## 過去の記録

### 2020年01月16日(木)

#### 情報数学セミナー

16:50-18:35   数理科学研究科棟(駒場) 122号室

アニーリング型量子計算の基礎 (Japanese)
[ 講演概要 ]

### 2020年01月14日(火)

#### トポロジー火曜セミナー

17:00-18:00   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00

SO(3)-invariant G2-geometry (JAPANESE)
[ 講演概要 ]
Berger's classification of holonomy groups of Riemannian manifolds includes exceptional cases of the Lie groups G2 and Spin(7). Many authors have studied G2- and Spin(7)-manifolds with torus symmetry. In this talk, we generalize the celebrated examples due to Bryant and Salamon and study G2-manifolds with SO(3)-symmetry. Such torsion-free G2-structures are described as a dynamical system of SU(3)-structures on an SO(3)-fibration over a 3-manifold. As a main result, we reduce this system into a constrained Hamiltonian dynamical system on the cotangent bundle over the space of all Riemannian metrics on the 3-manifold. The Hamiltonian function is very similar to that of the Hamiltonian formulation of general relativity.

#### トポロジー火曜セミナー

18:00-19:00   数理科学研究科棟(駒場) 056号室

Algebraic entropy of sign-stable mutation loops (JAPANESE)
[ 講演概要 ]
Since its discovery, the cluster algebra has been developed with friutful connections with other branches of mathematics, unifying several combinatorial operations as well as their positivity notions. A mutation loop induces several dynamical systems via cluster transformations, and they form a group which can be seen as a combinatorial generalization of the mapping class groups of marked surfaces.
We introduce a new property of mutation loops called the sign stability, with a focus on an asymptotic behavior of the iteration of the tropicalized cluster X-transformation. A sign-stable mutation loop has a numerical invariant which we call the "cluster stretch factor", in analogy with the stretch factor of a pseudo-Anosov mapping class on a marked surface. We compute the algebraic entropies of the cluster A- and X-transformations induced by a sign-stable mutation loop, and conclude that these two coincide with the logarithm of the cluster stretch factor. This talk is based on a joint work with Shunsuke Kano.

#### 解析学火曜セミナー

16:50-18:20   数理科学研究科棟(駒場) 128号室
Erik Skibsted 氏 (オーフス大学)
Scattering near a two-cluster threshold (English)
[ 講演概要 ]
For a one-body Schr\"odinger operator with an attractive slowly decaying potential the scattering matrix is well-defined at the energy zero, and the structure of its singularities is well-studied. The usual (non-relativistic) model for the Hydrogen atom is a particular example of such Schr\"odinger operator.
Less is known on scattering at a two-cluster threshold of an $N$-body Schr\"odinger operator for which the effective interaction between the two bound clusters is attractive Coulombic. An example of interest is scattering at a two-cluster threshold of a neutral atom/molecule. We present results of an ongoing joint work with X.P. Wang on the subject, including a version of the Sommerfeld uniqueness result and its applications.
We shall also present general results on spectral theory at a two-cluster threshold (not requiring the effective interaction to be attractive Coulombic). This includes a general structure theorem on the bound and resonance states at the threshold as well as a resolvent expansion in weighted spaces above the threshold (under more restrictive conditions). Applications to scattering theory will be indicated.

### 2020年01月10日(金)

#### 講演会

10:00-11:30   数理科学研究科棟(駒場) 126号室
Javier Fresan 氏 (Ecole Polytechnique)
Nori motives over function fields and period functions (ENGLISH)
[ 講演概要 ]
Around twenty years ago, Nori introduced a tannakian category of mixed motives over a subfield of the complex numbers, thus giving the first unconditional construction of the motivic Galois group. In this series of lectures, I will first survey on Nori's theory and its relationship to other categories of motives. I will then explain how to extend his construction to functions fields and why the resulting tannakian group governs
algebraic relations between period functions.
This last part is based on an ongoing work with Peter Jossen.

### 2020年01月09日(木)

#### 情報数学セミナー

16:50-18:35   数理科学研究科棟(駒場) 122号室

AI/IoTによる製造業の革新と経営学 (Japanese)
[ 講演概要 ]

#### 講演会

14:00-17:30   数理科学研究科棟(駒場) 126号室
Javier Fresan 氏 (Ecole Polytechnique)
Nori motives over function fields and period functions (ENGLISH)
[ 講演概要 ]
Around twenty years ago, Nori introduced a tannakian category of mixed motives over a subfield of the complex numbers, thus giving the first unconditional construction of the motivic Galois group. In this series of lectures, I will first survey on Nori's theory and its relationship to other categories of motives. I will then explain how to extend his construction to functions fields and why the resulting tannakian group governs
algebraic relations between period functions.
This last part is based on an ongoing work with Peter Jossen.

#### 講演会

16:00-17:30   数理科学研究科棟(駒場) 126号室
Javier Fresan 氏 (Ecole Polytechnique)
Nori motives over function fields and period functions (ENGLISH)
[ 講演概要 ]
Around twenty years ago, Nori introduced a tannakian category of mixed motives over a subfield of the complex numbers, thus giving the first unconditional construction of the motivic Galois group. In this series of lectures, I will first survey on Nori's theory and its relationship to other categories of motives. I will then explain how to extend his construction to functions fields and why the resulting tannakian group governs
algebraic relations between period functions.
This last part is based on an ongoing work with Peter Jossen.

### 2020年01月07日(火)

#### トポロジー火曜セミナー

17:00-18:00   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00

Magnitude homology of crushable spaces (JAPANESE)
[ 講演概要 ]
The magnitude homology and the blurred magnitude homology are novel notions of homology theory for general metric spaces 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 has been revealed. In this talk, we see that the blurred magnitude homology is trivial when a metric space is contractible by a distance decreasing homotopy. We use techniques from singular homology theory.

#### トポロジー火曜セミナー

18:00-19:00   数理科学研究科棟(駒場) 056号室

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.

### 2019年12月27日(金)

#### 統計数学セミナー

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.

#### 統計数学セミナー

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).

References:
[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

### 2019年12月26日(木)

#### 作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 122号室

Categorical quantization of symmetric spaces and reflection equation

### 2019年12月25日(水)

#### 作用素環セミナー

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
(English)

### 2019年12月20日(金)

#### 談話会・数理科学講演会

15:30-16:30   数理科学研究科棟(駒場) 056号室

[ 講演概要 ]

その理論根拠となるはずの統計的学習理論の考え方を紹介する。

その表現力とStone-Weierstrassの定理との関係、

は様々な数学の視点が有用ではないかと感じている。

#### 基礎論セミナー

13:00-14:30   数理科学研究科棟(駒場) 156号室

On supercompactness of $\omega_1$
[ 講演概要 ]
In ZFC, all the large cardinals are much bigger than $\omega_1$, the least uncountable cardinal,
while without assuming the Axiom of Choice, $\omega_1$ could have some large cardinal properties.
Jech and Takeuti independently proved that if the axiom system ZFC + There is a measurable cardinal is consistent,
then so is ZF + $\omega_1$ is a measurable cardinal.
Takeuti also proved that one can replace "measurable cardinal" above with "supercompact cardinal" as well as some other large cardinals.
Woodin proved that one can reduce the assumption, i.e., the consistency of ZFC + a supercompact cardinal,
to that of ZFC + There are proper class many Woodin cardinals which are limits of Woodin cardinals,
to obtain the consistency of ZF + $\omega_1$ is a supercompact cardinal.
Furthermore, the model he constructed also satisfies the Axiom of Determinacy (AD).
In this talk, after giving some background on the connections between large cardinals and determinacy, we discuss some consequences of the axiom system ZF + $\omega_1$ is a supercompact cardinal.
This is joint work with Nam Trang.

### 2019年12月19日(木)

#### 情報数学セミナー

16:50-18:35   数理科学研究科棟(駒場) 122号室

AI研究の活動事例 (Japanese)
[ 講演概要 ]

#### 応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 128 号室

[ 講演概要 ]

### 2019年12月18日(水)

#### 作用素環セミナー

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

### 2019年12月17日(火)

#### トポロジー火曜セミナー

17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00

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。

#### 東京無限可積分系セミナー

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

(-2) blow-up formula (JAPANESE)
[ 講演概要 ]
(-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.
これは中島-吉岡による爆発公式の類似と考えられる.
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.

### 2019年12月16日(月)

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室

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.

#### 数値解析セミナー

16:50-18:20   数理科学研究科棟(駒場) 117号室

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.

### 2019年12月12日(木)

#### 情報数学セミナー

16:50-18:35   数理科学研究科棟(駒場) 122号室

５Gとは？ (Japanese)
[ 講演概要 ]
5G時代に向けたモバイルブロードバンドの進展と今後の展望について、事例も踏まえながらお話をさせていただければと考えております。

### 2019年12月11日(水)

#### 複素解析幾何セミナー

16:00-17:00   数理科学研究科棟(駒場) 156号室
Joel Merker 氏 (Paris Sud)
Einstein-Weyl structures (English)
[ 講演概要 ]
On a conformal 3D manifold with electromagnetic field, Einstein-Weyl equations are the counterpart of Einstein's classical field equations. In 1943, Elie Cartan showed, using abstract arguments, that the general solution depends on 4 functions of 2 variables. I will present families of explicit solutions depending on 9 functions of 1 variable, much beyond what was known before. Such solutions are generic in the sense that the Cotton tensor is nonzero. This is joint work with Pawel Nurowski.