過去の記録 ~12/13本日 12/14 | 今後の予定 12/15~



10:30-12:00   数理科学研究科棟(駒場) 128号室
細野 元気 氏 (東北大学)
A simplified proof of the optimal L^2 extension theorem and its application (Japanese)
[ 講演概要 ]
I will explain a simplified proof of an optimal version of the Ohsawa-Takegoshi L^2-extension theorem. In the proof, I use a method of Berndtsson-Lempert and skip some argument by the method of McNeal-Varolin. As an application, I will explain a result on extensions from possibly non-reduced varieties.


16:50-18:20   数理科学研究科棟(駒場) 117号室
上田祐暉 氏 (The Hong Kong Polytechnic University)
A second-order stabilization method for linearizing and decoupling nonlinear parabolic systems (Japanese)
[ 講演概要 ]
We present a new time discretization method for strongly nonlinear parabolic systems. Our method is based on backward finite difference for the first derivative with second-order accuracy and the first-order linear discrete-time scheme for nonlinear systems which has been introduced by H. Murakawa. We propose a second-order stabilization method by combining these schemes.
Our error estimate requires testing the error equation by two test functions and showing $W^{1,\infty}$-boundedness which is proved by ($H^2$ or) $H^3$ energy estimate. We overcome the difficulty for establishing energy estimate by using the generating function technique which is popular in studying ordinary differential equations. Several numerical examples are provided to support the theoretical result.



17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
入江 慶 氏 (東京大学大学院数理科学研究科)
Symplectic homology of fiberwise convex sets and homology of loop spaces (JAPANESE)
[ 講演概要 ]
シンプレクティック・ベクトル空間の(コンパクト)部分集合に対して、シンプレクティック・ホモロジー(Floer ホモロジーの一種)を用いてそのシンプレクティック容量(capacity)を定義することができる。一般に、Floerホモロジーの定義には非線形偏微分方程式(いわゆるFloer方程式)の解の数え上げが関わるため、容量を定義から直接計算したり評価したりするのは難しい。この講演では(シンプレクティック・ベクトル空間をEuclid空間の余接空間とみなしたとき)fiberwiseに凸な集合のシンプレクティック・ホモロジーおよび容量をループ空間のホモロジーから計算する公式を示し、その応用を二つ与える。


15:00-16:00   数理科学研究科棟(駒場) 駒場国際教育研究棟(旧6号館)108号室
大川領 氏 (早稲田大)
(-2) blow-up formula (JAPANESE)
[ 講演概要 ]
この講演では, アフィンA_1ディンキン図形に対応するADHM dataのモジュライを考える. これらは, 安定性条件の取り方に応じて,
(-2)曲線, あるいは群作用付きの平面上の枠付き連接層のモジュライとなる.
これら2種のモジュライ上の積分は, それぞれ組合せ論的な記述をもち, 特に(-2)曲線上ではNekrasov関数の広田微分がえられる.
これら2種のモジュライ上の積分が, ある場合に等しくなること, またそれに応じた関数等式について紹介する.
また, Bershtein-ShchechkinによるPainleve tau functionの研究との関係についても触れたい.



16:45-18:15   数理科学研究科棟(駒場) 126号室
Pasquale Marra 氏 (東大数理)
The Hofstadter model, fractality, and topology


18:00-19:00   数理科学研究科棟(駒場) 002号室
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.



16:50-18:35   数理科学研究科棟(駒場) 122号室
根本 茂 氏 (株式会社ブロードバンドタワー AI2オープンイノベーション研究所)
AI研究の活動事例 (Japanese)
[ 講演概要 ]


16:00-17:30   数理科学研究科棟(駒場) 128 号室
可香谷隆 氏 (九州大学)
接触角条件付き表面拡散に対する進行波解の非一意性と非凸性について (Japanese)
[ 講演概要 ]



15:30-16:30   数理科学研究科棟(駒場) 056号室
楠岡成雄 氏 (東京大学・明治大学)
機械学習に関する一考察 (日本語)
[ 講演概要 ]
特に、深層学習(neural network)に関して、




16:45-18:15   数理科学研究科棟(駒場) 126号室
Bin Gui 氏 (Rutgers Univ.)
Connes fusion on the unit circle



16:45-18:15   数理科学研究科棟(駒場) 122号室
山下真 氏 (Oslo Univ.)
Categorical quantization of symmetric spaces and reflection equation



15:00-16:10   数理科学研究科棟(駒場) 126号室
Xiao Fang 氏 (Chinese University of Hong Kong)
High order distributional approximations by Stein's method
[ 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.


16:30-17:40   数理科学研究科棟(駒場) 126号室
Nikolai Leonenko 氏 (Cardiff University)
Heavy-Tailed Fractional Pearson Diffusions
[ 講演概要 ]
We define fractional Pearson diffusions [5,7,8] by non-Markovian time change in the corresponding Pearson diffusions [1,2,3,4]. They are governed by the time-fractional diffusion equations with polynomial coefficients depending on the parameters of the corresponding Pearson distribution. We present the spectral representation of transition densities of fractional Pearson diffusions, which depend heavily on the structure of the spectrum of the infinitesimal generator of the corresponding non-fractional Pearson diffusion. Also, we present the strong solutions of the Cauchy problems associated with heavy-tailed fractional Pearson diffusions and the correlation structure of these diffusions [6] .
Continuous time random walks have random waiting times between particle jumps. We define the correlated continuous time random walks (CTRWs) that converge to fractional Pearson diffusions (fPDs) [9,10,11]. The jumps in these CTRWs are obtained from Markov chains through the Bernoulli urn-scheme model, Wright-Fisher model and Ehrenfest-Brillouin-type models. The jumps are correlated so that the limiting processes are not Lévy but diffusion processes with non-independent increments.

This is a joint work with M. Meerschaert (Michigan State University, USA), I. Papic (University of Osijek, Croatia), N.Suvak (University of Osijek, Croatia) and A. Sikorskii (Michigan State University and Arizona University, USA).

[1] Avram, F., Leonenko, N.N and Suvak, N. (2013), On spectral analysis of heavy-tailed Kolmogorov-Pearson diffusion, Markov Processes and Related Fields, Volume 19, N 2 , 249-298
[2] Avram, F., Leonenko, N.N and Suvak, N., (2013), Spectral representation of transition density of Fisher-Snedecor diffusion, Stochastics, 85 (2013), no. 2, 346—369
[3] Bourguin, S., Campese, S., Leonenko, N. and Taqqu,M.S. (2019) Four moments theorems on Markov chaos, Annals of Probability, 47, N3, 1417–1446
[4] Kulik, A.M. and Leonenko, N.N. (2013) Ergodicity and mixing bounds for the Fisher-Snendecor diffusion, Bernoulli, Vol. 19, No. 5B, 2294-2329
[5] Leonenko, N.N., Meerschaert, M.M and Sikorskii, A. (2013) Fractional Pearson diffusions, Journal of Mathematical Analysis and Applications, vol. 403, 532-546
[6] Leonenko, N.N., Meerschaert, M.M and Sikorskii, A. (2013) Correlation Structure of Fractional Pearson diffusion, Computers and Mathematics with Applications, 66, 737-745
[7] Leonenko,N.N., Meerschaert,M.M., Schilling,R.L. and Sikorskii, A. (2014) Correlation Structure of Time-Changed Lévy Processes, Communications in Applied and Industrial Mathematics, Vol. 6 , No. 1, p. e-483 (22 pp.)
[8] Leonenko, N.N., Papic, I., Sikorskii, A. and Suvak, N. (2017) Heavy-tailed fractional Pearson diffusions, Stochastic Processes and their Applications, 127, N11, 3512-3535
[9] Leonenko, N.N., Papic, I., Sikorskii, A. and Suvak, N. (2018) Correlated continuous time random walks and fractional Pearson diffusions, Bernoulli, Vol. 24, No. 4B, 3603-3627
[10] Leonenko, N.N., Papic, I., Sikorskii, A. and Suvak, N. (2019) Ehrenfest-Brillouin-type correlated continuous time random walks and fractional Jacoby diffusion, Theory Probablity and Mathematical Statistics, Vol. 99,123-133.
[11] Leonenko, N.N., Papic, I., Sikorskii, A. and Suvak, N. (2019) Approximation of heavy-tailed fractional Pearson diffusions in Skorokhod topology, submitted



17:00-18:00   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
浅尾 泰彦 氏 (東京大学大学院数理科学研究科)
Magnitude homology of crushable spaces (JAPANESE)
[ 講演概要 ]
Magnitude homology and its variant blurred magnitude homology are novel notions of homology theory for general metric space coined by Leinster et al. They are expected to be dealt with in the context of Topological Data Analysis since its original idea is based on a kind of "persistence of points clouds". However, little property of them have been revealed. In this talk, we see that magnitude homology and blurred magnitude homology is trivial when a metric space is contractible by a distance decreasing homotopy. We use techniques from singular homology theory.


18:00-19:00   数理科学研究科棟(駒場) 056号室
浅野 知紘 氏 (東京大学大学院数理科学研究科)
Intersection number estimate of rational Lagrangian immersions in cotangent bundles via microlocal sheaf theory (JAPANESE)
[ 講演概要 ]
Guillermou associated sheaves to exact Lagrangian submanifolds in cotangent bundles and proved topological properties of the Lagrangian submanifolds. In this talk, I will give an estimate on the displacement energy of rational Lagrangian immersions in cotangent bundles with intersection number estimates via microlocal sheaf theory. This result overlaps with results by Chekanov, Liu, and Akaho via Floer theory. This is joint work with Yuichi Ike.



16:50-18:20   数理科学研究科棟(駒場) 056号室
Yves A. B. C. Barbosa 氏 (Politecnico di Milano)
Isogeometric Hierarchical Model Reduction: from analysis to patient-specific simulations (English)



10:30-12:00   数理科学研究科棟(駒場) 128号室
辻 元 氏 (上智大学)



13:00-14:30   数理科学研究科棟(駒場) 002号室
Colin McSwiggen 氏 (Brown Univ.)
Horn's problem, polytope volumes and tensor product decompositions (English)


16:45-18:15   数理科学研究科棟(駒場) 126号室
Cyril Houdayer 氏 (Univ. Paris-Sud)
Stationary actions of higher rank lattices on von Neumann algebras (English)



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)



15:30-17:00   数理科学研究科棟(駒場) 002号室
部屋がいつもと違います。The room is different from our usual.
Evgeny Shinder 氏
TBA (English)
[ 講演概要 ]