## Seminar information archive

### 2020/01/16

#### Information Mathematics Seminar

16:50-18:35   Room #122 (Graduate School of Math. Sci. Bldg.)
Hirotaka Irie (DENSO CORPORATION/RIKEN iTHEMS)
Foundation of Quantum Annealing (Japanese)
[ Abstract ]
Explanation of Quantum Annealing

### 2020/01/14

#### Tuesday Seminar on Topology

17:00-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Ryohei Chihara (The University of Tokyo)
SO(3)-invariant G2-geometry (JAPANESE)
[ Abstract ]
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.

#### Tuesday Seminar on Topology

18:00-19:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Tsukasa Ishibashi (The University of Tokyo)
Algebraic entropy of sign-stable mutation loops (JAPANESE)
[ Abstract ]
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.

#### Tuesday Seminar of Analysis

16:50-18:20   Room #128 (Graduate School of Math. Sci. Bldg.)
Erik Skibsted (Aarhus University)
Scattering near a two-cluster threshold (English)
[ Abstract ]
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.

### 2020/01/10

#### Lectures

10:00-11:30   Room #126 (Graduate School of Math. Sci. Bldg.)
Javier Fresan (Ecole Polytechnique)
Nori motives over function fields and period functions (ENGLISH)
[ Abstract ]
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.

### 2020/01/09

#### Information Mathematics Seminar

16:50-18:35   Room #122 (Graduate School of Math. Sci. Bldg.)
[ Abstract ]

#### Lectures

14:00-17:30   Room #126 (Graduate School of Math. Sci. Bldg.)
Javier Fresan (Ecole Polytechnique)
Nori motives over function fields and period functions (ENGLISH)
[ Abstract ]
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.

#### Lectures

16:00-17:30   Room #126 (Graduate School of Math. Sci. Bldg.)
Javier Fresan (Ecole Polytechnique)
Nori motives over function fields and period functions (ENGLISH)
[ Abstract ]
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.

### 2020/01/07

#### Tuesday Seminar on Topology

17:00-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Yasuhiko Asao (The University of Tokyo)
Magnitude homology of crushable spaces (JAPANESE)
[ Abstract ]
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.

#### Tuesday Seminar on Topology

18:00-19:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Tomohiro Asano (The University of Tokyo)
Intersection number estimate of rational Lagrangian immersions in cotangent bundles via microlocal sheaf theory (JAPANESE)
[ Abstract ]
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.

### 2019/12/27

#### Seminar on Probability and Statistics

15:00-16:10   Room #126 (Graduate School of Math. Sci. Bldg.)
Xiao Fang (Chinese University of Hong Kong)
High order distributional approximations by Stein's method
[ Abstract ]
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.

#### Seminar on Probability and Statistics

16:30-17:40   Room #126 (Graduate School of Math. Sci. Bldg.)
Nikolai Leonenko (Cardiff University)
Heavy-Tailed Fractional Pearson Diffusions
[ Abstract ]
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

### 2019/12/26

#### Operator Algebra Seminars

16:45-18:15   Room #122 (Graduate School of Math. Sci. Bldg.)
Makoto Yamashita (Oslo Univ.)
Categorical quantization of symmetric spaces and reflection equation

### 2019/12/25

#### Operator Algebra Seminars

16:45-18:15   Room #126 (Graduate School of Math. Sci. Bldg.)
Bin Gui (Rutgers Univ.)
Connes fusion on the unit circle
(English)

### 2019/12/20

#### Colloquium

15:30-16:30   Room #056 (Graduate School of Math. Sci. Bldg.)

#### Logic

13:00-14:30   Room #156 (Graduate School of Math. Sci. Bldg.)

### 2019/12/19

#### Information Mathematics Seminar

16:50-18:35   Room #122 (Graduate School of Math. Sci. Bldg.)
Shigeru Nemoto (BroadBand Tower,inc. AI2 Open Innovation Lab.)
Our activities in the research of artificial intelligence (Japanese)
[ Abstract ]
Explanation of activities in the research of artificial intelligence

#### Applied Analysis

16:00-17:30   Room #128 (Graduate School of Math. Sci. Bldg.)

### 2019/12/18

#### Operator Algebra Seminars

16:45-18:15   Room #126 (Graduate School of Math. Sci. Bldg.)
Pasquale Marra (Univ. Tokyo)
The Hofstadter model, fractality, and topology

### 2019/12/17

#### Tuesday Seminar on Topology

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Kei Irie (The University of Tokyo)
Symplectic homology of fiberwise convex sets and homology of loop spaces (JAPANESE)
[ Abstract ]
For any (compact) subset in the symplectic vector space, one can define its symplectic capacity by using symplectic homology, which is a version of Floer homology.
In general, it is very difficult to compute or estimate this capacity directly from its definition, since the definition of Floer homology involves counting solutions of nonlinear PDEs (so called Floer equations). In this talk, we consider the symplectic vector space as the cotangent bundle of the Euclidean space, and show a formula which computes symplectic homology and capacity of fiberwise convex sets from homology of loop spaces. We also explain two applications of this formula.

#### Infinite Analysis Seminar Tokyo

15:00-16:00   Room #駒場国際教育研究棟（旧６号館）108 (Graduate School of Math. Sci. Bldg.)
Ryo Ohkawa (Waseda University)
(-2) blow-up formula (JAPANESE)
[ Abstract ]
In this talk, we will consider the moduli of ADHM data
corresponding to the affine A_1 Dynkin diagram.
It is a moduli of framed sheaves on the (-2) curve or the projective
plane with a group action.
Each of these two types of moduli integrals has a combinatorial
description. In particular, the Hirota derivative of the Nekrasov
function can be obtained on the (-2) curve.
We introduce equalities among these two integrals and the
corresponding functional equations in some cases.
This is similar to the blow-up formula by Nakajima-Yoshioka.
I would also like to talk about relationships with the study of the
Painleve tau function by Bershtein-Shchechkin.

### 2019/12/16

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Genki Hosono (Tohoku Univ.)
A simplified proof of the optimal L^2 extension theorem and its application (Japanese)
[ Abstract ]
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.

#### Numerical Analysis Seminar

16:50-18:20   Room #117 (Graduate School of Math. Sci. Bldg.)
Yuki Ueda (The Hong Kong Polytechnic University)
A second-order stabilization method for linearizing and decoupling nonlinear parabolic systems (Japanese)
[ Abstract ]
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.

### 2019/12/12

#### Information Mathematics Seminar

16:50-18:35   Room #122 (Graduate School of Math. Sci. Bldg.)
Katsuya WATANABE (Internet Research Institute,　Inc.)
５G Strategy (Japanese)
[ Abstract ]
Explanation of ５G Strategy

### 2019/12/11

#### Seminar on Geometric Complex Analysis

16:00-17:00   Room #156 (Graduate School of Math. Sci. Bldg.)
Joel Merker (Paris Sud)
Einstein-Weyl structures (English)
[ Abstract ]
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.