過去の記録 ~12/04本日 12/05 | 今後の予定 12/06~


16:45-18:15   オンライン開催
山下真由子 氏 (京大数理研)
A new construction of deformation quantization for Lagrangian fiber bundles (English)
[ 参考URL ]



17:00-18:10   数理科学研究科棟(駒場) φ号室
Xiao Fang 氏 (Chinese University of Hong Kong)
High order distributional approximations by Stein's method (ENGLISH)
[ 講演概要 ]
Stein's method is a powerful tool to proving distributional approximations with error bounds. In this talk, we present two recent developments of Stein's method for high order approximations. (1) Together with Li Luo and Qi-Man Shao, we consider skewness correction in normal approximation. We prove a refined Cram¥'er-type moderate deviation result for a class of statistics possessing a local structure. We discuss applications to k-runs, U-statistics and subgraph counts. (2) Together with Anton Braverman and Jim Dai, we derive and justify new diffusion approximations with state-dependent diffusion coefficients for stationary distributions of Markov chains. We discuss applications to the Erlang-C system, a hospital inpatient flow model and the auto-regressive model.
[ 参考URL ]



16:45-18:15   オンライン開催
Felix Parraud 氏 (ENS Lyon)
Interpolation between random matrices and their free limit with the help of free stochastic processes (English)
[ 参考URL ]



16:45-18:15   オンライン開催
森迪也 氏 (東大数理)
Lattice isomorphisms between projection lattices of von Neumann algebras
[ 参考URL ]



17:30-18:30   オンライン開催
Arthur-César Le Bras 氏 (CNRS & Université Paris 13)
Prismatic Dieudonné theory (ENGLISH)
[ 講演概要 ]
I would like to explain a classification result for p-divisible groups, which unifies many of the existing results in the literature. The main tool is the theory of prisms and prismatic cohomology recently developed by Bhatt and Scholze. This is joint work with Johannes Anschütz.

東大数理,Morningside Center of Mathematics と IHES の双方向同時中継で行います.



17:00-18:10   数理科学研究科棟(駒場) φ号室
郷田昌稔 氏 (東京大学)
Hawkes process and Edgeworth expansion with application to Maximum Likelihood Estimator (JAPANESE)
[ 講演概要 ]
The Hawkes process is a point process with a self-exciting property. It has been used to model earthquakes, social media events, infections, etc. and is getting a lot of attention. However, as a real problem, there are often situations where we can not obtain data with sufficient observation time. In such cases, it is not appropriate to approximate the error distribution of an estimator by the normal distribution. We established the Edgeworth expansion for a functional of a geometric mixing process, and applied this scheme to a functional of the Hawkes process with an exponential kernel. Furthermore, we gave a more appropriate asymptotic distribution for the error of the Maximum Likelihood Estimator of the Hawks process, i.e. a higher-order asymptotic distribution than the normal distribution. Here, in addition to the details of these statements, we also present the simulation results.
[ 参考URL ]


16:45-18:15   オンライン開催
Cyril Houdayer 氏 (Univ. Paris-Sud)
Structure theorem for unitary representations of irreducible lattices in product groups
[ 参考URL ]



16:00-17:00   数理科学研究科棟(駒場) 117号室
河野 俊丈 氏 (東京大学大学院数理科学研究科)
モノドロミー表現とその高次圏への拡張 (JAPANESE)



15:30-17:00   数理科学研究科棟(駒場) 002号室
Evgeny Shinder 氏 (The University of Sheffield)
Semiorthogonal decompositions for singular varieties (English)
[ 講演概要 ]
I will define the semiorthogonal decomposition for derived categories of singular projective varieties due to Professor Kawamata, into finite-dimensional algebras, generalizing the concept of an exceptional collection in the smooth case. I will present known constructions of these for nodal curves (Burban), torsion-free toric surfaces (Karmazyn-Kuznetsov-Shinder) and two nodal threefolds (Kawamata). I will also explain obstructions coming from the K_{-1} group, and how it translates to maximal nonfactoriality in the nodal threefold case. This is joint work with M.Kalck and N.Pavic.



16:00-17:00   数理科学研究科棟(駒場) 370号室
Maximilian Moser 氏 (University of Regensburg)
Convergence of the Allen-Cahn equation with a nonlinear Robin-boundary condition to mean curvature flow with constant contact angle (English)
[ 講演概要 ]
In this talk I will present a result for the sharp interface limit of the Allen-Cahn equation with a nonlinear Robin boundary condition in a two-dimensional domain, in the situation where an interface has developed and intersects the boundary. The boundary condition is designed in such a way that one obtains as the limit problem the mean curvature flow with constant contact angle. Convergence using strong norms is shown for contact angles close to 90° and small times, when a smooth solution to the limit problem exists. For the proof the method of de Mottoni and Schatzman is used: we construct an approximate solution for the Allen-Cahn system using asymptotic expansions based on the solution to the limit problem. Then we estimate the difference of the exact and approximate solution with a spectral estimate for the linearized (at the approximate solution) Allen-Cahn operator.
This is joint work with Helmut Abels from Regensburg.



13:30-15:00   数理科学研究科棟(駒場) 370号室
Jakub Witaszek 氏 (Michigan)
Keel's theorem and quotients in mixed characteristic (English)
[ 講演概要 ]
In trying to understand characteristic zero varieties one can apply a wide range of techniques coming from analytic methods such as vanishing theorems. More complicated though they are, positive characteristic varieties come naturally with Frobenius action which sometimes allows for imitating analytic proofs or even showing results which are false over complex numbers. Of all the three classes, the mixed characteristic varieties are the most difficult to understand as they represent the worst of both worlds: one lacks the analytic methods as well the Frobenius action.

What is key for many applications of Frobenius in positive characteristic (to birational geometry, moduli theory, constructing quotients, etc.) is the fact that every universal homeomorphism of algebraic varieties factors through a power of Frobenius. In this talk I will discuss an analogue of this fact (and applications thereof) in mixed characteristic.
[ 参考URL ]



16:50-18:20   数理科学研究科棟(駒場) 128号室
Alessio Porretta 氏 (Tor Vergata university of Rome)
Long time behavior of mean field games systems (English)
[ 講演概要 ]
I will review several aspects related to the long time ergodic behavior of mean field game systems: the turnpike property, the exponential rate of convergence, the role of monotonicity of the couplings, the convergence of u up to translations, the limit of the vanishing discounted problem, the long time behavior of the master equation. All those aspects have independent interest and are correlated at the same time.


15:00-16:00   数理科学研究科棟(駒場) 002号室
Vincent Pasquier 氏 (IPhT Saclay)
Hydrodynamics of a one dimensional lattice gas.
[ 講演概要 ]
The simplest boxball model is a one dimensional lattice gas obtained as
a certain (cristal) limit of the six vertex model where the evolution
determined by the transfer matrix becomes deterministic. One can
study its thermodynamics in and out of equilibrium and we shall present
preliminary results in this direction.

Collaboration with Atsuo Kuniba and Grégoire Misguich.



10:30-12:00   数理科学研究科棟(駒場) 128号室
満渕 俊樹 氏 (大阪大学)
Precompactness of the moduli space of pseudo-normed graded algebras
[ 講演概要 ]
Graded algebras (such as canonical rings) coming from the spaces of sections of polarized algebraic varieties are studied by many mathematicians. On the other hand, the pseudo-norm project proposed by S.-T. Yau and C.-Y. Chi gives us a new differential geometric aspect of the Torelli type theorem.
In this talk, we give the details of how the geometry of pseudo-normed graded algebras allows us to obtain a natural compactification of the moduli space of pseudo-normed graded algebras.
(1) For a sequence of pseudo-normed graded algebras (of the same type), the above precompactness gives us some limit different from the Gromov-Hausdorff limit in Riemannian geometry.
(2) As an example of our construction, we have the Deligne-Mumford compactification, in which the notion of the orthogonal direct sum of pseudo-normed spaces comes up naturally. We also have a higher dimensional analogue by using weight filtration.


16:30-18:30   数理科学研究科棟(駒場) 126号室
Sanjay Ramassamy 氏 (IPhT, CEA Saclay)
Cluster algebras, dimer models and geometric dynamics
[ 講演概要 ]
Cluster algebras were introduced by Fomin and Zelevinsky at the beginning of the 21st century and have since then been related to several areas of mathematics. In this talk I will describe cluster algebras coming from quivers and give two concrete situations were they arise. The first is the bipartite dimer model coming from statistical mechanics. The second is in several dynamics on configurations of points/lines/circles/planes.

This is based on joint work with Niklas Affolter (TU Berlin), Max Glick (Google) and Pavlo Pylyavskyy (University of Minnesota).



17:00-18:00   数理科学研究科棟(駒場) 128号室
Piermarco Cannarsa 氏 (University of Rome Tor Vergata)
Bilinear control for evolution equations of parabolic type (ENGLISH)
[ 講演概要 ]
Recently, in a series of joint papers with F. Alabau-Boussouira and C. Urbani, I have studied the response of an evolution equation on a Hilbert space to the action of a bilinear control. As is well-known, a bilinear control is a scalar function of time multiplying one of the coefficient of the equation (usually, a lower order term). Therefore, this is a nonlinear control problem, even if the equation is linear in the state variable.
For such a problem, exact controllability is out of question, due to a well-known negative result by Ball, Marsden, and Slemrod back in the 80’s.
In this talk, equations of parabolic type will be considered, meaning that the infinitesimal generator - of the strongly continuous semigroup which drives the system - is assumed to be a self-adjoint accretive operator. It will be explained how, under some conditions relating the spectrum of the generator to the control coefficient, one can locally stabilise the system to the solution associated with the ground state at a doubly exponential speed, or even attain such a ground-state solution in finite time. Applications to concrete parabolic problems will also be provided.
[ 参考URL ]



16:30-18:30   数理科学研究科棟(駒場) 126号室
Sanjay Ramassamy 氏 (IPhT, CEA Saclay)
Embeddings adapted to two-dimensional models of statistical mechanics (English)
[ 講演概要 ]
A discrete model of statistical mechanics in 2D (for example simple random walk on the infinite square grid) can be defined on a graph without specifying a particular embedding of this graph. However, when stating that such a model converges to a conformally invariant object in the scaling limit, one needs to specify an embedding of the graph. For models which possess a local move, such as a star-triangle transformation, one would like the choice of the embedding to be compatible with that local move.

In this talk I will present a candidate for an embedding adapted to the 2D dimer model (a.k.a. random perfect matchings) on bipartite graphs, that is, graphs whose faces all have an even degree. This embedding is obtained by considering centers of circle patterns with the combinatorics of the graph on which the dimer model lives.

This is based on joint works with Dmitry Chelkak (École normale supérieure), Richard Kenyon (Yale University), Wai Yeung Lam (Université du Luxembourg) and Marianna Russkikh (MIT).



15:00-16:10   数理科学研究科棟(駒場) 126号室
Lorenzo Mercuri 氏 (University of Milan)
Handling the underlying noise of Stochastic Differential Equations in YUIMA project

[ 講演概要 ]
Some advances in the implementation of advanced mathematical tools and numerical methods for an object of class yuima.law are presented and discussed. An object of yuima.law-class refers to the mathematical description of the underlying noise specified in the formal definition of a general Stochastic Differential Equation. Its aim is to create a link between YUIMA and other R packages available on CRAN for managing specific Lévy noises. Here we present as examples the simulation and the estimation of a CARMA(p,q) and Point Process regression models.



15:00-16:00   数理科学研究科棟(駒場) 126号室
Simon Gindikin 氏 (Rutgers University)
Direct inversion of the horospherical transform on Riemannian symmetric spaces (English)
[ 講演概要 ]
It was a problem of Gelfand to find an inversion of the horospherical transform directly and as a result to find directly the Plancherel formula.
I will give such an inversion and it gives a formula different from Harish-Chandra's one.



9:15-10:30   数理科学研究科棟(駒場) 118号室
茅原 涼平 氏 (東京大学大学院数理科学研究科)
SO(3)-invariant G2-geometry
(SO(3)-不変 G2-幾何学)


10:45-12:00   数理科学研究科棟(駒場) 118号室
石橋 典 氏 (東京大学大学院数理科学研究科)
Geometry of cluster modular groups


12:45-14:00   数理科学研究科棟(駒場) 118号室
渡部 淳 氏 (東京大学大学院数理科学研究科)
Fibred Cusp b-Pseudodifferential Operators and Its Applications
(Fibred Cusp b-擬微分作用素とその応用)


14:15-15:30   数理科学研究科棟(駒場) 118号室
田森 宥好 氏 (東京大学大学院数理科学研究科)
Classification and construction of minimal representations


9:15-10:30   数理科学研究科棟(駒場) 122号室
岩井 雅崇 氏 (東京大学大学院数理科学研究科)
Studies on singular Hermitian metrics and their applications in algebraic geometry


10:45-12:00   数理科学研究科棟(駒場) 122号室
陳 韋中 氏 (東京大学大学院数理科学研究科)
Boundedness of Weak Fano Pairs with Alpha-invariants and Volumes Bounded Below

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