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Seminar information archive
Seminar information archive ～01/13｜Today's seminar 01/14 | Future seminars 01/15～
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
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.
Yukimi Goto (Gakushuin University)
Phase Transition in a Lattice Nambu–Jona-Lasinio Model (日本語)
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Yukimi Goto (Gakushuin University)
Phase Transition in a Lattice Nambu–Jona-Lasinio Model (日本語)
[ Abstract ]
量子色力学で重要な概念としてカイラル対称性の破れとそれに伴うフェルミオンの質量生成があるが、その証明は困難が多い。その理解に格子上の量子色力学は成功していると見られているものの、数学的結果はいまだ限られている。
この講演では格子上のフェルミオンの定式化のひとつであるスタッガード・フェルミオンをもちいて、それらが4つのフェルミオンと相互作用する模型（lattice Nambu–Jona-Lasinio model）を考える。この模型は離散的なカイラル対称性しかもたないものの、質量が自発的に生成することと、それに伴う対称性の破れを証明できる。また、連続的なフレーバー対称性をもつ場合は南部・ゴールドストーン・モードと呼ばれるスペクトルにギャップのない無限系の基底状態が出現することを説明する。
本講演は高麗徹氏との共同研究にもとづく。
量子色力学で重要な概念としてカイラル対称性の破れとそれに伴うフェルミオンの質量生成があるが、その証明は困難が多い。その理解に格子上の量子色力学は成功していると見られているものの、数学的結果はいまだ限られている。
この講演では格子上のフェルミオンの定式化のひとつであるスタッガード・フェルミオンをもちいて、それらが4つのフェルミオンと相互作用する模型（lattice Nambu–Jona-Lasinio model）を考える。この模型は離散的なカイラル対称性しかもたないものの、質量が自発的に生成することと、それに伴う対称性の破れを証明できる。また、連続的なフレーバー対称性をもつ場合は南部・ゴールドストーン・モードと呼ばれるスペクトルにギャップのない無限系の基底状態が出現することを説明する。
本講演は高麗徹氏との共同研究にもとづく。
FJ-LMI Seminar
13:30-14:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Sourav GHOSH (Ashoka University, India)
Affine Anosov representations
https://fj-lmi.cnrs.fr/seminars/
Sourav GHOSH (Ashoka University, India)
Affine Anosov representations
[ Abstract ]
In this survey talk I will give a brief overview of affine Anosov representations. These are appropriate analogues of Anosov representations inside affine Lie groups and are closely related with proper affine actions of hyperbolic groups.
[ Reference URL ]In this survey talk I will give a brief overview of affine Anosov representations. These are appropriate analogues of Anosov representations inside affine Lie groups and are closely related with proper affine actions of hyperbolic groups.
https://fj-lmi.cnrs.fr/seminars/
2024/06/07
Algebraic Geometry Seminar
13:30-15:00 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Ivan Cheltsov (University of Edinburgh)
K-stability of pointless Fano 3-folds (English)
Ivan Cheltsov (University of Edinburgh)
K-stability of pointless Fano 3-folds (English)
[ Abstract ]
In this talk we will show how to prove that all pointless smooth Fano 3-folds defined over a subfield of the field of complex numbers are Kahler-Einstein unless they belong to 8 exceptional deformation families. This is a joint work in progress with Hamid Abban (Nottingham) and Frederic Mangolte (Marseille).
In this talk we will show how to prove that all pointless smooth Fano 3-folds defined over a subfield of the field of complex numbers are Kahler-Einstein unless they belong to 8 exceptional deformation families. This is a joint work in progress with Hamid Abban (Nottingham) and Frederic Mangolte (Marseille).
Tokyo-Nagoya Algebra Seminar
16:30-18:00 Online
Taiki Shibata (Okayama University of Science)
スーパー代数群の表現と奇鏡映について (Japanese)
[ Reference URL ]
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Taiki Shibata (Okayama University of Science)
スーパー代数群の表現と奇鏡映について (Japanese)
[ Reference URL ]
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2024/06/04
Operator Algebra Seminars
16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
Ryoya Arimoto (RIMS, Kyoto Univ.)
Simplicity of crossed products of the actions of totally disconnected locally compact groups on their boundaries
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Ryoya Arimoto (RIMS, Kyoto Univ.)
Simplicity of crossed products of the actions of totally disconnected locally compact groups on their boundaries
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Tuesday Seminar on Topology
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Katsumi Ishikawa (RIMS, Kyoto University)
The trapezoidal conjecture for the links of braid index 3 (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Katsumi Ishikawa (RIMS, Kyoto University)
The trapezoidal conjecture for the links of braid index 3 (JAPANESE)
[ Abstract ]
The trapezoidal conjecture is a classical famous conjecture posed by Fox, which states that the coefficient sequence of the Alexander polynomial of any alternating link is trapezoidal. In this talk, we show this conjecture for any alternating links of braid index 3. Although the result holds for any choice of the orientation, we shall mainly discuss the case of the closures of alternating 3-braids with parallel orientations.
[ Reference URL ]The trapezoidal conjecture is a classical famous conjecture posed by Fox, which states that the coefficient sequence of the Alexander polynomial of any alternating link is trapezoidal. In this talk, we show this conjecture for any alternating links of braid index 3. Although the result holds for any choice of the orientation, we shall mainly discuss the case of the closures of alternating 3-braids with parallel orientations.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/05/31
Colloquium
15:30-16:30 Room #大講義室(auditorium) (Graduate School of Math. Sci. Bldg.)
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at [Reference URL].
Hiroshi Sakai (Graduate School of Mathematical Sciences, The University of Tokyo)
Introduction to large cardinals (JAPANESE)
https://forms.gle/ZmHhZW6bxUyKewro8
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at [Reference URL].
Hiroshi Sakai (Graduate School of Mathematical Sciences, The University of Tokyo)
Introduction to large cardinals (JAPANESE)
[ Abstract ]
Set theory is a branch of mathematics which studies infinite sets, and various infinite cardinals are considered in set theory. Among them, large cardinals are uncountable cardinals which have some transcendental properties to smaller cardinals. So far, many large cardinals are formulated by set theorists. They are so large that their existences are not provable in the standard axiom system ZFC of set theory. The axioms asserting their existences are called large cardinal axioms. One of interesting points of large cardinals is that, while large cardinals are much larger than the cardinality of the set of real numbers, we can prove various facts on sets of real numbers using large cardinal axioms. In this talk, I will explain outline of large cardinal theory. I will also talk about large cardinal properties of small uncountable cardinals, which I am interested in.
[ Reference URL ]Set theory is a branch of mathematics which studies infinite sets, and various infinite cardinals are considered in set theory. Among them, large cardinals are uncountable cardinals which have some transcendental properties to smaller cardinals. So far, many large cardinals are formulated by set theorists. They are so large that their existences are not provable in the standard axiom system ZFC of set theory. The axioms asserting their existences are called large cardinal axioms. One of interesting points of large cardinals is that, while large cardinals are much larger than the cardinality of the set of real numbers, we can prove various facts on sets of real numbers using large cardinal axioms. In this talk, I will explain outline of large cardinal theory. I will also talk about large cardinal properties of small uncountable cardinals, which I am interested in.
https://forms.gle/ZmHhZW6bxUyKewro8
2024/05/30
Applied Analysis
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Tim Laux (University of Regensburg, Germany)
Energy convergence of the Allen-Cahn equation for mean convex mean curvature flow (English)
https://forms.gle/8KnFWfHFbkn9fAqaA
Tim Laux (University of Regensburg, Germany)
Energy convergence of the Allen-Cahn equation for mean convex mean curvature flow (English)
[ Abstract ]
In this talk, I'll present a work in progress in which I positively answer a question of Ilmanen (JDG 1993) on the strong convergence of the Allen-Cahn equation to mean curvature flow when starting from well-prepared initial data around a mean convex surface. As a corollary, the conditional convergence result with Simon (CPAM 2018) becomes unconditional in the mean convex case.
[ Reference URL ]In this talk, I'll present a work in progress in which I positively answer a question of Ilmanen (JDG 1993) on the strong convergence of the Allen-Cahn equation to mean curvature flow when starting from well-prepared initial data around a mean convex surface. As a corollary, the conditional convergence result with Simon (CPAM 2018) becomes unconditional in the mean convex case.
https://forms.gle/8KnFWfHFbkn9fAqaA
2024/05/29
Numerical Analysis Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Satoshi Hayakawa (Sony Group Corporation)
Random convex hulls and kernel quadrature (Japanese)
[ Reference URL ]
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Satoshi Hayakawa (Sony Group Corporation)
Random convex hulls and kernel quadrature (Japanese)
[ Reference URL ]
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
2024/05/28
Tuesday Seminar on Topology
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Andreani Petrou (Okinawa Institute of Science and Technology)
Knot invariants and their Harer-Zagier transform (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Andreani Petrou (Okinawa Institute of Science and Technology)
Knot invariants and their Harer-Zagier transform (ENGLISH)
[ Abstract ]
The Harer-Zagier (HZ) transform is a discrete Laplace transform that can be applied to knot polynomials, mapping them into a rational function of two variables $\lambda$ and $q$. The HZ transform of the HOMFLY-PT polynomial has a simple form, as it can be written as a sum of factorised terms. For some special families of knots, it can be fully factorised and it is completely determined by a set of exponents. There is an interesting relation between such exponents and Khovanov homology. Moreover, we conjecture that there is an 1-1 correspondence with such factorisability and a relation between the HOMFLY-PT and Kauffman polynomials. Furthermore, we suggest that by fixing the variable $\lambda= q^n$ for some "magical" exponent $n$, the HZ transform of any knot can obtain a factorised form in terms of cyclotomic polynomials. Finally, the zeros of the HZ transform show an interesting behaviour, which shall be discussed.
[ Reference URL ]The Harer-Zagier (HZ) transform is a discrete Laplace transform that can be applied to knot polynomials, mapping them into a rational function of two variables $\lambda$ and $q$. The HZ transform of the HOMFLY-PT polynomial has a simple form, as it can be written as a sum of factorised terms. For some special families of knots, it can be fully factorised and it is completely determined by a set of exponents. There is an interesting relation between such exponents and Khovanov homology. Moreover, we conjecture that there is an 1-1 correspondence with such factorisability and a relation between the HOMFLY-PT and Kauffman polynomials. Furthermore, we suggest that by fixing the variable $\lambda= q^n$ for some "magical" exponent $n$, the HZ transform of any knot can obtain a factorised form in terms of cyclotomic polynomials. Finally, the zeros of the HZ transform show an interesting behaviour, which shall be discussed.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/05/27
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Taiji Marugame (The Univ. of Electro-Communications)
Hyperkähler ambient metrics associated with twistor CR manifolds (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Taiji Marugame (The Univ. of Electro-Communications)
Hyperkähler ambient metrics associated with twistor CR manifolds (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.
Ryoichiro Noda (Kyoto University)
測度付き抵抗距離空間上の確率過程の局所時間のスケール極限について (日本語)
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Ryoichiro Noda (Kyoto University)
測度付き抵抗距離空間上の確率過程の局所時間のスケール極限について (日本語)
[ Abstract ]
抵抗距離空間は電気回路の一般化であり，ディリクレ形式の理論により測度付き抵抗距離空間には確率過程が定まる．Croydon-Hambly-Kumagai (2017)は収束する抵抗距離空間が一様体積倍化条件を満たすならば対応する確率過程とその局所時間が収束することを示した．その後Croydon (2018)はより弱い条件である非爆発条件の下で確率過程の収束を示したが，局所時間の収束については未解決のままであった．本講演では非爆発条件及び距離エントロピーに関する適当な条件の下で確率過程とその局所時間の収束が従うこと，そしてこの結果の応用例について解説する．また同様の結果は離散時間マルコフ連鎖とその局所時間に対しても成立し，時間が許せばこの結果についても紹介する．
抵抗距離空間は電気回路の一般化であり，ディリクレ形式の理論により測度付き抵抗距離空間には確率過程が定まる．Croydon-Hambly-Kumagai (2017)は収束する抵抗距離空間が一様体積倍化条件を満たすならば対応する確率過程とその局所時間が収束することを示した．その後Croydon (2018)はより弱い条件である非爆発条件の下で確率過程の収束を示したが，局所時間の収束については未解決のままであった．本講演では非爆発条件及び距離エントロピーに関する適当な条件の下で確率過程とその局所時間の収束が従うこと，そしてこの結果の応用例について解説する．また同様の結果は離散時間マルコフ連鎖とその局所時間に対しても成立し，時間が許せばこの結果についても紹介する．
2024/05/24
Algebraic Geometry Seminar
13:30-15:00 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Kenta Sato (Kyusyu University)
Boundedness of weak Fano threefolds with fixed Gorenstein index in positive characteristic
Kenta Sato (Kyusyu University)
Boundedness of weak Fano threefolds with fixed Gorenstein index in positive characteristic
[ Abstract ]
In this talk, we give a partial affirmative answer to the BAB conjecture for 3-folds in characteristic p>5. Specifically, we prove that a set of weak Fano 3-folds over an uncountable algebraically closed field is bounded, if each element X satisfies certain conditions regarding the Gorenstein index, a complement and Kodaira type vanishing. In the course of the proof, we also study a uniform lower bound for Seshadri constants of nef and big invertible sheaves on projective 3-folds.
In this talk, we give a partial affirmative answer to the BAB conjecture for 3-folds in characteristic p>5. Specifically, we prove that a set of weak Fano 3-folds over an uncountable algebraically closed field is bounded, if each element X satisfies certain conditions regarding the Gorenstein index, a complement and Kodaira type vanishing. In the course of the proof, we also study a uniform lower bound for Seshadri constants of nef and big invertible sheaves on projective 3-folds.
2024/05/23
Applied Analysis
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Adina Ciomaga (University Paris Cité (Laboratoire Jacques Louis Lions), France “O Mayer” Institute of the Romanian Academy, Iasi, Roumania)
Homogenization of nonlocal Hamilton Jacobi equations (English)
Adina Ciomaga (University Paris Cité (Laboratoire Jacques Louis Lions), France “O Mayer” Institute of the Romanian Academy, Iasi, Roumania)
Homogenization of nonlocal Hamilton Jacobi equations (English)
[ Abstract ]
I will present the framework of periodic homogenisation of nonlocal Hamilton-Jacobi equations, associated with Levy-Itô integro-differential operators. A typical equation is the fractional diffusion coupled with a transport term, where the diffusion is only weakly elliptical. Homogenization is established in two steps: (i) the resolution of a cellular problem - where Lipshitz regularity of the corrector plays a key role and (ii) the convergence of the oscillating solutions towards an averaged profile - where comparison principles are involved. I shall discuss recent results on the regularity of solutions and comparison principles for nonlocal equations, and the difficulties we face when compared with local PDEs. The talked is based on recent developments obtained in collaboration with D. Ghilli, O.Ley, E. Topp, T. Minh Le.
I will present the framework of periodic homogenisation of nonlocal Hamilton-Jacobi equations, associated with Levy-Itô integro-differential operators. A typical equation is the fractional diffusion coupled with a transport term, where the diffusion is only weakly elliptical. Homogenization is established in two steps: (i) the resolution of a cellular problem - where Lipshitz regularity of the corrector plays a key role and (ii) the convergence of the oscillating solutions towards an averaged profile - where comparison principles are involved. I shall discuss recent results on the regularity of solutions and comparison principles for nonlocal equations, and the difficulties we face when compared with local PDEs. The talked is based on recent developments obtained in collaboration with D. Ghilli, O.Ley, E. Topp, T. Minh Le.
2024/05/22
Number Theory Seminar
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Takumi Watanabe (University of Tokyo)
On the (φ,Γ)-modules corresponding to crystalline representations and semi-stable representations
Takumi Watanabe (University of Tokyo)
On the (φ,Γ)-modules corresponding to crystalline representations and semi-stable representations
[ Abstract ]
From the 1980s to the 1990s, J.-M. Fontaine constructed an equivalence of categories between the category of (φ, Γ)-modules and the category of p-adic Galois representations. After recalling it, I will present my result on the (φ, Γ)-modules corresponding to crystalline representations and semi-stable representations. As for the crystalline case, this can be seen, in a sense, as a generalization of Wach module in the ramified case. If time permits, I will explain my ongoing research on the (φ, Γ)-modules corresponding to de Rham representations.
From the 1980s to the 1990s, J.-M. Fontaine constructed an equivalence of categories between the category of (φ, Γ)-modules and the category of p-adic Galois representations. After recalling it, I will present my result on the (φ, Γ)-modules corresponding to crystalline representations and semi-stable representations. As for the crystalline case, this can be seen, in a sense, as a generalization of Wach module in the ramified case. If time permits, I will explain my ongoing research on the (φ, Γ)-modules corresponding to de Rham representations.
2024/05/21
Tuesday Seminar on Topology
17:30-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Yuichi Ike (Institute of Mathematics for Industry, Kyushu University)
γ-supports and sheaves (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Yuichi Ike (Institute of Mathematics for Industry, Kyushu University)
γ-supports and sheaves (JAPANESE)
[ Abstract ]
The space of smooth compact exact Lagrangians of a cotangent bundle carries the spectral metric γ, and we consider its completion. With an element of the completion, Viterbo associated a closed subset called γ-support. In this talk, I will explain how we can use sheaf-theoretic methods to explore the completion and γ-supports. I will show that we can associate a sheaf with an element of the completion, and its (reduced) microsupport is equal to the γ-support through the correspondence. With this equality, I will also show several properties of γ-supports. This is joint work with Tomohiro Asano (RIMS), Stéphane Guillermou (Nantes Université), Vincent Humilière (Sorbonne Université), and Claude Viterbo (Université Paris-Saclay).
[ Reference URL ]The space of smooth compact exact Lagrangians of a cotangent bundle carries the spectral metric γ, and we consider its completion. With an element of the completion, Viterbo associated a closed subset called γ-support. In this talk, I will explain how we can use sheaf-theoretic methods to explore the completion and γ-supports. I will show that we can associate a sheaf with an element of the completion, and its (reduced) microsupport is equal to the γ-support through the correspondence. With this equality, I will also show several properties of γ-supports. This is joint work with Tomohiro Asano (RIMS), Stéphane Guillermou (Nantes Université), Vincent Humilière (Sorbonne Université), and Claude Viterbo (Université Paris-Saclay).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Operator Algebra Seminars
16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
Michiya Mori (Univ．Tokyo)
Optimal version of the fundamental theorem of chronogeometry
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Michiya Mori (Univ．Tokyo)
Optimal version of the fundamental theorem of chronogeometry
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
2024/05/20
Seminar on Geometric Complex Analysis
10:50-12:20 Room #128 (Graduate School of Math. Sci. Bldg.)
Lijie Sun (Yamaguchi Univ.)
Kähler metrics in the Siegel domain (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
Lijie Sun (Yamaguchi Univ.)
Kähler metrics in the Siegel domain (Japanese)
[ Abstract ]
The Siegel domain is endowed with an intrinsic Kähler structure, making it an exemplary model for the complex hyperbolic plane. Its boundary, characterized as the one-point compactification of the Heisenberg group, plays an important role in studying the geometry of the Siegel domain. In this talk, using the CR structure of the Heisenberg group we introduce a variety of Kähler structures within the Siegel domain. We conclude by demonstrating that all these metrics are PCR-Kähler equivalent, that is, essentially the same when confined to the CR structure. This talk is based on a joint work with Ioannis Platis and Joonhyung Kim.
[ Reference URL ]The Siegel domain is endowed with an intrinsic Kähler structure, making it an exemplary model for the complex hyperbolic plane. Its boundary, characterized as the one-point compactification of the Heisenberg group, plays an important role in studying the geometry of the Siegel domain. In this talk, using the CR structure of the Heisenberg group we introduce a variety of Kähler structures within the Siegel domain. We conclude by demonstrating that all these metrics are PCR-Kähler equivalent, that is, essentially the same when confined to the CR structure. This talk is based on a joint work with Ioannis Platis and Joonhyung Kim.
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.
Soma Nishino (Tokyo Metropolitan University)
2曲線間に制限されたパス空間上でのWiener測度に対する高階の部分積分公式 (日本語)
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Soma Nishino (Tokyo Metropolitan University)
2曲線間に制限されたパス空間上でのWiener測度に対する高階の部分積分公式 (日本語)
[ Abstract ]
2曲線間に制限されたパス空間上でのWiener測度に対する1階微分の部分積分公式は既に知られている。本講演では、この結果を高階微分の部分積分公式に拡張する。高階微分の部分積分公式においては、従来の1階微分の場合にはない非自明な境界項が追加で現れ、さらに、その証明において、Brownian excursionやBrownian house-movingと呼ばれる確率過程のランダムウォーク近似による構成方法が新たに必要となる。また、証明の中で、1次および2次の無限小確率の概念を導入する。この概念を導入することで、部分積分公式の各項に現れる数式に対して確率論的な解釈が可能となり、部分積分公式を整理する上で有益な概念であることを説明する。なお、本講演内容は、東京都立大学の石谷謙介氏との共同研究(arXiv:2405.05595)に基づく。
2曲線間に制限されたパス空間上でのWiener測度に対する1階微分の部分積分公式は既に知られている。本講演では、この結果を高階微分の部分積分公式に拡張する。高階微分の部分積分公式においては、従来の1階微分の場合にはない非自明な境界項が追加で現れ、さらに、その証明において、Brownian excursionやBrownian house-movingと呼ばれる確率過程のランダムウォーク近似による構成方法が新たに必要となる。また、証明の中で、1次および2次の無限小確率の概念を導入する。この概念を導入することで、部分積分公式の各項に現れる数式に対して確率論的な解釈が可能となり、部分積分公式を整理する上で有益な概念であることを説明する。なお、本講演内容は、東京都立大学の石谷謙介氏との共同研究(arXiv:2405.05595)に基づく。
2024/05/17
Algebraic Geometry Seminar
13:30-15:00 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Yuya Matsumoto (Tokyo University of Science)
非分離Kummer曲面 (日本語)
Yuya Matsumoto (Tokyo University of Science)
非分離Kummer曲面 (日本語)
[ Abstract ]
Kummer曲面Km(A)とは，+-1倍写像によるアーベル曲面Aの商の最小特異点解消として得られる曲面である．Aが標数≠2の場合（resp. 標数2で，超特異ではない場合）は，Km(A)はK3曲面であり，例外曲線は互いに交わらない（resp. 所定の交わり方をする）16本の有理曲線である．Aが標数2で超特異の場合はKm(A)はK3曲面にならない．また，Km(A)が標数2の超特異K3曲面になることはない．
本講演では，標数2の超特異K3曲面とその上の16本の有理曲線で所定の交わり方をするものに対し，非分離2重被覆Aを構成することができること，Aは非特異部分に群構造が入り「アーベル曲面もどき」になることを示す．Aの分類のために，RDP K3曲面のRDPの補集合から最小特異点解消への B_n \Omega^1（Cartier作用素を何回か適用すると消える1次微分形式の層）の延長に関する結果を用いるので，これにも言及したい．
プレプリントは https://arxiv.org/abs/2403.02770 でご覧いただけます．
Kummer曲面Km(A)とは，+-1倍写像によるアーベル曲面Aの商の最小特異点解消として得られる曲面である．Aが標数≠2の場合（resp. 標数2で，超特異ではない場合）は，Km(A)はK3曲面であり，例外曲線は互いに交わらない（resp. 所定の交わり方をする）16本の有理曲線である．Aが標数2で超特異の場合はKm(A)はK3曲面にならない．また，Km(A)が標数2の超特異K3曲面になることはない．
本講演では，標数2の超特異K3曲面とその上の16本の有理曲線で所定の交わり方をするものに対し，非分離2重被覆Aを構成することができること，Aは非特異部分に群構造が入り「アーベル曲面もどき」になることを示す．Aの分類のために，RDP K3曲面のRDPの補集合から最小特異点解消への B_n \Omega^1（Cartier作用素を何回か適用すると消える1次微分形式の層）の延長に関する結果を用いるので，これにも言及したい．
プレプリントは https://arxiv.org/abs/2403.02770 でご覧いただけます．
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