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Seminar information archive
Seminar information archive ～01/14｜Today's seminar 01/15 | Future seminars 01/16～
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.
Hironobu Sakagawa (Keio University)
Maximum of the Gaussian interface model in random external fields (日本語)
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Hironobu Sakagawa (Keio University)
Maximum of the Gaussian interface model in random external fields (日本語)
[ Abstract ]
相分離の界面モデルの一つとして格子上のGauss型界面モデル（離散Gauss自由場）を取り上げ，そこにランダムな外場（化学ポテンシャル）を加えた（ランダムな）Gibbs測度の下での最大値について考える．特に，外場の確率変数の末尾確率の挙動に応じて最大値の挙動が変わることを示し，その主要項を特徴付ける．
相分離の界面モデルの一つとして格子上のGauss型界面モデル（離散Gauss自由場）を取り上げ，そこにランダムな外場（化学ポテンシャル）を加えた（ランダムな）Gibbs測度の下での最大値について考える．特に，外場の確率変数の末尾確率の挙動に応じて最大値の挙動が変わることを示し，その主要項を特徴付ける．
2024/07/04
Algebraic Geometry Seminar
13:00-14:30 Room #ハイブリッド開催/118 (Graduate School of Math. Sci. Bldg.)
Stefan Reppen (University of Tokyo)
On a principle of Ogus: the Hasse invariant's order of vanishing and "Frobenius and the Hodge filtration'' (English)
Stefan Reppen (University of Tokyo)
On a principle of Ogus: the Hasse invariant's order of vanishing and "Frobenius and the Hodge filtration'' (English)
[ Abstract ]
In joint work with W. Goldring we generalize a result of Ogus that, under certain technical conditions, the vanishing order of the Hasse invariant of a family $Y/X$ of $n$-dimensional Calabi-Yau varieties in characteristic $p$ at a point $x$ of $X$ equals the "conjugate line position" of $H^n_{\dR}(Y/X)$ at $x$, i.e. the largest $i$ such that the line of the conjugate filtration is contained in $\text{Fil}^i$ of the Hodge filtration. For every triple $(G,\mu,r)$ consisting of a connected, reductive $\mathbb{F}_p$-group $G$, a cocharacter $\mu \in X_*(G)$ and an $\mathbb{F}_p$-representation $r$ of $G$, we state a generalized Ogus Principle. If $\zeta:X \to \GZip^{\mu}$ is a smooth morphism, then the group theoretic Ogus Principle implies an Ogus Principle on $X$. We deduce an Ogus Principle for several Hodge and abelian-type Shimura varieties and the moduli space of K3 surfaces. In the talk I will present this work.
In joint work with W. Goldring we generalize a result of Ogus that, under certain technical conditions, the vanishing order of the Hasse invariant of a family $Y/X$ of $n$-dimensional Calabi-Yau varieties in characteristic $p$ at a point $x$ of $X$ equals the "conjugate line position" of $H^n_{\dR}(Y/X)$ at $x$, i.e. the largest $i$ such that the line of the conjugate filtration is contained in $\text{Fil}^i$ of the Hodge filtration. For every triple $(G,\mu,r)$ consisting of a connected, reductive $\mathbb{F}_p$-group $G$, a cocharacter $\mu \in X_*(G)$ and an $\mathbb{F}_p$-representation $r$ of $G$, we state a generalized Ogus Principle. If $\zeta:X \to \GZip^{\mu}$ is a smooth morphism, then the group theoretic Ogus Principle implies an Ogus Principle on $X$. We deduce an Ogus Principle for several Hodge and abelian-type Shimura varieties and the moduli space of K3 surfaces. In the talk I will present this work.
2024/07/03
Lectures
16:00-17:30 Room #052 (Graduate School of Math. Sci. Bldg.)
Kelvin Lam (Department of Mathematics, University of Washington, U.S.A.)
Boundary Rigidity and the Geodesic X-ray Transform in Low Regularity (English)
Kelvin Lam (Department of Mathematics, University of Washington, U.S.A.)
Boundary Rigidity and the Geodesic X-ray Transform in Low Regularity (English)
2024/07/02
Tuesday Seminar on Topology
17:00-18:30 Room #ハイブリッド開催/117 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Kokoro Tanaka (Tokyo Gakugei University)
The second quandle homology group of the knot $n$-quandle (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Kokoro Tanaka (Tokyo Gakugei University)
The second quandle homology group of the knot $n$-quandle (JAPANESE)
[ Abstract ]
We compute the second quandle homology group of the knot $n$-quandle for each integer $n>1$, where the knot $n$-quandle is a certain quotient of the knot quandle (of an oriented classical knot in the $3$-sphere). Although the second quandle homology group of the knot quandle can only detect the unknot, it turns out that that of its 3-quandle can detect the unknot, the trefoil and the cinqfoil. This is a joint work with Yuta Taniguchi.
[ Reference URL ]We compute the second quandle homology group of the knot $n$-quandle for each integer $n>1$, where the knot $n$-quandle is a certain quotient of the knot quandle (of an oriented classical knot in the $3$-sphere). Although the second quandle homology group of the knot quandle can only detect the unknot, it turns out that that of its 3-quandle can detect the unknot, the trefoil and the cinqfoil. This is a joint work with Yuta Taniguchi.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/06/28
Tokyo-Nagoya Algebra Seminar
16:30-18:00 Online
Shunya Saito (The University of Tokyo)
Classifying KE-closed subcategories (Japanese)
[ Reference URL ]
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Shunya Saito (The University of Tokyo)
Classifying KE-closed subcategories (Japanese)
[ Reference URL ]
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Seminar on Probability and Statistics
13:00-14:10 Room #128 (Graduate School of Math. Sci. Bldg.)
原田 和治 (東京医科大学医療データサイエンス分野)
医学における予測モデルの活用と階層構造を持つ順序回帰の提案 (日本語)
[ Reference URL ]
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZUpd-ispjIqG9NfJk7_kjW2pBcvq_KMXHPW
原田 和治 (東京医科大学医療データサイエンス分野)
医学における予測モデルの活用と階層構造を持つ順序回帰の提案 (日本語)
[ Reference URL ]
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZUpd-ispjIqG9NfJk7_kjW2pBcvq_KMXHPW
Algebraic Geometry Seminar
13:30-15:00 Room #ハイブリッド開催/117 (Graduate School of Math. Sci. Bldg.)
Taro Yoshino (The University of Tokyo)
Stable rationality of hypersurfaces in mock toric varieties (日本語)
Taro Yoshino (The University of Tokyo)
Stable rationality of hypersurfaces in mock toric varieties (日本語)
[ Abstract ]
In recent years, there has been a development in approaching rationality problems through motivic methods. This approach requires the explicit construction of degeneration families over curves with favorable properties. However, the specific construction is generally difficult. Nicaise and Ottem combined combinatorial methods to construct degeneration families of hypersurfaces in toric varieties and mentioned the stable rationality of a very general hypersurface in projective spaces. In this talk, we mention the following two points: First, I introduce the notion of mock toric varieties, which are generalizations of toric varieties. Second, I combinatorially construct degeneration families of hypersurfaces in mock toric varieties, and I mention the irrationality of a very general hypersurface in the complex Grassmannian variety Gr(2, n).
In recent years, there has been a development in approaching rationality problems through motivic methods. This approach requires the explicit construction of degeneration families over curves with favorable properties. However, the specific construction is generally difficult. Nicaise and Ottem combined combinatorial methods to construct degeneration families of hypersurfaces in toric varieties and mentioned the stable rationality of a very general hypersurface in projective spaces. In this talk, we mention the following two points: First, I introduce the notion of mock toric varieties, which are generalizations of toric varieties. Second, I combinatorially construct degeneration families of hypersurfaces in mock toric varieties, and I mention the irrationality of a very general hypersurface in the complex Grassmannian variety Gr(2, n).
2024/06/27
Applied Analysis
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Ryo OIZUMI (National Institute of Population and Social Security Research)
A Control Theory in Mathematical Demography (Japanese)
Ryo OIZUMI (National Institute of Population and Social Security Research)
A Control Theory in Mathematical Demography (Japanese)
[ Abstract ]
Multistate Age-Structured Population Model is a fundamental mathematical model in mathematical demography that describes population structure and dynamics with state variables that are not uniform with age (e.g., body size, place of residence, genetic characteristics, etc.). The model's eigensystems have been used in various demographic analyses, providing essential indicators for discussing evolutionary theory. In this study, we derive a control equation (HJB equation) that maximizes the spectral radius from the eigensystem of the multistate age-structured population model and discuss the control process that generates an evolutionarily adaptive life history.
Multistate Age-Structured Population Model is a fundamental mathematical model in mathematical demography that describes population structure and dynamics with state variables that are not uniform with age (e.g., body size, place of residence, genetic characteristics, etc.). The model's eigensystems have been used in various demographic analyses, providing essential indicators for discussing evolutionary theory. In this study, we derive a control equation (HJB equation) that maximizes the spectral radius from the eigensystem of the multistate age-structured population model and discuss the control process that generates an evolutionarily adaptive life history.
2024/06/25
Operator Algebra Seminars
16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
Mao Hoshino (Univ. Tokyo)
Polynomial family of quantum flag manifolds via deformed QEA
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Mao Hoshino (Univ. Tokyo)
Polynomial family of quantum flag manifolds via deformed QEA
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Joint with RIKEN iTHEMS. Pre-registration required. See our seminar webpage.
Emmy Murphy (University of Toronto)
Liouville symmetry groups and pseudo-isotopies (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Joint with RIKEN iTHEMS. Pre-registration required. See our seminar webpage.
Emmy Murphy (University of Toronto)
Liouville symmetry groups and pseudo-isotopies (ENGLISH)
[ Abstract ]
Even though $\mathbb{C}^n$ is the most basic symplectic manifold, when $n>2$ its compactly supported symplectomorphism group remains mysterious. For instance, we do not know if it is connected. To understand it better, one can define various subgroups of the symplectomorphism group, and a number of Serre fibrations between them. This leads us to the Liouville pseudo-isotopy group of a contact manifold, important for relating (for instance) compactly supported symplectomorphisms of $\mathbb{C}^n$, and contactomorphisms of the sphere at infinity. After explaining this background, the talk will focus on a new result: that the pseudo-isotopy group is connected, under a Liouville-vs-Weinstein hypothesis.
[ Reference URL ]Even though $\mathbb{C}^n$ is the most basic symplectic manifold, when $n>2$ its compactly supported symplectomorphism group remains mysterious. For instance, we do not know if it is connected. To understand it better, one can define various subgroups of the symplectomorphism group, and a number of Serre fibrations between them. This leads us to the Liouville pseudo-isotopy group of a contact manifold, important for relating (for instance) compactly supported symplectomorphisms of $\mathbb{C}^n$, and contactomorphisms of the sphere at infinity. After explaining this background, the talk will focus on a new result: that the pseudo-isotopy group is connected, under a Liouville-vs-Weinstein hypothesis.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/06/24
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Kazumasa Narita (Nagoya Univ.)
. (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Kazumasa Narita (Nagoya Univ.)
. (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
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.
Fumihiko Nakano (Tohoku University)
Temperley - Lieb 演算子の持ち上げとRazumov - Stroganov 予想について (日本語)
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Fumihiko Nakano (Tohoku University)
Temperley - Lieb 演算子の持ち上げとRazumov - Stroganov 予想について (日本語)
[ Abstract ]
Razumov - Stroganov 予想とはリンクパターン上の生成する線型空間上のあるハミルトニアンの基底状態に対応するFPLの個数が現れるという予想で、２０１０年に解決されたが、O(1)-loop model, 交代符号行列を介して２次元統計力学の模型や組み合わせ論との様々なつながりがあり、今も注目されている。Temperley - Lieb 演算子の持ち上げを用いたRS予想のより平易な証明について議論する。
Razumov - Stroganov 予想とはリンクパターン上の生成する線型空間上のあるハミルトニアンの基底状態に対応するFPLの個数が現れるという予想で、２０１０年に解決されたが、O(1)-loop model, 交代符号行列を介して２次元統計力学の模型や組み合わせ論との様々なつながりがあり、今も注目されている。Temperley - Lieb 演算子の持ち上げを用いたRS予想のより平易な証明について議論する。
2024/06/21
Tokyo-Nagoya Algebra Seminar
16:30-18:00 Online
Daigo Ito (UC Berkeley)
松井スペクトラムを用いた復元定理の再解釈 (Japanese)
[ Reference URL ]
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Daigo Ito (UC Berkeley)
松井スペクトラムを用いた復元定理の再解釈 (Japanese)
[ Reference URL ]
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Colloquium
15:30-16:30 Room #大講義室(auditorium) (Graduate School of Math. Sci. Bldg.)
In order to contact you in case of an outbreak of infections, we appreciate your regitration by following the link in the [Reference URL] field below.
Mircea Mustaţă (The University of Michigan)
The minimal exponent of hypersurface singularities (English)
https://docs.google.com/forms/d/e/1FAIpQLSdUrEZYZ4fvi8So3pUVkxF08M2jbVdo7hTew_B1S5l-opFyzg/viewform?usp=sharing
In order to contact you in case of an outbreak of infections, we appreciate your regitration by following the link in the [Reference URL] field below.
Mircea Mustaţă (The University of Michigan)
The minimal exponent of hypersurface singularities (English)
[ Abstract ]
The log canonical threshold of a hypersurface is an invariant of singularities that plays an important role in birational geometry, but which arises in many other contexts and admits different characterizations. A refinement of this invariant is Saito's minimal exponent, whose definition relies on the theory of b-functions, an important concept in D-module theory. The new information (by comparison with the log canonical threshold) provides a numerical measure of rational singularities. In this talk I will give an introduction to minimal exponents, highlighting recent progress and open questions.
[ Reference URL ]The log canonical threshold of a hypersurface is an invariant of singularities that plays an important role in birational geometry, but which arises in many other contexts and admits different characterizations. A refinement of this invariant is Saito's minimal exponent, whose definition relies on the theory of b-functions, an important concept in D-module theory. The new information (by comparison with the log canonical threshold) provides a numerical measure of rational singularities. In this talk I will give an introduction to minimal exponents, highlighting recent progress and open questions.
https://docs.google.com/forms/d/e/1FAIpQLSdUrEZYZ4fvi8So3pUVkxF08M2jbVdo7hTew_B1S5l-opFyzg/viewform?usp=sharing
Algebraic Geometry Seminar
13:30-15:00 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Kien Nguyen Huu (Normandie Université/KU Leuven)
ON THE POWER SERIES OF DENEF AND LOESER'S MOTIVIC VANISHING CYCLES OF JET POLYNOMIALS (English)
Kien Nguyen Huu (Normandie Université/KU Leuven)
ON THE POWER SERIES OF DENEF AND LOESER'S MOTIVIC VANISHING CYCLES OF JET POLYNOMIALS (English)
[ Abstract ]
Let f be a non-constant polynomial in n variables over a field k of characteristic
0. Denef and Loeser introduced the notion of motivic vanishing cycles of f as an element in
the localization Mμˆ of the Grothendieck ring Kμˆ(Var ) of k-varieties with a good action of k0k
μˆ := lim μm by inverting the affne line equipped with the trivial action of μˆ, where μm
is the group scheme over k of mth roots of unity. In particular, if k is the field of complex
numbers then Denef and Loeser showed that their motivic vanishing cycles and the complex
φf [n − 1] has the same Hodge characteristic, where φf is the complex of vanishing cycles
in the usual sense. Motivated by the Igusa conjecture for exponential sums and the strong
monodromy conjecture, we introduce the notion of Poincaré series of Denef-Loeser's van-
ishing cycles of jet polynomials of f, where jet polynomials of f are polynomials appearing
naturally when we compute the jet schemes of f. By using Davison-Meinhardt's conjecture
which was proved by Nicaise and Payne in 2019, we can show that our Poincaré series is a
rational function over a quotient ring of Mμˆ by very natural relations. In particular, we can k
recovery Denef and Loeser's motivic vanishing cycles from our Poincaré series. Moreover, we can show that our Poincaré series owns a universal property in the sense that if k is a number field then the Igusa local zeta functions, the motivic Igusa zeta functions, the Poincaré series of exponential sums modulo pm of f can be obtained from our Poincaré se- ries by suitable specialization maps preserving the rationality. If time permits, I will present some initial consequences that have arisen during the study of our Poincaré series.
Let f be a non-constant polynomial in n variables over a field k of characteristic
0. Denef and Loeser introduced the notion of motivic vanishing cycles of f as an element in
the localization Mμˆ of the Grothendieck ring Kμˆ(Var ) of k-varieties with a good action of k0k
μˆ := lim μm by inverting the affne line equipped with the trivial action of μˆ, where μm
is the group scheme over k of mth roots of unity. In particular, if k is the field of complex
numbers then Denef and Loeser showed that their motivic vanishing cycles and the complex
φf [n − 1] has the same Hodge characteristic, where φf is the complex of vanishing cycles
in the usual sense. Motivated by the Igusa conjecture for exponential sums and the strong
monodromy conjecture, we introduce the notion of Poincaré series of Denef-Loeser's van-
ishing cycles of jet polynomials of f, where jet polynomials of f are polynomials appearing
naturally when we compute the jet schemes of f. By using Davison-Meinhardt's conjecture
which was proved by Nicaise and Payne in 2019, we can show that our Poincaré series is a
rational function over a quotient ring of Mμˆ by very natural relations. In particular, we can k
recovery Denef and Loeser's motivic vanishing cycles from our Poincaré series. Moreover, we can show that our Poincaré series owns a universal property in the sense that if k is a number field then the Igusa local zeta functions, the motivic Igusa zeta functions, the Poincaré series of exponential sums modulo pm of f can be obtained from our Poincaré se- ries by suitable specialization maps preserving the rationality. If time permits, I will present some initial consequences that have arisen during the study of our Poincaré series.
2024/06/20
Tuesday Seminar on Topology
17:00-18:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Joint with RIKEN iTHEMS. Pre-registration required. See our seminar webpage.
Dominik Inauen (University of Leipzig)
Rigidity and Flexibility of Iosmetric Embeddings (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Joint with RIKEN iTHEMS. Pre-registration required. See our seminar webpage.
Dominik Inauen (University of Leipzig)
Rigidity and Flexibility of Iosmetric Embeddings (ENGLISH)
[ Abstract ]
The problem of embedding abstract Riemannian manifolds isometrically (i.e. preserving the lengths) into Euclidean space stems from the conceptually fundamental question of whether abstract Riemannian manifolds and submanifolds of Euclidean space are the same. As it turns out, such embeddings have a drastically different behaviour at low regularity (i.e. $C^1$) than at high regularity (i.e. $C^2$). For example, by the famous Nash--Kuiper theorem it is possible to find $C^1$ isometric embeddings of the standard $2$-sphere into arbitrarily small balls in $\mathbb{R}^3$, and yet, in the $C^2$ category there is (up to translation and rotation) just one isometric embedding, namely the standard inclusion. Analoguous to the Onsager conjecture in fluid dynamics, one might ask if there is a sharp regularity threshold in the Hölder scale which distinguishes these flexible and rigid behaviours. In my talk I will review some known results and argue why the Hölder exponent 1/2 can be seen as a critical exponent in the problem.
[ Reference URL ]The problem of embedding abstract Riemannian manifolds isometrically (i.e. preserving the lengths) into Euclidean space stems from the conceptually fundamental question of whether abstract Riemannian manifolds and submanifolds of Euclidean space are the same. As it turns out, such embeddings have a drastically different behaviour at low regularity (i.e. $C^1$) than at high regularity (i.e. $C^2$). For example, by the famous Nash--Kuiper theorem it is possible to find $C^1$ isometric embeddings of the standard $2$-sphere into arbitrarily small balls in $\mathbb{R}^3$, and yet, in the $C^2$ category there is (up to translation and rotation) just one isometric embedding, namely the standard inclusion. Analoguous to the Onsager conjecture in fluid dynamics, one might ask if there is a sharp regularity threshold in the Hölder scale which distinguishes these flexible and rigid behaviours. In my talk I will review some known results and argue why the Hölder exponent 1/2 can be seen as a critical exponent in the problem.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/06/19
Number Theory Seminar
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Abhinandan (University of Tokyo)
Prismatic $F$-crystals and Wach modules (English)
Abhinandan (University of Tokyo)
Prismatic $F$-crystals and Wach modules (English)
[ Abstract ]
For an absolutely unramified extension $K/\mathbb{Q}_p$ with perfect residue field, by the works of Fontaine, Colmez, Wach and Berger, it is well known that the category of Wach modules over a certain integral period ring is equivalent to the category of lattices inside crystalline representations of $G_K$ (the absolute Galois group of $K$). Moreover, by the recent works of Bhatt and Scholze, we also know that lattices inside crystalline representations of $G_K$ are equivalent to the category of prismatic $F$-crystals on the absolute prismatic site of $O_K$, the ring of integers of $K$. The goal of this talk is to present a direct construction of the categorical equivalence between Wach modules and prismatic $F$-crystals over the absolute prismatic site of $O_K$. If time permits, we will also mention a generalisation of these results to the case of a "small" base ring.
For an absolutely unramified extension $K/\mathbb{Q}_p$ with perfect residue field, by the works of Fontaine, Colmez, Wach and Berger, it is well known that the category of Wach modules over a certain integral period ring is equivalent to the category of lattices inside crystalline representations of $G_K$ (the absolute Galois group of $K$). Moreover, by the recent works of Bhatt and Scholze, we also know that lattices inside crystalline representations of $G_K$ are equivalent to the category of prismatic $F$-crystals on the absolute prismatic site of $O_K$, the ring of integers of $K$. The goal of this talk is to present a direct construction of the categorical equivalence between Wach modules and prismatic $F$-crystals over the absolute prismatic site of $O_K$. If time permits, we will also mention a generalisation of these results to the case of a "small" base ring.
2024/06/18
Operator Algebra Seminars
16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
Hiroshi Ando (Chiba Univ.)
Lie theoretic approach to the unitary groups of $C^*$-algebras
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Hiroshi Ando (Chiba Univ.)
Lie theoretic approach to the unitary groups of $C^*$-algebras
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Tuesday Seminar of Analysis
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
MORI Ryunosuke (Meiji University)
Blocking and propagation in two-dimensional cylinders with spatially undulating boundary (Japanese)
https://forms.gle/TrFmSZQ1ZeqvSjfP7
MORI Ryunosuke (Meiji University)
Blocking and propagation in two-dimensional cylinders with spatially undulating boundary (Japanese)
[ Abstract ]
We consider blocking and propagation phenomena of mean curvature flow with a driving force in two-dimensional cylinders with spatially undulating boundary. In this problem, Matano, Nakamura and Lou in 2006, 2013 characterize the effect of the shape of the boundary to blocking and propagation of the solutions under some slop condition about the boundary that implies time global existence of the classical solutions. In this talk, we consider the effect of the shape of the boundary to blocking and propagation of this problem under more general situation that the solutions may develop singularities near the boundary.
[ Reference URL ]We consider blocking and propagation phenomena of mean curvature flow with a driving force in two-dimensional cylinders with spatially undulating boundary. In this problem, Matano, Nakamura and Lou in 2006, 2013 characterize the effect of the shape of the boundary to blocking and propagation of the solutions under some slop condition about the boundary that implies time global existence of the classical solutions. In this talk, we consider the effect of the shape of the boundary to blocking and propagation of this problem under more general situation that the solutions may develop singularities near the boundary.
https://forms.gle/TrFmSZQ1ZeqvSjfP7
Seminar on Probability and Statistics
13:00-14:10 Room #128 (Graduate School of Math. Sci. Bldg.)
Lorenzo Mercuri (University of Milan)
A compound CARMA(p,q)-Hawkes process for pricing financial derivatives (English)
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZ0rcOmvpjwuGNHx8ht0rMs1rD3HcEajoJv6
Lorenzo Mercuri (University of Milan)
A compound CARMA(p,q)-Hawkes process for pricing financial derivatives (English)
[ Abstract ]
Recently, a new self-exciting point process with a continuous-time autoregressive moving average intensity process, named CARMA(p,q)-Hawkes model, has been introduced. The model generalizes the well-known Hawkes process by substituting the Ornstein-Uhlenbeck intensity with a CARMA(p,q) model where the associated state process is driven by the counting process itself. The new model maintains the same level of tractability of the Hawkes (e.g., Infinitesimal generator, backward and forward Kolmogorov equation, joint characteristic function and so on). However, it is able to reproduce more complex time-dependency structure observed in several market data.
Starting from this model, we introduce a Compound CARMA(p,q)-Hawkes with a random jump size independent of the counting and the intensity processes. This can be used as the main block for a new option pricing model, due to log-affine structure of the characteristic function of the underlying log-price driven by a pure jump compound CARMA(p,q)-Hawkes.
Further, we extend this model by scaling it with a measurable function of the time and the left-limit of the price itself. Exploiting the Markov structure of the new model, we derive the forward Kolmogorov equation that leads us to a Dupire-like formula. Some numerical results will also be presented.
[ Reference URL ]Recently, a new self-exciting point process with a continuous-time autoregressive moving average intensity process, named CARMA(p,q)-Hawkes model, has been introduced. The model generalizes the well-known Hawkes process by substituting the Ornstein-Uhlenbeck intensity with a CARMA(p,q) model where the associated state process is driven by the counting process itself. The new model maintains the same level of tractability of the Hawkes (e.g., Infinitesimal generator, backward and forward Kolmogorov equation, joint characteristic function and so on). However, it is able to reproduce more complex time-dependency structure observed in several market data.
Starting from this model, we introduce a Compound CARMA(p,q)-Hawkes with a random jump size independent of the counting and the intensity processes. This can be used as the main block for a new option pricing model, due to log-affine structure of the characteristic function of the underlying log-price driven by a pure jump compound CARMA(p,q)-Hawkes.
Further, we extend this model by scaling it with a measurable function of the time and the left-limit of the price itself. Exploiting the Markov structure of the new model, we derive the forward Kolmogorov equation that leads us to a Dupire-like formula. Some numerical results will also be presented.
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZ0rcOmvpjwuGNHx8ht0rMs1rD3HcEajoJv6
2024/06/17
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yuta Kusakabe (Kyushu Univ.)
Oka tubes in holomorphic line bundles (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Yuta Kusakabe (Kyushu Univ.)
Oka tubes in holomorphic line bundles (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Tokyo Probability Seminar
15:40-17:45 Room #126 (Graduate School of Math. Sci. Bldg.)
Lectures and TeaTime start earlier. We are having teatime from 15:00 in the common room on the second floor. Please join us.
Kento Ueda (The University of Tokyo) 15:40-16:40
非整数ブラウン運動で駆動される確率微分方程式の数値解の漸近展開 (日本語)
Homogenization results for reflecting diffusions in a continuum percolation cluster (日本語)
Lectures and TeaTime start earlier. We are having teatime from 15:00 in the common room on the second floor. Please join us.
Kento Ueda (The University of Tokyo) 15:40-16:40
非整数ブラウン運動で駆動される確率微分方程式の数値解の漸近展開 (日本語)
[ Abstract ]
本研究は非整数ブラウン運動(fBm)で駆動される確率微分方程式の数値解に対する極限定理(漸近誤差)に関する研究である。このfBmおよびそれによって駆動される方程式は非マルコフな時系列モデルとして用いられ、その数値解に対する極限定理は数学的興味のほか、数値シミュレーションの誤差の推定への応用が期待される。数値解の極限定理は駆動するfBmが1次元か否か、また1次元ならドリフト項が存在するか否か、さらにfBmのハースト指数、そして対象とする数値解法によって定理の主張も適用できる証明法も異なり、そのために条件ごとに様々な先行研究が存在する。このうち、本研究は1次元かつドリフト項が存在する場合に誤差分布の導出と正当化を行ったものであり、一般の数値解法に適用できる。同範囲の先行研究では高次ミルシュタイン法、クランク-ニコルソン法に対してハースト指数が1/3より大きい場合に関して漸近誤差を特定できるが、本研究では高次ミルシュタイン法の漸近誤差を任意のハースト指数に対して完全に決定するとともに、クランク-ニコルソン法に対してもハースト指数が1/4以上の場合に漸近誤差を特定している。なお、本講演では導出した誤差分布を視覚的に観察し、漸近誤差への直観的な理解を深められるよう、漸近誤差に対する数値実験の結果を詳しく説明する。
Yutaka Takeuchi ( Keio University) 16:45-17:45本研究は非整数ブラウン運動(fBm)で駆動される確率微分方程式の数値解に対する極限定理(漸近誤差)に関する研究である。このfBmおよびそれによって駆動される方程式は非マルコフな時系列モデルとして用いられ、その数値解に対する極限定理は数学的興味のほか、数値シミュレーションの誤差の推定への応用が期待される。数値解の極限定理は駆動するfBmが1次元か否か、また1次元ならドリフト項が存在するか否か、さらにfBmのハースト指数、そして対象とする数値解法によって定理の主張も適用できる証明法も異なり、そのために条件ごとに様々な先行研究が存在する。このうち、本研究は1次元かつドリフト項が存在する場合に誤差分布の導出と正当化を行ったものであり、一般の数値解法に適用できる。同範囲の先行研究では高次ミルシュタイン法、クランク-ニコルソン法に対してハースト指数が1/3より大きい場合に関して漸近誤差を特定できるが、本研究では高次ミルシュタイン法の漸近誤差を任意のハースト指数に対して完全に決定するとともに、クランク-ニコルソン法に対してもハースト指数が1/4以上の場合に漸近誤差を特定している。なお、本講演では導出した誤差分布を視覚的に観察し、漸近誤差への直観的な理解を深められるよう、漸近誤差に対する数値実験の結果を詳しく説明する。
Homogenization results for reflecting diffusions in a continuum percolation cluster (日本語)
[ Abstract ]
アブストラクト: ランダム媒質の研究において均一化は重要な問題の一つである. 均一化はいくつかの定式化が知られている, 本講演ではランダム媒質上の確率過程に関する極限定理であるquenched invariance principleと, その精密化である局所中心極限定理を考える. この様な定式化について, 離散的なモデルの場合には多くの結果が知られている. 連続的なモデルに関しても, random environment 上の拡散過程に関する結果は多く知られている. 一方拡散過程が反射壁を持つ場合に関しては, 境界の影響等により問題が複雑化するためquenchedな結果は知られていなかった. 本講演では連続パーコレーションが幾何的な条件を満たす場合, その上の反射壁を持つ拡散過程に関してquenched invariance principleと局所中心極限定理が成り立つという結果を紹介する.
アブストラクト: ランダム媒質の研究において均一化は重要な問題の一つである. 均一化はいくつかの定式化が知られている, 本講演ではランダム媒質上の確率過程に関する極限定理であるquenched invariance principleと, その精密化である局所中心極限定理を考える. この様な定式化について, 離散的なモデルの場合には多くの結果が知られている. 連続的なモデルに関しても, random environment 上の拡散過程に関する結果は多く知られている. 一方拡散過程が反射壁を持つ場合に関しては, 境界の影響等により問題が複雑化するためquenchedな結果は知られていなかった. 本講演では連続パーコレーションが幾何的な条件を満たす場合, その上の反射壁を持つ拡散過程に関してquenched invariance principleと局所中心極限定理が成り立つという結果を紹介する.
2024/06/11
Operator Algebra Seminars
16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
Taro Sogabe (Kyoto Univ.)
The ext groups and homotopy groups of the automorphism groups of Cuntz-Krieger algebras
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Taro Sogabe (Kyoto Univ.)
The ext groups and homotopy groups of the automorphism groups of Cuntz-Krieger algebras
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Tuesday Seminar on Topology
17:00-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Nariya Kawazumi (The University of Tokyo)
A topological proof of Wolpert's formula of the Weil-Petersson symplectic form in terms of the Fenchel-Nielsen coordinates (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Nariya Kawazumi (The University of Tokyo)
A topological proof of Wolpert's formula of the Weil-Petersson symplectic form in terms of the Fenchel-Nielsen coordinates (JAPANESE)
[ Abstract ]
Wolpert explicitly described the Weil-Petersson symplectic form on the Teichmüller space in terms of the Fenchel-Nielsen coordinate system, which comes from a pants decomposition of a surface. By introducing a natural cell-decomposition associated with the decomposition, we give a topological proof of Wolpert's formula, where the symplectic form localizes near the simple closed curves defining the decomposition.
[ Reference URL ]Wolpert explicitly described the Weil-Petersson symplectic form on the Teichmüller space in terms of the Fenchel-Nielsen coordinate system, which comes from a pants decomposition of a surface. By introducing a natural cell-decomposition associated with the decomposition, we give a topological proof of Wolpert's formula, where the symplectic form localizes near the simple closed curves defining the decomposition.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/06/10
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Katsusuke Nabeshima (Tokyo Univ. of Science)
Computing Noetherian operators of polynomial ideals
--How to characterize a polynomial ideal by partial differential operators -- (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
Katsusuke Nabeshima (Tokyo Univ. of Science)
Computing Noetherian operators of polynomial ideals
--How to characterize a polynomial ideal by partial differential operators -- (Japanese)
[ Abstract ]
Describing ideals in polynomial rings by using systems of differential operators in one of the major approaches to study them. In 1916, F.S. Macaulay brought the notion of an inverse system, a system of differential conditions that describes an ideal. In 1937, W. Groebner mentioned the importance of the Macaulay's inverse system in the study of linear differential equations with constant coefficient, and in 1938, he introduced differential operators to characterize ideals that are primary to a rational maximal ideal. After that the important results and the terminology came from L. Ehrenpreise and V. P. Palamodov in 1961 and 1970, that is the characterization of primary ideals by the differential operators. The differential operators allow one to characterize the primary ideal by differential conditions on the associated characteristic variety. The differential operators are called Noetherian operators.
In this talk, we consider Noetherian operators in the context of symbolic computation. Upon utilizing the theory of holonomic D-modules, we present a new computational method of Noetherian operators associated to a polynomial ideal. The computational method that consists mainly of linear algebra techniques is given for computing them. Moreover, as applications, new computational methods of polynomial ideals are discussed by utilizing the Noetherian operators.
[ Reference URL ]Describing ideals in polynomial rings by using systems of differential operators in one of the major approaches to study them. In 1916, F.S. Macaulay brought the notion of an inverse system, a system of differential conditions that describes an ideal. In 1937, W. Groebner mentioned the importance of the Macaulay's inverse system in the study of linear differential equations with constant coefficient, and in 1938, he introduced differential operators to characterize ideals that are primary to a rational maximal ideal. After that the important results and the terminology came from L. Ehrenpreise and V. P. Palamodov in 1961 and 1970, that is the characterization of primary ideals by the differential operators. The differential operators allow one to characterize the primary ideal by differential conditions on the associated characteristic variety. The differential operators are called Noetherian operators.
In this talk, we consider Noetherian operators in the context of symbolic computation. Upon utilizing the theory of holonomic D-modules, we present a new computational method of Noetherian operators associated to a polynomial ideal. The computational method that consists mainly of linear algebra techniques is given for computing them. Moreover, as applications, new computational methods of polynomial ideals are discussed by utilizing the Noetherian operators.
https://forms.gle/gTP8qNZwPyQyxjTj8
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