過去の記録 ~05/23本日 05/24 | 今後の予定 05/25~



15:00-17:30   数理科学研究科棟(駒場) 056号室
Nicolai Reshetikhin 氏 (University of California, Berkeley)
Introduction to BV quantization I (ENGLISH)
[ 講演概要 ]
The lectures will focus on Batalin-Vilkovisky (BV) framework for gauge field theories. We will start with examples of gauge theories such Yang-Mills, BF-theory, Chern-Simons and others. The Hamiltonian structure for field theories will be explained on these examples. Then the classical BV-BFV (Batalin-Fradkin-Vilkovisky) setting will be introduced as a Z-graded extension of the Hamiltonian structure of field theories. The AKSZ (Aleksandrov-Kontsevich-Swartz-Zaboronskij) construction of topological field theories will be introduced. We will construct corresponding BV-BFV theory and its extension to strata of all codimensions. We will also see that Chern-Simons theory, BF theory are of the AKSZ type. The geometry of BV theories is also known as derived geometry. The classical part will be followed by an outline of what is a quantum gauge theory and what is a path integral quantization of a classical gauge theory in the BV-BFV setting. Then we will discuss BV-integrals, fibered BV integrals and perturbative quantization.
[ 講演参考URL ]


15:00-16:30   数理科学研究科棟(駒場) 128号室
Jens Starke 氏 (Queen Mary University of London)
Implicit multiscale analysis of the macroscopic behaviour in microscopic models (ENGLISH)
[ 講演概要 ]
A numerical multiscale approach (equation-free analysis) is further improved in the framework of slow-fast dynamical systems and demonstrated for the example of a particle model for traffic flow. The method allows to perform numerical investigations of the macroscopic behavior of microscopically defined systems including continuation and bifurcation analysis on the coarse or macroscopic level where no explicit equations are available. This approach fills a gap in the analysis of many complex real-world applications including particle models with intermediate number of particles where the microscopic system is too large for a direct numerical analysis of the full system and too small to justify large-particle limits.
An implicit equation-free method is presented which reduces numerical errors of the equation-free analysis considerably. It can be shown that the implicitly defined coarse-level time stepper converges to the true dynamics on the slow manifold. The method is applied to perform a coarse bifurcation analysis of microscopic particle models describing car traffic on single lane highways. The results include an equation-free continuation of traveling wave solutions, identification of bifurcations as well as two-parameter continuations of bifurcation points. This is joint work with Christian Marschler and Jan Sieber.
[ 講演参考URL ]


17:00-17:50   数理科学研究科棟(駒場) 002号室
Hans-Otto Walther 氏 (University of Giessen)
Shilnikov chaos due to state-dependent delay, by means of the fixed point index (ENGLISH)


16:50-18:20   数理科学研究科棟(駒場) 126号室
David Sauzin 氏 (CNRS, France)
Nonlinear analysis with endlessly continuable functions (joint work with Shingo Kamimoto) (English)
[ 講演概要 ]
We give estimates for the convolution products of an arbitrary number of endlessly continuable functions. This allows us to deal with nonlinear operations for the corresponding resurgent series, e.g. substitution into a convergent power series.



17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea : Common Room 16:30 -- 17:00
齋藤 翔 氏 (カブリ数物連携宇宙研究機構)
Delooping theorem in K-theory (JAPANESE)
[ 講演概要 ]
There is an important special class of infinite dimensional vector spaces, formed by those called Tate vector spaces. Since their first appearance in Tate’s work on residues of differentials on curves, they have been playing important roles in several different contexts including the study of formal loop spaces and semi-infinite Hodge theory. They have more sophisticated linear algebraic invariant than finite dimensional vector spaces, for instance the dimension of a Tate vector spaces is not a single integer, but a torsor acted upon by the all integers, and the determinant of an automorphism is not a single invertible scalar, but a torsor acted upon by the all invertible scalars. In this talk I will show how a delooping theorem in K-theory provides a clarified perspective on this phenomenon, using the recently developed higher categorical framework of infinity-topoi.


13:30-14:30   数理科学研究科棟(駒場) 056号室
※ 通常と時間が異なります。
Mohammad Hassan Farshbaf Shaker 氏 (Weierstrass Institute, Berlin)
Multi-material phase field approach to structural topology optimization and its relation to sharp interface approach (English)
[ 講演概要 ]
A phase field approach for structural topology optimization which allows for topology changes and multiple materials is analyzed. First order optimality conditions are rigorously derived and it is shown via formally matched asymptotic expansions that these conditions converge to classical first order conditions obtained in the context of shape calculus. Finally, we present several numerical results for mean compliance problems and a cost involving the least square error to a target displacement. This is joint work with Luise Blank, Harald Garcke and Vanessa Styles.



16:50-18:20   数理科学研究科棟(駒場) 128号室
石渡 聡 氏 (山形大学理学部)
Heat kernel on connected sums of parabolic manifolds (日本語)


10:30-12:00   数理科学研究科棟(駒場) 128号室
丸亀 泰二 氏 (東京大学)
On the volume expansion of the Blaschke metric on strictly convex domains
[ 講演概要 ]
The Blaschke metric is a projectively invariant metric on a strictly convex domain in a projective manifold, which is a real analogue of the complete Kahler-Einstein metric on strictly pseudoconvex domains. We consider the asymptotic expansion of the volume of subdomains and construct a global conformal invariant of the boundary. We also give some variational formulas under a deformation of the domain.


15:30-17:00   数理科学研究科棟(駒場) 122号室
Evangelos Routis 氏 (IPMU)
Weighted Compactifications of Configuration Spaces (English)
[ 講演概要 ]
In the early 90's, Fulton and MacPherson provided a natural and beautiful way of compactifying the configuration space F(X,n) of n distinct labeled points on an arbitrary nonsingular variety. In this talk, I will present an alternate compactification of F(X,n), which generalizes the work of Fulton and MacPherson and is parallel to Hassett's weighted generalization of the moduli space of n-pointed stable curves. After discussing its main properties, I will give a presentation of its intersection ring and as an application, I will describe the intersection ring of Hassett's spaces in genus 0. Finally, as time permits, I will discuss some additional moduli problems associated with weighted compactifications.



13:00-18:00   数理科学研究科棟(駒場) 128号室
加藤 睦也 氏 (名古屋大学) 13:30-15:00
Embedding relations between $L^p$--Sobolev and $\alpha$--modulation spaces
[ 講演概要 ]
$\alpha$--モジュレーション空間($0 \leq \alpha \leq 1$)はGr\"obnerによって導入された空間であり、モジュレーション空間は$\alpha=0$の特別な場合である。
本講演で は$\alpha$--モジュレーション空間と$L^p$--ソボレフ空間($1 \leq p \leq \infty$)との包含関係について紹介する。
モジュレーション空間とソボレフ空間との包含関係は Kobayashi--
Sugimotoによって最適なものが得られており、今 回の結果は$\alpha=0$としたときに彼らのものと完全に一致する。また、時間が許せば局所ハーディー空間と$\alpha$--モジュレーション空間との関係についても紹介したい。
冨田 直人 氏 (大阪大学) 15:30-17:00
[ 講演概要 ]
ここで現れた滑らかさn/2, n/p-n/2というオーダーは最小であることが知られている.そして,双線形の場合には,この線形の場合に対応する結果を,宮地晶彦氏との共同研究で得ていた.
結果としては,線形,双線形の場合の一般化ではあるが,これらの場合の議論をそのまま焼き直せばよいという単純なものではないことをお話したい.なお,この講演は,L. Grafakos氏,宮地晶彦氏,H. Nguyen氏との共同研究に基づく.



10:00-11:30   数理科学研究科棟(駒場) 126号室
高橋良輔 氏 (名古屋大学 多元数理科学研究科)
ケーラー・リッチソリトンの漸近的安定性 (Japanese)
[ 講演概要 ]
ケーラー・リッチソリトンは,Hamilton のリッチフローのような幾何解析に起源をもつ Fano 多様体上の標準計量であり,ここ数年広範囲に渡って研究されてきた.標準計量の存在は何らかの幾何学的不変式論的安定性と密接に関係することが期待されている.例えば,Donaldsonは,スカラー曲率一定ケーラー計量を許容しかつ自己同型群が離散な任意の偏極多様体は balanced 計量の列を持ち,さらにこの列はスカラー曲率一定ケーラー計量に収束することを証明した.本講演では,同じような結果がケーラー・リッチソリトンに対しても成り立つことを説明する.なお,この結果は Berman-Witt Nystr¥"om の先行結果を一般化するものであり,端的ケーラー計量の漸近的相対 Chow 安定性に関する満渕氏の結果の類似を与えている.



17:00-18:00   数理科学研究科棟(駒場) 056号室
Alan Lauder 氏 (University of Oxford)
Stark points and p-adic iterated integrals attached to modular forms of weight one (English)
[ 講演概要 ]
Given an elliptic curve over Q the only well-understood construction of global points is that of "Heegner points", which are defined over ring class fields of imaginary quadratic fields and are non-torsion only in rank one settings. I will present some new constructions and explicit formulae, in situations of rank one and two, of global points over ring class fields of real or imaginary quadratic fields, cyclotomic fields, and extensions of Q with Galois group A_4, S_4 or A_5. Our constructions and formulae are proven in certain cases - when they can be related to Heegner points - and conjectural, but supported by experimental evidence, otherwise. This is joint work with Henri Darmon and Victor Rotger.



10:30-11:30   数理科学研究科棟(駒場) 056号室
Tuomo Kuusi 氏 (Aalto University)
Nonlocal self-improving properties (English)
[ 講演概要 ]
The classical Gehring lemma for elliptic equations with measurable coefficients states that an energy solution, which is initially assumed to be $W^{1,2}$-Sobolev regular, is actually in a better Sobolev space space $W^{1,q}$ for some $q>2$. This is a consequence of a self-improving property that so-called reverse Hölder inequality implies. In the case of nonlocal equations a self-improving effect appears: Energy solutions are also more differentiable. This is a new, purely nonlocal phenomenon, which is not present in the local case. The proof relies on a nonlocal version of the Gehring lemma involving new exit time and dyadic decomposition arguments. This is a joint work with G. Mingione and Y. Sire.


16:50-18:20   数理科学研究科棟(駒場) 126号室
Otto Liess 氏 (University of Bologna, Italy)
On the Phragmén-Lindelöf principle for holomorphic functions and factor classes of higher order complex forms in several complex variables
[ 講演概要 ]
In this talk we will discuss maximum principles in unbounded domains in one or several complex variables. We will mainly be interested in these principles for plurisubharmonic (in the one-dimensional case, "subharmonic") or holomorphic functions, when the principles are of
Phragmen-Lindel{\"o}f principle (henceforth called "PL") type. It will turn out that for 2 or more complex variables it will be useful to study our principles together with associated principles for factor classes of complex (0,q) forms with growth type conditions at infinity.
In this abstract we only say something concerning the case of functions. We consider then an open set U in C^n in one or several complex variables. We assume that we are given two real-valued continuous functions f and g on U. We say that PL holds for plurisubharmonic (respectively for holomorphic) functions, if the following implication is true for every plurisubharmonic function $ \rho $ (respectively for every $ \rho $ of form log |h| with h holomorphic) on U: if we know that $ \rho \leq f$ on the boundary of U and if $ (\rho - f)$ is bounded on U, then it must follow that $ \rho \leq g$ on U. ($\rho \leq f$ on the boundary has the following meaning: for ever z in the boundary of U and for every sequence of points y_j in U which tends to z, we have limsup (\rho - f)(y_j) leq 0.) A trivial condition under which PL is true, is when there exists a plurisubharmonic function u on U such that
(*) -g(z) \leq u(z) \leq - f(z) for every z in U.
In fact, if such a function exists, then we can apply the classical maximal principle for unbounded domains to the function $ \rho'= \rho+u$ to obtain at first $ \rho' \leq 0$ and then $ \rho \leq - u \leq g$. It is one of the main goals of the talk to explain how far (*) is from being also a necessary condition for PL. Some examples are intended to justify our approach and applications will be given to problems in convex analysis.



10:30-12:00   数理科学研究科棟(駒場) 128号室
後藤 竜司 氏 (大阪大学)
Flat structures on moduli spaces of generalized complex surfaces
[ 講演概要 ]
The 2 dimensional complex projective space $P^2$ is rigid as a complex manifold, however $P^2$ admits 2 dimensional moduli spaces of generalized complex structures which has a torsion free flat connection on a open strata. We show that logarithmic generalized complex structure with smooth elliptic curve as type changing loci has unobstructed deformations which are parametrized by an open set of the second de Rham cohomology group of the complement of type changing loci. Then we will construct moduli spaces of generalized del Pezzo surfaces. We further investigate deformations of logarithmic generalized complex structures in the cases of type changing loci with singularities. By using types of singularities, we obtain a stratification of moduli spaces of generalized complex structures on complex surfaces and it turns out that each strata corresponding to nodes admits a flat torsion free connection.


16:50-18:20   数理科学研究科棟(駒場) 128号室
齊藤 圭司 氏 (慶應義塾大学理工学部)
[ 講演概要 ]



16:50-17:50   数理科学研究科棟(駒場) 大講義室号室
Gerhard Huisken 氏 (The Mathematisches Forschungsinstitut Oberwolfach )
Mean curvature flow with surgery
[ 講演概要 ]
We study the motion of hypersurfaces in a Riemannian manifold
with normal velocity equal to the mean curvature of the
evolving hypersurface. In general this quasilinear, parabolic
evolution system may have complicated singularities in finite time.
However, under natural assumptions such as embeddedness of the surface
and positivity of the mean curvature (case of 2-dimensional surfaces)
all singularities can be classified and developing "necks" can be
removed by a surgery procedure similar to techniques employed
by Hamilton and Perelman in the Ricci-flow of Riemannian metrics.
The lecture describes results and techniques for mean curvature flow
with surgery developed in joint work with C. Sinestrari and S. Brendle.
[ 講演参考URL ]


16:00-17:00   数理科学研究科棟(駒場) 126号室
Damiran Tseveennamjil 氏 (モンゴル生命科学大学)
Twistor理論からみた一般Schlesinger系の合流 (JAPANESE)
[ 講演概要 ]



15:00-16:10   数理科学研究科棟(駒場) 052号室
Stefano Iacus 氏 (University of Milan)
The use of S4 classes and methods in the Yuima R package
[ 講演概要 ]
In this talk we present the basic concept of S4 classes and methods approach for object oriented programming in R. As a working example, we introduce the structure of the Yuima package for simulation and inference of stochastic differential equations. We will describe the basic classes and objects as well as some recent extensions which allows for Carma and Co-Garch processes handling in Yuima.


14:00-15:30   数理科学研究科棟(駒場) 002号室
Simon Wood 氏 (The Australian National University)
Classifying simple modules at admissible levels through
symmetric polynomials (ENGLISH)
[ 講演概要 ]
From infinite dimensional Lie algebras such as the Virasoro
algebra or affine Lie (super)algebras one can construct universal
vertex operator algebras. These vertex operator algebras are simple at
generic central charges or levels and only contain proper ideals at so
called admissible levels. The simple quotient vertex operator algebras
at these admissible levels are called minimal model algebras. In this
talk I will present free field realisations of the universal vertex
operator algebras and show how they allow one to elegantly classify
the simple modules over the simple quotient vertex operator algebras
by using a deep connection to symmetric polynomials.



17:00-18:30   数理科学研究科棟(駒場) 126号室
Alexander Voronov 氏 (Univ. of Minnesota)
Operads and their applications to Mathematical Physics (ENGLISH)
[ 講演参考URL ]



17:00-18:30   数理科学研究科棟(駒場) 126号室
Alexander Voronov 氏 (Univ. of Minnesota)
Operads and their applications to Mathematical Physics (ENGLISH)
[ 講演参考URL ]


15:30-16:30   数理科学研究科棟(駒場) 056号室
Zhi Chen 氏 (Hefei University of Technology)
Lifting of maps between surfaces (ENGLISH)
[ 講演概要 ]
The Thom conjecture says the algebraic curves have minimal genus among those surfaces Imbedded in CP^2 having fixed degree. This conjecture was solved by Kronheimer and Mrowka by using Seiberg-Witten invariants. In this talk we try to understand the content of this conjecture. We will construct these imbedded surface with minimal genus explicitly, and present some kind of generalization of this conjecture.
[ 講演参考URL ]



17:00-18:00   数理科学研究科棟(駒場) 056号室
Emmanuel Ullmo 氏 (IHES)
The hyperbolic Ax-Lindemann conjecture (English)
[ 講演概要 ]
The hyperbolic Ax Lindemann conjecture is a functional transcendental statement which describes the Zariski closure of "algebraic flows" on Shimura varieties. We will describe the proof of this conjecture and its consequences for the André-Oort conjecture. This is a joint work with Bruno Klingler and Andrei Yafaev.



10:30-11:30   数理科学研究科棟(駒場) 056号室
Monika Muszkieta 氏 (Wroclaw University of Technology)
Duality based approaches to total variation-like flows with applications to image processing (English)
[ 講演概要 ]
During the last years, total variation models have became very popular in image processing and analysis. They have been used to solve such problems as image restoration, image deblurring or image inpainting. Their interesting and successful applications became the motivation for many authors to rigorous analysis of properties of solutions to the corresponding total variation flows. The main difficulty in numerical approximation of solutions to these flows is caused by the lack of di fferentiability of the total variation term, and the commonly used approach to overcome this difficulty consists in considering of the dual formulation. In the talk, we consider two total variation flow models. The first one is the anisotropic total variation flow on $L^2$ with additional regularization, and the second one, is the total variation flow on $H^{-s}$. We introduce duality based numerical schemes for approximate solutions to corresponding equations and present some applications to image processing.
This talk is based on joint work with Y. Giga, P. Mucha and P. Rybka.

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