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Seminar information archive
Seminar information archive ～05/13｜Today's seminar 05/14 | Future seminars 05/15～
2025/02/07
Seminar on Probability and Statistics
14:00-15:10 Room #128 (Graduate School of Math. Sci. Bldg.)
ハイブリッド開催
Juho Leppänen (Tokai University)
A multivariate Berry–Esseen theorem for deterministic dynamical systems (English)
https://u-tokyo-ac-jp.zoom.us/meeting/register/lmbyLgO6RNi1GnoovqW_Sg
ハイブリッド開催
Juho Leppänen (Tokai University)
A multivariate Berry–Esseen theorem for deterministic dynamical systems (English)
[ Abstract ]
Many chaotic deterministic dynamical systems with a random initial state satisfy limit theorems similar to those of independent random variables. A classical example is the Central Limit Theorem, which, for a broad class of ergodic measure-preserving systems, is known to follow from a sufficiently rapid decay of correlations. Much work has also been done on the rate of convergence in the CLT. Results in this area typically rely on additional structure, such as suitable martingale approximation schemes or a spectral gap for the Perron–Frobenius operator.
In this talk, we present an adaptation of Stein's method for multivariate normal approximation of deterministic dynamical systems. For vector-valued processes generated by a class of fibred systems with good distortion properties (Gibbs–Markov maps), we derive bounds on the convex distance between the distribution of scaled partial sums and a multivariate normal distribution. These bounds, which are deduced as a consequence of certain correlation decay criteria, involve a multiplicative constant whose dependence on the dimension and dynamical quantities is explicit.
[ Reference URL ]Many chaotic deterministic dynamical systems with a random initial state satisfy limit theorems similar to those of independent random variables. A classical example is the Central Limit Theorem, which, for a broad class of ergodic measure-preserving systems, is known to follow from a sufficiently rapid decay of correlations. Much work has also been done on the rate of convergence in the CLT. Results in this area typically rely on additional structure, such as suitable martingale approximation schemes or a spectral gap for the Perron–Frobenius operator.
In this talk, we present an adaptation of Stein's method for multivariate normal approximation of deterministic dynamical systems. For vector-valued processes generated by a class of fibred systems with good distortion properties (Gibbs–Markov maps), we derive bounds on the convex distance between the distribution of scaled partial sums and a multivariate normal distribution. These bounds, which are deduced as a consequence of certain correlation decay criteria, involve a multiplicative constant whose dependence on the dimension and dynamical quantities is explicit.
https://u-tokyo-ac-jp.zoom.us/meeting/register/lmbyLgO6RNi1GnoovqW_Sg
2025/02/06
Tokyo Probability Seminar
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Jacek Wesolowski (Warsaw University of Technology)
Asymptotics of random Motzkin paths
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Jacek Wesolowski (Warsaw University of Technology)
Asymptotics of random Motzkin paths
[ Abstract ]
We study Motzkin paths of length L with general weights on the edges and end points. We investigate the limit behavior of the initial and final segments of the random Motzkin path viewed as a pair of processes starting from each of the two end points as L becomes large. Macroscopic limits of the resulting processes (under two different asymptotic regimes) appear to be non-Brownian parts of stationary measures for the KPZ equation and hypothetical KPZ fixed point on the half-line. The talk is based on a joint paper with W. Bryc (Univ. of Cincinnati) and A. Kuztetsov (York Univ., Toronto) - to appear in IMRN, available also on arXiv: https://arxiv.org/abs/2402.00265
We study Motzkin paths of length L with general weights on the edges and end points. We investigate the limit behavior of the initial and final segments of the random Motzkin path viewed as a pair of processes starting from each of the two end points as L becomes large. Macroscopic limits of the resulting processes (under two different asymptotic regimes) appear to be non-Brownian parts of stationary measures for the KPZ equation and hypothetical KPZ fixed point on the half-line. The talk is based on a joint paper with W. Bryc (Univ. of Cincinnati) and A. Kuztetsov (York Univ., Toronto) - to appear in IMRN, available also on arXiv: https://arxiv.org/abs/2402.00265
2025/01/24
thesis presentations
11:00-12:15 Room #118 (Graduate School of Math. Sci. Bldg.)
MAO Tianle (Graduate School of Mathematical Sciences University of Tokyo)
Stability conditions on the canonical line bundle of P^3
(射影空間P^3の標準束の安定性条件）
MAO Tianle (Graduate School of Mathematical Sciences University of Tokyo)
Stability conditions on the canonical line bundle of P^3
(射影空間P^3の標準束の安定性条件）
thesis presentations
13:00-14:15 Room #118 (Graduate School of Math. Sci. Bldg.)
ITO Kei (Graduate School of Mathematical Sciences University of Tokyo)
Structure of Kajiwara-Watatani algebras and their Cartan subalgebras
(梶原-綿谷代数の構造とそのカルタン部分代数）
ITO Kei (Graduate School of Mathematical Sciences University of Tokyo)
Structure of Kajiwara-Watatani algebras and their Cartan subalgebras
(梶原-綿谷代数の構造とそのカルタン部分代数）
thesis presentations
14:45-16:00 Room #118 (Graduate School of Math. Sci. Bldg.)
YOSHINO Taro (Graduate School of Mathematical Sciences University of Tokyo)
Stable rationality of hypersurfaces in schön affine varieties
(シェーンアファイン多様体の超曲面の安定的有理性について)
YOSHINO Taro (Graduate School of Mathematical Sciences University of Tokyo)
Stable rationality of hypersurfaces in schön affine varieties
(シェーンアファイン多様体の超曲面の安定的有理性について)
thesis presentations
11:00-12:15 Room #122 (Graduate School of Math. Sci. Bldg.)
KOSUGE Ryotaro (Graduate School of Mathematical Sciences University of Tokyo)
Studies on Chillingworth subgroups of mapping class groups and Andreadakis-Johnson filtrations via Bar cohomology
（写像類群のチリングワース部分群とバーコホモロジーによるアンドレアダキス-ジョンソンフィルトレーションの研究）
KOSUGE Ryotaro (Graduate School of Mathematical Sciences University of Tokyo)
Studies on Chillingworth subgroups of mapping class groups and Andreadakis-Johnson filtrations via Bar cohomology
（写像類群のチリングワース部分群とバーコホモロジーによるアンドレアダキス-ジョンソンフィルトレーションの研究）
thesis presentations
13:00-14:15 Room #122 (Graduate School of Math. Sci. Bldg.)
ZOU Yongpan (Graduate School of Mathematical Sciences University of Tokyo)
Studies on the positivity of direct image sheaves of adjoint bundles and cohomology vanishing theorems
（随伴束の順像層の正値性とコホモロジー消滅定理の研究）
ZOU Yongpan (Graduate School of Mathematical Sciences University of Tokyo)
Studies on the positivity of direct image sheaves of adjoint bundles and cohomology vanishing theorems
（随伴束の順像層の正値性とコホモロジー消滅定理の研究）
thesis presentations
11:00-12:15 Room #126 (Graduate School of Math. Sci. Bldg.)
BABA Tomoya (Graduate School of Mathematical Sciences University of Tokyo)
Log-rank test with nonparametric matching
(ノンパラメトリックなマッチングを用いたログランク検定）
BABA Tomoya (Graduate School of Mathematical Sciences University of Tokyo)
Log-rank test with nonparametric matching
(ノンパラメトリックなマッチングを用いたログランク検定）
thesis presentations
13:00-14:15 Room #126 (Graduate School of Math. Sci. Bldg.)
KURISAKI Masahiro (Graduate School of Mathematical Sciences University of Tokyo)
A New Proof for the Linear Filtering and Smoothing Equations, and Asymptotic Expansion of Nonlinear Filtering
(線形フィルタリングおよび平滑化方程式の新たな証明と、非線形フィルターの漸近展開)
KURISAKI Masahiro (Graduate School of Mathematical Sciences University of Tokyo)
A New Proof for the Linear Filtering and Smoothing Equations, and Asymptotic Expansion of Nonlinear Filtering
(線形フィルタリングおよび平滑化方程式の新たな証明と、非線形フィルターの漸近展開)
thesis presentations
14:45-16:00 Room #126 (Graduate School of Math. Sci. Bldg.)
SAKUMA Masaki (Graduate School of Mathematical Sciences University of Tokyo)
Extensions of the concentration compactness principle and their applications to critical p-fractional Choquard-type equations
(凝集コンパクト性原理の拡張と臨界p-非整数階Choquard 型方程式への応用)
SAKUMA Masaki (Graduate School of Mathematical Sciences University of Tokyo)
Extensions of the concentration compactness principle and their applications to critical p-fractional Choquard-type equations
(凝集コンパクト性原理の拡張と臨界p-非整数階Choquard 型方程式への応用)
thesis presentations
11:00-12:15 Room #128 (Graduate School of Math. Sci. Bldg.)
SAITO Yuta (Graduate School of Mathematical Sciences University of Tokyo)
Lubin-Tate (φ, Γ)-modules and generalization of their coefficient rings
(Lubin-Tate (φ, Γ) 加群とその係数環の一般化）
SAITO Yuta (Graduate School of Mathematical Sciences University of Tokyo)
Lubin-Tate (φ, Γ)-modules and generalization of their coefficient rings
(Lubin-Tate (φ, Γ) 加群とその係数環の一般化）
thesis presentations
13:00-14:15 Room #128 (Graduate School of Math. Sci. Bldg.)
BANDO Katsuyuki (Graduate School of Mathematical Sciences University of Tokyo)
Derived Satake category and Affine Hecke category in mixed characteristics
(混標数の導来佐武圏とアファインヘッケ圏）
BANDO Katsuyuki (Graduate School of Mathematical Sciences University of Tokyo)
Derived Satake category and Affine Hecke category in mixed characteristics
(混標数の導来佐武圏とアファインヘッケ圏）
thesis presentations
14:45-16:00 Room #128 (Graduate School of Math. Sci. Bldg.)
WANG PEIDUO (Graduate School of Mathematical Sciences University of Tokyo)
On generalized Fuchs theorem over relative p-adic polyannuli
(p進相対多重穴あき円板上の一般化フックス定理について）
WANG PEIDUO (Graduate School of Mathematical Sciences University of Tokyo)
On generalized Fuchs theorem over relative p-adic polyannuli
(p進相対多重穴あき円板上の一般化フックス定理について）
2025/01/23
thesis presentations
13:00-14:15 Room #118 (Graduate School of Math. Sci. Bldg.)
MATSUDA Koji (Graduate School of Mathematical Sciences University of Tokyo)
Rational points and Brauer–Manin obstruction on Shimura varieties classifying abelian varieties with quaternionic multiplication
(四元数乗法を持つアーベル多様体を分類する志村多様体の有理点とブラウアー-マニン障害)
MATSUDA Koji (Graduate School of Mathematical Sciences University of Tokyo)
Rational points and Brauer–Manin obstruction on Shimura varieties classifying abelian varieties with quaternionic multiplication
(四元数乗法を持つアーベル多様体を分類する志村多様体の有理点とブラウアー-マニン障害)
thesis presentations
14:45-16:00 Room #118 (Graduate School of Math. Sci. Bldg.)
SASAKI Yuya (Graduate School of Mathematical Sciences University of Tokyo)
On naturality of automorphisms of Hilbert schemes of points of some simple abelian varieties
(単純アーベル多様体の点のヒルベルトスキームの自己同型の自然性について)
SASAKI Yuya (Graduate School of Mathematical Sciences University of Tokyo)
On naturality of automorphisms of Hilbert schemes of points of some simple abelian varieties
(単純アーベル多様体の点のヒルベルトスキームの自己同型の自然性について)
thesis presentations
13:00-14:15 Room #122 (Graduate School of Math. Sci. Bldg.)
NATORI Masaki (Graduate School of Mathematical Sciences University of Tokyo)
A proof of Bott periodicity via Quot schemes and bulk-edge correspondence
(Quotスキームを用いたBott周期性の別証明とバルクエッジ対応)
NATORI Masaki (Graduate School of Mathematical Sciences University of Tokyo)
A proof of Bott periodicity via Quot schemes and bulk-edge correspondence
(Quotスキームを用いたBott周期性の別証明とバルクエッジ対応)
thesis presentations
14:45-16:00 Room #122 (Graduate School of Math. Sci. Bldg.)
YOSHIOKA Leo (Graduate School of Mathematical Sciences University of Tokyo)
Some non-trivial cycles of the space of long embeddings detected by configuration space integral invariants using g-loop graphs
( g ループグラフを用いた配置空間積分不変量で検出される埋め込みの空間の非自明なサイクルについて)
YOSHIOKA Leo (Graduate School of Mathematical Sciences University of Tokyo)
Some non-trivial cycles of the space of long embeddings detected by configuration space integral invariants using g-loop graphs
( g ループグラフを用いた配置空間積分不変量で検出される埋め込みの空間の非自明なサイクルについて)
thesis presentations
11:00-12:15 Room #126 (Graduate School of Math. Sci. Bldg.)
Liu Peijiang (Graduate School of Mathematical Sciences University of Tokyo)
Weak admissibility of exponentially twisted cohomology associated with some nondegenerate functions
(非退化関数に付随する捻じれコホモロジーの弱許容性について)
Liu Peijiang (Graduate School of Mathematical Sciences University of Tokyo)
Weak admissibility of exponentially twisted cohomology associated with some nondegenerate functions
(非退化関数に付随する捻じれコホモロジーの弱許容性について)
thesis presentations
14:45-16:00 Room #126 (Graduate School of Math. Sci. Bldg.)
MUKOUHARA Miho (Graduate School of Mathematical Sciences University of Tokyo)
On a Galois correspondence for compact group actions on simple C*-algebras
(単純C*環へのコンパクト群作用に対するガロア対応について)
MUKOUHARA Miho (Graduate School of Mathematical Sciences University of Tokyo)
On a Galois correspondence for compact group actions on simple C*-algebras
(単純C*環へのコンパクト群作用に対するガロア対応について)
thesis presentations
11:00-12:15 Room #128 (Graduate School of Math. Sci. Bldg.)
KEN Eitetsu (Graduate School of Mathematical Sciences University of Tokyo)
Games with backtracking options corresponding to the ordinal analysis of PA
(ペアノ算術の順序数解析に対応する、撤回を許したゲーム）
KEN Eitetsu (Graduate School of Mathematical Sciences University of Tokyo)
Games with backtracking options corresponding to the ordinal analysis of PA
(ペアノ算術の順序数解析に対応する、撤回を許したゲーム）
thesis presentations
14:45-16:00 Room #128 (Graduate School of Math. Sci. Bldg.)
YAMAMOTO Yuta (Graduate School of Mathematical Sciences University of Tokyo)
Two-dimensional structure of the duality of values and continuations
(値と継続の双対性の持つ2次元的構造)
YAMAMOTO Yuta (Graduate School of Mathematical Sciences University of Tokyo)
Two-dimensional structure of the duality of values and continuations
(値と継続の双対性の持つ2次元的構造)
thesis presentations
13:00-14:15 Room #126 (Graduate School of Math. Sci. Bldg.)
ISOBE Noboru (Graduate School of Mathematical Sciences University of Tokyo)
Mathematical Analysis for Evolution Equations Arising in Deep Learning Theory
(深層学習理論に現れる発展方程式の数理解析）
ISOBE Noboru (Graduate School of Mathematical Sciences University of Tokyo)
Mathematical Analysis for Evolution Equations Arising in Deep Learning Theory
(深層学習理論に現れる発展方程式の数理解析）
2025/01/22
Algebraic Geometry Seminar
13:30-15:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Hiromu Tanaka (The University of Tokyo)
Liftability and vanishing theorems for Fano threefolds in positive characteristic (日本語)
Hiromu Tanaka (The University of Tokyo)
Liftability and vanishing theorems for Fano threefolds in positive characteristic (日本語)
[ Abstract ]
Smooth Fano threefolds in positive characteristic satisfy Kodaira vanishing and lift to characteristic zero. This is joint work with Tatsuro Kawakami.
Smooth Fano threefolds in positive characteristic satisfy Kodaira vanishing and lift to characteristic zero. This is joint work with Tatsuro Kawakami.
2025/01/21
Tuesday Seminar on Topology
17:00-18:00 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Ryotaro Kosuge (The University of Tokyo)
Rational abelianizations of Chillingworth subgroups of mapping class groups and automorphism groups of free groups (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Ryotaro Kosuge (The University of Tokyo)
Rational abelianizations of Chillingworth subgroups of mapping class groups and automorphism groups of free groups (JAPANESE)
[ Abstract ]
The Chillingworth subgroup of the mapping class group of a surface is defined as the subgroup consisting of elements that preserve nonsingular vector fields up to homotopy. The action of the mapping class group on the set of homotopy classes of nonsingular vector fields is described using the concept of the winding number. By employing a cohomological approach, we extend the notion of the winding number to general manifolds, introducing the definition of the Chillingworth subgroup for both the mapping class group of general manifolds and the automorphism group of a free group. In this work, we determine the rational abelianization of the Chillingworth subgroup of the mapping class group of a surface and, under a certain assumption, also determine the rational abelianization of the Chillingworth subgroup for the automorphism group of a free group.
[ Reference URL ]The Chillingworth subgroup of the mapping class group of a surface is defined as the subgroup consisting of elements that preserve nonsingular vector fields up to homotopy. The action of the mapping class group on the set of homotopy classes of nonsingular vector fields is described using the concept of the winding number. By employing a cohomological approach, we extend the notion of the winding number to general manifolds, introducing the definition of the Chillingworth subgroup for both the mapping class group of general manifolds and the automorphism group of a free group. In this work, we determine the rational abelianization of the Chillingworth subgroup of the mapping class group of a surface and, under a certain assumption, also determine the rational abelianization of the Chillingworth subgroup for the automorphism group of a free group.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2025/01/20
Tokyo Probability Seminar
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Arka Adhikari (University of Maryland)
Spectral measure for uniform d-regular digraphs
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Arka Adhikari (University of Maryland)
Spectral measure for uniform d-regular digraphs
[ Abstract ]
Consider the matrix $\sfA_\GG$ chosen uniformly at random from the finite
set of all $N$-dimensional matrices of zero main-diagonal and binary entries,
having each row and column of $\sfA_\GG$ sum to $d$.
That is, the adjacency matrix for the uniformly random
$d$-regular simple digraph $\GG$. Fixing $d \ge 3$, it has long been conjectured
that as $N \to \infty$ the corresponding empirical eigenvalue distributions converge
weakly, in probability, to an explicit non-random limit,
given by the Brown measure of the free sum of $d$ Haar unitary operators.
We reduce this conjecture to bounding the decay in $N$ of the probability that
the minimal singular value of the shifted matrix $\sfA(w) = \sfA_\GG - w \sfI$
is very small. While the latter remains a challenging task, the required bound is
comparable to the recently established control on the singularity of $\sfA_\GG$.
The reduction is achieved here by sharp estimates
on the behavior at large $N$, near the real line, of the Green's function (aka resolvent)
of the Hermitization of $\sfA(w)$, which is of independent interest.
Joint w/ A. Dembo
Consider the matrix $\sfA_\GG$ chosen uniformly at random from the finite
set of all $N$-dimensional matrices of zero main-diagonal and binary entries,
having each row and column of $\sfA_\GG$ sum to $d$.
That is, the adjacency matrix for the uniformly random
$d$-regular simple digraph $\GG$. Fixing $d \ge 3$, it has long been conjectured
that as $N \to \infty$ the corresponding empirical eigenvalue distributions converge
weakly, in probability, to an explicit non-random limit,
given by the Brown measure of the free sum of $d$ Haar unitary operators.
We reduce this conjecture to bounding the decay in $N$ of the probability that
the minimal singular value of the shifted matrix $\sfA(w) = \sfA_\GG - w \sfI$
is very small. While the latter remains a challenging task, the required bound is
comparable to the recently established control on the singularity of $\sfA_\GG$.
The reduction is achieved here by sharp estimates
on the behavior at large $N$, near the real line, of the Green's function (aka resolvent)
of the Hermitization of $\sfA(w)$, which is of independent interest.
Joint w/ A. Dembo
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