and Hilbert spaces -historical review-

Abstract:

16. 2015N 6 6iyj10:00 -- , 6K u
J W iwj
L^p-mapping properties for Schrodinger operators in open sets of R^d

Abstract: Paper:
uł, VfBK[pf̊֐$L^p$ԂɂLE ɂĉ. VfBK[pf H ȋłƂ, XyNg藝păVfBK[pf̊֐ f(H) $L^2$ ԏ̍pfƂĒł. Ɋ֐ f LEȂ, pf ֐ f(H) $L^2$ ԏŗLEł. , $L^p$ ($p \neq 2$) ŗLEɂȂ邩ۂ͎ł͂Ȃ. VfBK[pf̊֐ f(H) $L^p$LEɂĂ, SԂł͊ɌĂ, ֐Ԙ_ ΔɉpĂ. {uł, JWŒꂽV fBK[pfɑ΂, pf̊֐ f(H) $L^p$ LEl. |eV͉^|eV.
{u, Rov (w) Ɗ⟺i (sw) Ƃ ɊÂĂ.

17. 2015N 6 5ij13:00-- , 6K u
R ov iwj
Kirchhoff Gevrey
(Gevrey class solutions to the Kirchhoff equation)

Abstract: Paper: http://arxiv.org/abs/1508.05305
{ułKirchhoff̎ԑIGevrey̑ ɂĉBKirchhoff́A vɖm֐$L^2$ m|2KoȌ^ΔłẢ ̐Ucɑ傫ꍇɋߎꂽ^ƂāA 1883N G. Kirchhoff 񏥂BKirchhoff ȗ57N̔N o1940N S. Bernstein ͉݂̑ؖA35N 1975NAPohozhaev ʎBernsteiňʂgB Gevrey ͎͓INX $H^\infty$ NX̊ԂɂNX ł邪AKirchhoff Gevrey 𐫂͖ɉĂȂB ȂAlSobolevm\͂ʂB ؖ̌́AԂɈˑWoȌ^Δ ̃GlM[sKirchhoff̋Ǐ̎Ɋւ ォ̕]łB͔ؖw@ŐsB
{úAMichael Ruzhansky (Imperial College London) Ƃ ɊÂĂB

18. 2015N57i؁j13:00 -- 15:30, 6K u
Matthias Keller (Univ. Jena)
Intrinsic metric on graphs

Abstract:There are various results in Riemannian manifolds which are consequences of the close relationship between the Laplace- Beltrami operator and the Riemannian distance. For graphs many of these results fail to be true if one considers the combinatorial graph distance. Now by using the concept of intrinsic metrics re- cently introduced in the context of general regular Dirichlet forms by Frank/Lenz/Wingert analogous results can be proven in the context of weighted graphs. This solves various problems that have been open for several years and decades.

19. Vincenzo Ferone (Univ. di Napoli) Isoperimetric inequalities and symmetrization methods: an approach to PDE's and to functional inequalities

13 April 2015 (M), 13:30~15:00, Middle lecture room 2F GSIS
14 April 2015 (T), 15:00~18:00, Middle lecture room 2F GSIS
15 April 2015 (W), 15:00~18:00, Middle lecture room 2F GSIS

Abstract: The series of lectures will be devoted to give an introduction to the "so-called" symmetrization methods which have been successfully used in the study of solutions to elliptic and parabolic problems and in the study of functional inequalities. The starting point will be the classical isoperimetric inequality and Schwarz symmetrization. In particular, their role in the quoted contexts will be highlighted discussing some model results that nowadays can be considered classical. Typical questions which will be addressed are the following ones.
• Comparison results for nonlinear elliptic and parabolic partial differential equations.
• Existence and regularity for solutions to nonlinear elliptic and parabolic partial differential equations in the case of non-regular data.
• Isoperimetric inequalities concerning functionals of the Calculus of Variations and investigation about the best constants in functional inequalities.
• Optimization problems for functionals defined on classes of equimeasurable functions.
• Other symmetrization methods.
Some recent developments on the subject will be presented.

2014Nx

20. Andrea Colesanti (Univ. di Firenze) From the Brunn-Minkowski inequality to elliptic PDE's

9 March 2015 (M), 13:30~16:45, Conference room 2F GSIS
10 March 2015 (T), 13:30~16:45, Conference room 2F GSIS
11 March 2015 (W), 10:30~12:00, 13:30~15:00, Conference room 2F GSIS

Abstract: The main scope of this series of lectures is to describe in details the Brunn-Minkowski inequality, in the realm of Convex Geometry, and its links to the Calculus of Variations and elliptic PDE's. The first part will be dedicated to background material in Convex Geometry. In particular we will introduce the space of convex bodies (compact, convex subsets of the n-dimensional Euclidean space), along with basic tools like the Minkowski addition, the Hausdorff metric and the support function. We will then pass to the Brunn-Minkowski inequality, presenting its proof through the Prekopa-Leindler inequality, and describing how it is connected with other fundamental inequalities in analysis such the isoperimetric and the Poincare inequality. In the third part we will speak about functionals defined on the class of convex bodies that verify an inequality of Brunn-Minkowski type. This will create the main link with elliptic PDE's. Indeed many classical functionals, like the principal frequency of a domain, the Newtonian capacity and the torsional rigidity, verify an inequality of this type. We will present these examples in some details, explaining some of the techniques used to prove the corresponding Brunn-Minkowski inequality.

Overview of the course:

21. 2015N 127() 15:30 --- 16:30, 2K u
H aY (HƑwHw)
Harmonic maps between asymptotically hyperbolic manifolds

Abstract:
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2̑QߓIɑoȓI[}l$M, N$lC̊Ԃ̒aʑɑ΂ ɂDirichletlC̑ݒ藝ƈӐ藝ЉD Ń^[Qbgl$N$͔񐳋ȗ肵CEʑ$C^1$ ̃GlM[xƂŏȂꍇlĂD X̌ʂLi-Tam̑oȋԂ̊Ԃ̒aʑɑ΂錋ʂ̈ʉ^D $M, N$̃g|W[͑lŁC͂܂LEells-Sampsoňʂ RpNgłƂ􂹂邱ƂɒӂĂD

22. 2015N 126() 13:30 --- 17:00, 6 Ku
H aY (HƑwHw)
The Yamabe invariant and singular Einstein metrics

Abstract:
̍üꕔ́CGilles Carron (ig) Rafe Mazzeo (X^tH[h) Ƃ̋ɊÂĂD
Rӂ̖(wǃ[}I)xԂƌĂ΂ً $(X, d, \mu)$ ŒC̎RӒ萔 $Y(X, d, \mu)$ ыǏRӒ萔 $Y_{\ell}(X, d, \mu)$ `CAubin^̕s
Y(X, d, \mu) \leq Y_{\ell}(X, d, \mu)\ (\, \leq Y(S^n) \,)
D ǏRӒ萔$Y_{\ell}(X, d, \mu)$́C$X$ (ɂ͈ˑ)ٕ̂ Ō܂萔łD āC$(X, d, \mu)$ ʏ $C^{\infty}$ l̂łꍇ́C $Y_{\ell}(X, d, \mu) = Y(S^n)$ łD L̕sstrictȕs $Y(X, d, \mu) < Y_{\ell}(X, d, \mu)$ łƂC Rӂ̖͉łD $Y(X, d, \mu) = Y_{\ell}(X, d, \mu)$ ̏ꍇ́Cًԏł Rӂ̖͈ʂɉł͂ȂƂmĂD

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The Geometry and Analysis Seminar at Research Center for Pure and Applied Mathematics (RCPAM) GSIS Tohoku University takes place in the Graduate School of Information Sciences (GSIS) building Tohoku University at Sendai. The Seminar will deal with the topics in Geometry and Analysis, as well as their interactions emphasising the ideas behind the theory. The audience includes graduate students, non-experts and experts, and we encourage active discussion during the seminar in a relaxed atmosphere.

The seminar is organised by Reika Fukuizumi, Kei Funano, Shigeru Sakaguchi, Junya Takahashi.