過去の記録 ~06/12本日 06/13 | 今後の予定 06/14~


17:00-18:10   数理科学研究科棟(駒場) 056号室
Ioane Muni Toke 氏 (University of New Caledonia)
Order flow intensities for limit order book modelling
[ 講演概要 ]
Limit order books are at the core of electronic financial markets. Mathematical models of limit order books use point processes to model the arrival of limit, market and cancellation orders in the order book, but it is not clear what a "good" parametric model for the intensities of these point processes should be.

In the first part of the talk, we show that despite their simplicity basic Poisson processes can be used to accurately model a few features of the order book that more advanced models reproduce with volume-dependent intensities.

In the second part of the talk we present ongoing investigations in a more advanced statistical modelling of these order flow intensities using in particular normal mixture distributions and exponential models.



17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea : Common Room 16:30 -- 17:00
片長 敦子 氏 (信州大学)
Topology of some three-dimensional singularities related to algebraic geometry (ENGLISH)
[ 講演概要 ]
In this talk, we deal with hypersurface isolated singularities. First, we will recall
some topological results of singularities. Next, we will sketch the classification of
singularities in algebraic geometry. Finally, we will focus on the three-dimensional
case and discuss some results obtained so far.


18:00-19:00   数理科学研究科棟(駒場) 117号室
Dennis Gaitsgory 氏 (Harvard University & IHES)
The Tamagawa number formula over function fields. (English)
[ 講演概要 ]
Let G be a semi-simple and simply connected group and X an algebraic curve. We consider $Bun_G(X)$, the moduli space of G-bundles on X. In their celebrated paper, Atiyah and Bott gave a formula for the cohomology of $Bun_G$, namely $H^*(Bun_G)=Sym(H_*(X)\otimes V)$, where V is the space of generators for $H^*_G(pt)$. When we take our ground field to be a finite field, the Atiyah-Bott formula implies the Tamagawa number conjecture for the function field of X.

The caveat here is that the A-B proof uses the interpretation of $Bun_G$ as the space of connection forms modulo gauge transformations, and thus only works over complex numbers (but can be extend to any field of characteristic zero). In the talk we will outline an algebro-geometric proof that works over any ground field. As its main geometric ingredient, it uses the fact that the space of rational maps from X to G is homologically contractible. Because of the nature of the latter statement, the proof necessarily uses tools from higher category theory. So, it can be regarded as an example how the latter can be used to prove something concrete: a construction at the level of 2-categories leads to an equality of numbers.

(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)



10:30-12:00   数理科学研究科棟(駒場) 128号室
宮地 秀樹 氏 (大阪大学)
Towards the complex geometry of Teichmuller space with extremal length (English)
[ 講演概要 ]
In this talk, in aiming for studying a relation between the topological aspect and the complex analytical aspect of Teichmuller space, I will discuss a complex analytic property of extremal length functions. More precisely, I will give a concrete formula of the Levi form of the extremal length functions for ``generic” measured foliations and show that the reciprocal of the extremal length function is plurisuperharmonic. As a corollary, I will give alternate proofs of S. Krushkal results that the distance function for the Teichmuller distance is plurisubharmonic, and Teichmuller space is hyperconvex. If time permits, I will give a topological description of the Levi form with using the Thurston's symplectic form.


15:00-16:00,16:30-17:00   数理科学研究科棟(駒場) 大講義室号室
Yakov Eliashberg 氏 (Stanford University)
Crossroads of symplectic rigidity and flexibility (ENGLISH)
[ 講演概要 ]
The development of flexible and rigid sides of symplectic and contact topology towards each other shaped this subject since its inception, and continues shaping its modern development.
In the series of lectures I will discuss the history of this struggle, as well as describe recent breakthroughs on the flexible side.
[ 参考URL ]


15:30-17:00   数理科学研究科棟(駒場) 122号室
Artan Sheshmani 氏 (IPMU/ Ohio State University)
Counting curves on surface in Calabi-Yau threefolds and the proof of S-duality modularity conjecture (English)
[ 講演概要 ]
I will talk about recent joint works with Amin Gholampour, Richard Thomas and Yukinobu Toda, on an algebraic-geometric proof of the S-duality conjecture in superstring theory, made formerly by physicists Gaiotto, Strominger, Yin, regarding the modularity of DT invariants of sheaves supported on hyperplane sections of the quintic Calabi-Yau threefold. Our strategy is to first use degeneration and localization techniques to reduce the threefold theory to a certain intersection theory over the relative Hilbert scheme of points on surfaces and then prove modularity; More precisely, together with Gholampour we have proven that the generating series, associated to the top intersection numbers of the Hilbert scheme of points, relative to an effective divisor, on a smooth quasi-projective surface is a modular form. This is a generalization of the result of Okounkov-Carlsson, where they used representation theory and the machinery of vertex operators to prove this statement for absolute Hilbert schemes. These intersection numbers eventually, together with the generating series of Noether-Lefschetz numbers as I will explain, will provide the ingredients to achieve a complete algebraic-geometric proof of S-duality modularity conjecture.



13:00-18:00   数理科学研究科棟(駒場) 128号室
中村 昌平 氏 (首都大学東京) 13:30-15:00
The sufficient condition for the Fatou property of weighted block spaces
[ 講演概要 ]
In this talk, we discuss the weighted block space which corresponds to the predual space of the Samko type weighted Morrey space. Recently, Prof.s Sawano and Tanaka proved the Fatou property of unweighted block spaces.
Meanwhile, we proposed a new condition, so called the weighted integral condition, to show the boundedness of some classical operators on weighted Morrey spaces.
Our purpose is to prove that the weighted integral condition becomes a sufficient condition for the Fatou property of the weighted block space.
町原 秀二 氏 (埼玉大学) 15:30-17:00
[ 講演概要 ]



15:00-16:00,16:30-17:30   数理科学研究科棟(駒場) 大講義室号室
Yakov Eliashberg 氏 (Stanford University)
Crossroads of symplectic rigidity and flexibility (ENGLISH)
[ 講演概要 ]
The development of flexible and rigid sides of symplectic and contact topology towards each other shaped this subject since its inception, and continues shaping its modern development.
In the series of lectures I will discuss the history of this struggle, as well as describe recent breakthroughs on the flexible side.
[ 参考URL ]


10:00-11:30   数理科学研究科棟(駒場) 126号室
正井 秀俊 氏 (東京大学)
ランダム閉3次元写像トーラスの対称性について (Japanese)
[ 講演概要 ]



17:30-18:30   数理科学研究科棟(駒場) 056号室
Tea : Common Room 17:00 -- 17:30
五味 清紀 氏 (信州大学理学部)
Topological T-duality for "Real" circle bundle (JAPANESE)
[ 講演概要 ]
Topological T-duality originates from T-duality in superstring theory,
and is first studied by Bouwkneght, Evslin and Mathai. The duality
basically consists of two parts: The first part is that, for any pair
of a principal circle bundle with `H-flux', there is another `T-dual'
pair on the same base space. The second part states that the twisted
K-groups of the total spaces of principal circle bundles in duality
are isomorphic under degree shift. This is the most simple topological
T-duality following Bunke and Schick, and there are a number of
generalizations. The generalization I will talk about is a topological
T-duality for "Real" circle bundles, motivated by T-duality in type II
orbifold string theory. In this duality, a variant of Z_2-equivariant
K-theory appears.



15:30-17:00   数理科学研究科棟(駒場) 122号室
伊藤由佳理 氏 (名古屋大学)
3-dimensional McKay correspondence (English)
[ 講演概要 ]
The original McKay correspondence is a relation between group theory of a finite subgroup G of SL(2,C) and geometry of the minimal resolution of the quotient singularity by G, and was generalized several ways. In particular, 3-dimensional generalization was extended to derived categorical eqivalence and the G-Hilbert scheme was useful to explain the correspondence. However, most results hold only for abelian subgroups. In this talk, I would like to introduce an iterated G-Hilbert scheme and show more geometrical McKay correspondence for non-abelian subgroups.



15:30-17:00   数理科学研究科棟(駒場) 126号室
いつもと部屋と曜日が違います。The day of the week and room are different from usual.
大川新之介 氏 (阪大)
Compact moduli of marked noncommutative del Pezzo surfaces via quivers (English)
[ 講演概要 ]
I will introduce certain GIT construction via quivers of compactified moduli spaces of marked noncommutative del Pezzo surfaces. For projective plane, quadric surface, and those of degree 3, 2, 1, we obtain projective toric varieties of dimension 2, 3, 8, 9, 10, respectively. Then I will discuss relations with deformation theory of abelian categories, blow-up of noncommutative projective planes, and three-block exceptional collections due to Karpov and Nogin. This talk is based on joint works in progress with Tarig Abdelgadir and Kazushi Ueda.


16:00-17:30   数理科学研究科棟(駒場) 123号室
Henri Berestycki 氏 (フランス高等社会科学院(EHESS))
The effect of a line with fast diffusion on Fisher-KPP propagation (ENGLISH)
[ 講演概要 ]
I will present a system of equations describing the effect of inclusion of a line (the "road") with fast diffusion on biological invasions in the plane. Outside of the road, the propagation is of the classical Fisher-KPP type. We find that past a certain precise threshold for the ratio of diffusivity coefficients, the presence of the road enhances the speed of global propagation. I will discuss several further effects such as transport or reaction on the road. I will also discuss the influence of various parameters on the asymptotic behaviour of the invasion speed and shape. I report here on results from a series of joint works with Jean-Michel Roquejoffre and Luca Rossi.



10:30-12:00   数理科学研究科棟(駒場) 128号室
下部 博一 氏 (大阪大学)
A class of non-Kahler manifolds (Japanese)
[ 講演概要 ]
We consider a special case of compact complex manifolds which are said to be super strongly Gauduchon manifolds. A super strongly Gauduchon manifold is a complex manifold with a super strongly Gauduchon metric. We mainly consider non-Kähler super strongly Gauduchon manifolds. We give a cohomological condition for a compact complex manifold to have a super strongly Gauduchon metric, and give examples of non-trivial super strongly Gauduchon manifolds from nil-manifolds. We also consider its stability under small deformations and proper modifications of super strongly Gauduchon manifolds.


16:50-18:20   数理科学研究科棟(駒場) 128号室
久保田 直樹 氏 (日本大学理工学部)
Concentrations for the travel cost of the simple random walk in random potentials

[ 講演概要 ]
そこで本講演では到達コストに対するconcentration inequalityを取り扱うことで,



15:00-16:15   数理科学研究科棟(駒場) 128号室
Arnaud Ducrot 氏 (University of Bordeaux)
Asymptotic behaviour of a nonlocal logistic equation (ENGLISH)
[ 講演概要 ]
In this talk we consider a nonlocal logistic equation endowed with periodic boundary conditions modelling the motion of cells. This equation takes into account birth and death process using a simple logistic effect while the motion of particles follows a nonlocal Darcy law with a smooth kernel.
We first investigate the well-posedness of the problem before investigating the long time behaviour of the solutions. The lack of asymptotic compactness of the semiflow is overcome by using a Young measure framework. Using a suitable energy functional, we
establish the convergence of the solutions with respect to the Young measure topology.
[ 参考URL ]


16:30-17:45   数理科学研究科棟(駒場) 128号室
Peter Bates 氏 (Michigan State University)
How should a drop of liquid on a smooth curved surface move in zero gravity? (ENGLISH)
[ 講演概要 ]
Questions such as this may be formulated as questions regarding solutions to nonlinear evolutionary partial differential equations having a small coefficient on the leading order derivative term. Evolutionary partial differential equations may be regarded as (semi-) dynamical systems in an infinite-dimensional space. An abstract theorem is proved giving the existence of an invariant manifold for a semi-dynamical system when an approximately invariant manifold exists with a certain topological nondegeneracy condition in a neighborhood. This is then used to prove the existence of eternal solutions to the nonlinear PDE and answer the question about the motion of a droplet on a curved manifold. The abstract theorem extends fundamental work of Hirsch-Pugh-Shub and Fenichel on the perturbation of invariant manifolds from the 1970's to infinite-dimensional semi-dynamical systems.
This represents joint work with Kening Lu and Chongchun Zeng.
[ 参考URL ]



14:55-16:40   数理科学研究科棟(駒場) 128演習室号室
大泉嶺 氏 (厚生労働省)
r/K選択説における確率制御理論の応用 (JAPANESE)
[ 講演概要 ]
r/K 選択説が提唱されてから半世紀になろうとしている.この仮説は生物の生活


16:45-18:15   数理科学研究科棟(駒場) 118号室
酒匂宏樹 氏 (新潟大)
Uniformly locally finite metric spaces and Folner type conditions



18:00-19:00   数理科学研究科棟(駒場) 002号室
朝倉政典 氏 (北海道大学)
On the period conjecture of Gross-Deligne for fibrations (English)
[ 講演概要 ]
The period conjecture of Gross-Deligne asserts that the periods of algebraic varieties with complex multiplication are products of values of the gamma function at rational numbers. This is proved for CM elliptic curves by Lerch-Chowla-Selberg, and for abelian varieties by Shimura-Deligne-Anderson. However the question in the general case is still open. In this talk, we verify an alternating variant of the period conjecture for the cohomology of fibrations with relative multiplication. The proof relies on the Saito-Terasoma product formula for epsilon factors of integrable regular singular connections and the Riemann-Roch-Hirzebruch theorem. This is a joint work with Javier Fresan.

(本講演は「東京北京パリ数論幾何セミナー」として, インターネットによる東大数理, Morningside Center of MathematicsとIHESの双方向同時中継で行います.)


17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea : Common Room 16:30 -- 17:00
Yuanyuan Bao 氏 (東京大学大学院数理科学研究科)
Heegaard Floer homology for graphs (JAPANESE)
[ 講演概要 ]
Ozsváth and Szabó defined the Heegaard Floer homology (HF) for a closed oriented 3-manifold. The definition was then generalized to links embedded in a 3-manifold and the manifolds with boundary (sutured and bordered manifolds). In the case of links, there is a beautiful combinatorial way to rewrite the original definition of HF, which was defined on a Heegaard diagram of the given link, by using grid diagram. For a balanced bipartite graph, we defined its Heegaard diagram and the HF for it. Around the same time, Harvey and O’Donnol defined the combinatorial HF for transverse graphs (see the definition in [arXiv:1506.04785v1]). In this talk, we compare these two methods.


15:00-16:30   数理科学研究科棟(駒場) 056号室
Jianfeng Lin 氏 (UCLA)
The unfolded Seiberg-Witten-Floer spectrum and its applications
[ 講演概要 ]
Following Furuta's idea of finite dimensional approximation in
the Seiberg-Witten theory, Manolescu defined the Seiberg-Witten-Floer
stable homotopy type for rational homology three-spheres in 2003. In
this talk, I will explain how to construct similar invariants for a
general three-manifold and discuss some applications of these new
invariants. This is a joint work with Tirasan Khandhawit and Hirofumi



15:30-17:00   数理科学研究科棟(駒場) 122号室
Lawrence Ein 氏 (University of Illinois at Chicago)
Asymptotic syzygies and the gonality conjecture (English)
[ 講演概要 ]
We'll discuss my joint work with Lazarsfeld on the gonality conjecture about the syzygies of a smooth projective curve when it is embedded into the projective space by the complete linear system of a sufficiently very ample line bundles. We'll also discuss some results about the asymptotic syzygies f higher dimensional varieties.


10:30-12:00   数理科学研究科棟(駒場) 128号室
松本 和子 氏 (東京理科大学)
The Fubini-distance functions to pseudoconvex domains in $\mathbb{C}\mathbb{P}^2$ (Japanese)
[ 講演概要 ]
In this talk, we would like to present two explicit formulas for the Levi forms of the Fubini-Study distance functions to complex or real hypersurfaces in $\mathbb{C}\mathbb{P}^2$. This is the first step for us to approach the non-existence conjecture of Levi-flat real hypersurfaces in $\mathbb{C}\mathbb{P}^2$. We would like to also discuss a certain important quantity found in the formulas.


16:30-18:00   数理科学研究科棟(駒場) 056号室
Fredrik Lindgren 氏 (大阪大学)
Numerical approximation of spinodal decomposition in the presence of noise (English)
[ 講演概要 ]
Numerical approximations of stochastic partial differential equations (SPDE) has evolved to a vivid subfield of computational mathematics in the last decades. It poses new challenges both for numerical analysis and the theory of SPDE.

In this talk we will discuss the strength and weaknesses of the \emph{semigroup approach} to SPDE when it is combined with the idea of viewing a single-step method in time as a \emph{rational approximation of a semigroup}. We shall apply this framework to the stochastic Allen-Cahn equation, a parabolic semi-linear SPDE where the non-linearity is non-globally Lipschitz continuous, but has a \emph{one-sided Lipschitz condition}, and the deterministic equation has a Lyapunov functional.

We focus on semi-discretisation in time, the first step in Rothe's method, and show how the semigroup approach allows for convergence proofs under the assumption that the numerical solution admits moment bounds. However, this assumption turns out to be difficult to verify in the semi-group framework, and the rates achieved are not sharp. This is due to the fact that the one-sided Lipschitz condition, being a variational inequality, can't be utilised. We thus turn to variational methods to solve this issue.

If time admits we shall also comment on the stochastic Cahn-Hilliard equation where the non-linearity has a one-sided Lipschitz condition in a lower norm, only. However, the fact of convergence can still be proved.

This is joint work with Daisuke Furihata (Osaka University), Mih\'aly Kov\'acs (University of Otago, New Zealand), Stig Larsson (Chalmers University of Technology, Sweden) and Shuji Yoshikawa (Ehime University).

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