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過去の記録
過去の記録 ～03/27｜本日 03/28 | 今後の予定 03/29～
博士論文発表会
13:00-14:15 数理科学研究科棟(駒場) 122号室
名取 雅生 氏 (東京大学大学院数理科学研究科)
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)
名取 雅生 氏 (東京大学大学院数理科学研究科)
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)
博士論文発表会
14:45-16:00 数理科学研究科棟(駒場) 122号室
吉岡 玲音 氏 (東京大学大学院数理科学研究科)
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)
吉岡 玲音 氏 (東京大学大学院数理科学研究科)
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)
博士論文発表会
11:00-12:15 数理科学研究科棟(駒場) 126号室
劉 沛江 氏 (東京大学大学院数理科学研究科)
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)
劉 沛江 氏 (東京大学大学院数理科学研究科)
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)
博士論文発表会
14:45-16:00 数理科学研究科棟(駒場) 126号室
向原 未帆 氏 (東京大学大学院数理科学研究科)
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)
向原 未帆 氏 (東京大学大学院数理科学研究科)
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)
博士論文発表会
11:00-12:15 数理科学研究科棟(駒場) 128号室
権 英哲 氏 (東京大学大学院数理科学研究科)
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）
権 英哲 氏 (東京大学大学院数理科学研究科)
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）
博士論文発表会
14:45-16:00 数理科学研究科棟(駒場) 128号室
山本 雄太 氏 (東京大学大学院数理科学研究科)
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)
山本 雄太 氏 (東京大学大学院数理科学研究科)
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)
博士論文発表会
13:00-14:15 数理科学研究科棟(駒場) 126号室
磯部 伸 氏 (東京大学大学院数理科学研究科)
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）
磯部 伸 氏 (東京大学大学院数理科学研究科)
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年01月22日(水)
代数幾何学セミナー
13:30-15:00 数理科学研究科棟(駒場) 002号室
田中公 氏 (東京大学)
Liftability and vanishing theorems for Fano threefolds in positive characteristic (日本語)
田中公 氏 (東京大学)
Liftability and vanishing theorems for Fano threefolds in positive characteristic (日本語)
[ 講演概要 ]
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年01月21日(火)
トポロジー火曜セミナー
17:00-18:00 数理科学研究科棟(駒場) hybrid/056号室
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
小菅 亮太朗 氏 (東京大学大学院数理科学研究科)
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
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
小菅 亮太朗 氏 (東京大学大学院数理科学研究科)
Rational abelianizations of Chillingworth subgroups of mapping class groups and automorphism groups of free groups (JAPANESE)
[ 講演概要 ]
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.
[ 参考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年01月20日(月)
東京確率論セミナー
16:00-17:30 数理科学研究科棟(駒場) 126号室
15:15〜 ２階のコモンルームでTea timeを行います。ぜひこちらにもご参加ください。
Arka Adhikari 氏 (University of Maryland)
Spectral measure for uniform d-regular digraphs
15:15〜 ２階のコモンルームでTea timeを行います。ぜひこちらにもご参加ください。
Arka Adhikari 氏 (University of Maryland)
Spectral measure for uniform d-regular digraphs
[ 講演概要 ]
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
2025年01月16日(木)
談話会・数理科学講演会
15:30-16:30 数理科学研究科棟(駒場) 大講義室(Large Lecture Room)号室
万一感染クラスター発生時にご連絡差し上げるため、[参考URL]から参加登録をお願いいたします。
陳榮凱 氏 (國立臺灣大學)
On classification of threefolds of general type (English)
https://docs.google.com/forms/d/e/1FAIpQLSfuEUNS92y5dTPoEANkgieuPhmDDQLB_fI4d-GT2p0VkT8KOg/viewform?usp=header
万一感染クラスター発生時にご連絡差し上げるため、[参考URL]から参加登録をお願いいたします。
陳榮凱 氏 (國立臺灣大學)
On classification of threefolds of general type (English)
[ 講演概要 ]
In higher dimensional algebraic geometry, the following three types of varieties are considered to be the building blocks: Fano varieties, Calabi-Yau varieties, and varieties of general type. In the study of varieties of general type, one usually works on "good models" inside birationally equivalent classes. Minimal models and canonical models are natural choices of good models.
In the first part of the talk, we will try to introduce some aspects of the geography problem for threefolds of general type, which aim to study the distribution of birational invariants of threefolds of general type. In the second part of the talk, we will explore more geometric properties of those threefolds on or near the boundary. Some explicit examples will be described and we will compare various different models explicitly. If time permits, we also try to talk about their moduli spaces from different points of view.
[ 参考URL ]In higher dimensional algebraic geometry, the following three types of varieties are considered to be the building blocks: Fano varieties, Calabi-Yau varieties, and varieties of general type. In the study of varieties of general type, one usually works on "good models" inside birationally equivalent classes. Minimal models and canonical models are natural choices of good models.
In the first part of the talk, we will try to introduce some aspects of the geography problem for threefolds of general type, which aim to study the distribution of birational invariants of threefolds of general type. In the second part of the talk, we will explore more geometric properties of those threefolds on or near the boundary. Some explicit examples will be described and we will compare various different models explicitly. If time permits, we also try to talk about their moduli spaces from different points of view.
https://docs.google.com/forms/d/e/1FAIpQLSfuEUNS92y5dTPoEANkgieuPhmDDQLB_fI4d-GT2p0VkT8KOg/viewform?usp=header
東京無限可積分系セミナー
15:30-16:30 数理科学研究科棟(駒場) オンライン開催号室
参加希望の方は連絡をお願いします。
Jean-Emile Bourgine 氏 (SIMIS (Shanghai Institute for Mathematics and Interdisciplinary Sciences))
Free field representations of quantum groups and q-deformed W-algebras through cluster algebras (ENGLISH)
参加希望の方は連絡をお願いします。
Jean-Emile Bourgine 氏 (SIMIS (Shanghai Institute for Mathematics and Interdisciplinary Sciences))
Free field representations of quantum groups and q-deformed W-algebras through cluster algebras (ENGLISH)
[ 講演概要 ]
Following the development of the AGT correspondence, new relations between free field representations of quantum groups and W-algebras were obtained. The simplest one is the homomorphism between the level $(N,0)$ horizontal representation of the quantum toroidal gl(1) algebra and (dressed) q-deformed $W_N$ algebras. In this talk, I will explain how to extend this type of relations to the Wakimoto representations of quantum affine sl(N) algebras using the 'surface defect' deformation of the quantum toroidal sl(N) algebra.
Following the development of the AGT correspondence, new relations between free field representations of quantum groups and W-algebras were obtained. The simplest one is the homomorphism between the level $(N,0)$ horizontal representation of the quantum toroidal gl(1) algebra and (dressed) q-deformed $W_N$ algebras. In this talk, I will explain how to extend this type of relations to the Wakimoto representations of quantum affine sl(N) algebras using the 'surface defect' deformation of the quantum toroidal sl(N) algebra.
2025年01月14日(火)
解析学火曜セミナー
16:00-17:30 数理科学研究科棟(駒場) 128号室
対面・オンラインハイブリッド開催，場所にご注意ください
鈴木香奈子 氏 (茨城大学)
Existence and stability of discontinuous stationary solutions to reaction-diffusion-ODE systems (Japanese)
https://forms.gle/GtA4bpBuy5cNzsyX8
対面・オンラインハイブリッド開催，場所にご注意ください
鈴木香奈子 氏 (茨城大学)
Existence and stability of discontinuous stationary solutions to reaction-diffusion-ODE systems (Japanese)
[ 講演概要 ]
We consider reaction-diffusion-ODE systems, which consists of a single reaction-diffusion equation coupled with ordinary differential equations. Such systems arise, for example, from modeling of interactions between cellular processes and diffusing growth factors.
Reaction-diffusion-ODE systems in a bounded domain with Neumann boundary condition may have two types of stationary solutions, regular and discontinuous. We can show that all regular stationary solutions are unstable. This implies that reaction-diffusion-ODE systems cannot exhibit spatial patterns, and possible stable stationary solutions must be singular or discontinuous. In this talk, we present sufficient conditions for the existence and stability of discontinuous stationary solutions.
This talk is based on joint works with A. Marciniak-Czochra (Heidelberg University), G. Karch (University of Wroclaw) and S. Cygan (University of Wroclaw).
[ 参考URL ]We consider reaction-diffusion-ODE systems, which consists of a single reaction-diffusion equation coupled with ordinary differential equations. Such systems arise, for example, from modeling of interactions between cellular processes and diffusing growth factors.
Reaction-diffusion-ODE systems in a bounded domain with Neumann boundary condition may have two types of stationary solutions, regular and discontinuous. We can show that all regular stationary solutions are unstable. This implies that reaction-diffusion-ODE systems cannot exhibit spatial patterns, and possible stable stationary solutions must be singular or discontinuous. In this talk, we present sufficient conditions for the existence and stability of discontinuous stationary solutions.
This talk is based on joint works with A. Marciniak-Czochra (Heidelberg University), G. Karch (University of Wroclaw) and S. Cygan (University of Wroclaw).
https://forms.gle/GtA4bpBuy5cNzsyX8
トポロジー火曜セミナー
17:00-18:00 数理科学研究科棟(駒場) hybrid/056号室
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
吉岡 玲音 氏 (東京大学大学院数理科学研究科)
Some non-trivial cycles of the space of long embeddings detected by configuration space integral invariants using g-loop graphs (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
吉岡 玲音 氏 (東京大学大学院数理科学研究科)
Some non-trivial cycles of the space of long embeddings detected by configuration space integral invariants using g-loop graphs (JAPANESE)
[ 講演概要 ]
In this talk, we give some non-trivial cocycles and cycles of the space of long embeddings R^j --> R^n modulo immersions. First, we construct a cocycle through configuration space integrals with the simplest 2-loop graph cocycle of the Bott-Cattaneo-Rossi graph complex for odd n and j. Then, we give a cycle from a chord diagram on oriented lines, which is associated with the simplest 2-loop hairy graph. We show the non-triviality of this (co)cycle by pairing argument, which is reduced to pairing of graphs with the chord diagram. This construction of cycles and the pairing argument to show the non-triviality is also applied to general 2-loop (co)cycles of top degree. If time permits, we introduce a modified graph complex and configuration space integrals to give more general cocycles. This new graph complex is quasi-isomorphic to both the hairy graph complex and the graph complex introduced in embedding calculus by Arone and Turchin. With these modified cocycles, our pairing argument provides an alternative proof of the non-finite generation of the (j-1)-th rational homotopy group of the space of long j-knots R^j -->R^{j+2}, which Budney-Gabai and Watanabe first established.
[ 参考URL ]In this talk, we give some non-trivial cocycles and cycles of the space of long embeddings R^j --> R^n modulo immersions. First, we construct a cocycle through configuration space integrals with the simplest 2-loop graph cocycle of the Bott-Cattaneo-Rossi graph complex for odd n and j. Then, we give a cycle from a chord diagram on oriented lines, which is associated with the simplest 2-loop hairy graph. We show the non-triviality of this (co)cycle by pairing argument, which is reduced to pairing of graphs with the chord diagram. This construction of cycles and the pairing argument to show the non-triviality is also applied to general 2-loop (co)cycles of top degree. If time permits, we introduce a modified graph complex and configuration space integrals to give more general cocycles. This new graph complex is quasi-isomorphic to both the hairy graph complex and the graph complex introduced in embedding calculus by Arone and Turchin. With these modified cocycles, our pairing argument provides an alternative proof of the non-finite generation of the (j-1)-th rational homotopy group of the space of long j-knots R^j -->R^{j+2}, which Budney-Gabai and Watanabe first established.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2025年01月06日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
Yongpan Zou 氏 (東京大学)
Positivity of twisted direct image sheaves (English)
https://u-tokyo-ac-jp.zoom.us/j/87229568765
Yongpan Zou 氏 (東京大学)
Positivity of twisted direct image sheaves (English)
[ 講演概要 ]
For a projective surjective morphism $f: X \to Y$ of complex manifolds with connected fibers, let $L$ be a line bundle on $X$. We are interested in the direct image $f_*(K_{X/Y} \otimes L)$. In general, the positivity of the bundle $L$ induces positivity in the direct image sheaves. Specifically, when $L$ is a big and nef line bundle, the vector bundle $f_*(K_{X/Y} \otimes L)$ is big. This is joint work with Y. Watanabe.
[ 参考URL ]For a projective surjective morphism $f: X \to Y$ of complex manifolds with connected fibers, let $L$ be a line bundle on $X$. We are interested in the direct image $f_*(K_{X/Y} \otimes L)$. In general, the positivity of the bundle $L$ induces positivity in the direct image sheaves. Specifically, when $L$ is a big and nef line bundle, the vector bundle $f_*(K_{X/Y} \otimes L)$ is big. This is joint work with Y. Watanabe.
https://u-tokyo-ac-jp.zoom.us/j/87229568765
2024年12月26日(木)
離散数理モデリングセミナー
15:00-17:00 数理科学研究科棟(駒場) 002号室
Wookyung KIM 氏 (東京大学大学院数理科学研究科)
Integrable deformation of cluster map associated to finite type Dynkin diagram
Wookyung KIM 氏 (東京大学大学院数理科学研究科)
Integrable deformation of cluster map associated to finite type Dynkin diagram
[ 講演概要 ]
An integrable deformation of a cluster map is an integrable Poisson map which is composed of a sequence of deformed cluster mutations, namely, parametric birational maps preserving the presymplectic form but destroying the Laurent property, which is a necessary part of the structure of a cluster algebra. However, this does not imply that the deformed map does not arise from a cluster map: one can use so-called Laurentification, which is a lifting of the map into a higher-dimensional space where the Laurent property is recovered, and thus the deformed map can be generated from elements in a cluster algebra. This deformation theory was introduced recently by Hone and Kouloukas, who presented several examples, including deformed integrable cluster maps associated with Dynkin types A_2,A_3 and A_4. In this talk, we will consider the deformation of integrable cluster map corresponding to the general even dimensional case, Dynkin type A_{2N}. If time permits, we will review the deformation of the cluster maps of other finite type cases such as type C and D. This is joint work with Grabowski, Hone and Mase.
An integrable deformation of a cluster map is an integrable Poisson map which is composed of a sequence of deformed cluster mutations, namely, parametric birational maps preserving the presymplectic form but destroying the Laurent property, which is a necessary part of the structure of a cluster algebra. However, this does not imply that the deformed map does not arise from a cluster map: one can use so-called Laurentification, which is a lifting of the map into a higher-dimensional space where the Laurent property is recovered, and thus the deformed map can be generated from elements in a cluster algebra. This deformation theory was introduced recently by Hone and Kouloukas, who presented several examples, including deformed integrable cluster maps associated with Dynkin types A_2,A_3 and A_4. In this talk, we will consider the deformation of integrable cluster map corresponding to the general even dimensional case, Dynkin type A_{2N}. If time permits, we will review the deformation of the cluster maps of other finite type cases such as type C and D. This is joint work with Grabowski, Hone and Mase.
2024年12月24日(火)
解析学火曜セミナー
16:00-17:30 数理科学研究科棟(駒場) 128号室
対面・オンラインハイブリッド開催，場所にご注意ください
筧知之 氏 (筑波大学)
Snapshot problems for the wave equation and for the Euler-Poisson-Darboux equation (Japanese)
https://forms.gle/2otzqXYVD6DqM11S8
対面・オンラインハイブリッド開催，場所にご注意ください
筧知之 氏 (筑波大学)
Snapshot problems for the wave equation and for the Euler-Poisson-Darboux equation (Japanese)
[ 講演概要 ]
In this talk, we deal with snapshot problems for the wave equation and for the Euler-Poisson-Darboux equation. For simplicity, let us consider the wave equation $\partial_t^2 u - \Delta u =0$ on $\mathbb{R}^n$ with the condition $u|_{t=t_1} =f_1, \cdots, u|_{t=t_m} =f_m$. It is natural to ask when the above equation has a unique solution. We call the above problem the snapshot problem for the wave equation, and the set of $m$ functions $\{ f_1, \cdots, f_m \}$ the snapshot data. Roughly speaking, one of our main results is as follows.
Theorem. We assume that $m=3$ and $(t_3-t_1)/(t_2 -t_1)$ is irrational and not a Liouville number. In addition, we assume a certain compatibility condition on the snapshot data $\{ f_1, f_2, f_3 \}$. Then the snapshot problem for the wave equation has a unique solution.
We also consider a similar snapshot problem for the Euler-Poisson-Darboux equation. This is a joint work with Jens Christensen, Fulton Gonzalez, and Jue Wang.
[ 参考URL ]In this talk, we deal with snapshot problems for the wave equation and for the Euler-Poisson-Darboux equation. For simplicity, let us consider the wave equation $\partial_t^2 u - \Delta u =0$ on $\mathbb{R}^n$ with the condition $u|_{t=t_1} =f_1, \cdots, u|_{t=t_m} =f_m$. It is natural to ask when the above equation has a unique solution. We call the above problem the snapshot problem for the wave equation, and the set of $m$ functions $\{ f_1, \cdots, f_m \}$ the snapshot data. Roughly speaking, one of our main results is as follows.
Theorem. We assume that $m=3$ and $(t_3-t_1)/(t_2 -t_1)$ is irrational and not a Liouville number. In addition, we assume a certain compatibility condition on the snapshot data $\{ f_1, f_2, f_3 \}$. Then the snapshot problem for the wave equation has a unique solution.
We also consider a similar snapshot problem for the Euler-Poisson-Darboux equation. This is a joint work with Jens Christensen, Fulton Gonzalez, and Jue Wang.
https://forms.gle/2otzqXYVD6DqM11S8
2024年12月23日(月)
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 128号室
野口 潤次郎 氏 (東京大学)
Hyperbolicity and sections in a ramified cover over abelian varieties
with trace zero (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
野口 潤次郎 氏 (東京大学)
Hyperbolicity and sections in a ramified cover over abelian varieties
with trace zero (Japanese)
[ 講演概要 ]
We discuss a higher dimensional generalization of the Manin-Grauert Theorem ('63/'65) in relation with the function field analogue of Lang's conjecture on the finiteness of rational points in a Kobayashi hyperbolic algebraic variety over a number field. Let $B$ be a possibly open algebraic curve over $\mathbf{C}$, and let $\pi:X \to B$ be a smooth or normal projective fiber space. In '81 I proved such theorems for $\dim \geq 1$, assuming the ampleness of the cotangent bundle $T^*(X_t)$, and in '85 the Kobayashi hyperbolicity of $X_t$ with some boundary condition (BC) (hyperbolic embedding condition relative over $\bar{B}$).
It is interesting to study if (BC) is really necessary or not. If $\dim X_t=1$, (BC) is automatically satisfied, and if $T^*(X_t)$ is ample, (BC) is not necessary; thus in those cases, (BC) is unnecessary. Lately, Xie-Yuan in arXiv '23 obtained such a result without (BC) for $X$ which is a hyperbolic finite cover of an abelian variety $A/B$.
The aim of this talk is to present a simplified treatment of the Xie-Yuan theorem from the viewpoint of Kobayashi hyperbolic geometry. In particular, if the $K/\mathbf{C}$-trace $Tr(A/B)=0$ with $K=\mathbf{C}(B)$, there are only finitely many $X(K)$-points or sections in $X \to B$. In this case, Bartsch-Javanpeykar in arXiv '24 gave another proof based on Parshin's topological rigidity theorem ('90). We will discuss the proof which is based on the Kobayashi hyperbolicity.
[ 参考URL ]We discuss a higher dimensional generalization of the Manin-Grauert Theorem ('63/'65) in relation with the function field analogue of Lang's conjecture on the finiteness of rational points in a Kobayashi hyperbolic algebraic variety over a number field. Let $B$ be a possibly open algebraic curve over $\mathbf{C}$, and let $\pi:X \to B$ be a smooth or normal projective fiber space. In '81 I proved such theorems for $\dim \geq 1$, assuming the ampleness of the cotangent bundle $T^*(X_t)$, and in '85 the Kobayashi hyperbolicity of $X_t$ with some boundary condition (BC) (hyperbolic embedding condition relative over $\bar{B}$).
It is interesting to study if (BC) is really necessary or not. If $\dim X_t=1$, (BC) is automatically satisfied, and if $T^*(X_t)$ is ample, (BC) is not necessary; thus in those cases, (BC) is unnecessary. Lately, Xie-Yuan in arXiv '23 obtained such a result without (BC) for $X$ which is a hyperbolic finite cover of an abelian variety $A/B$.
The aim of this talk is to present a simplified treatment of the Xie-Yuan theorem from the viewpoint of Kobayashi hyperbolic geometry. In particular, if the $K/\mathbf{C}$-trace $Tr(A/B)=0$ with $K=\mathbf{C}(B)$, there are only finitely many $X(K)$-points or sections in $X \to B$. In this case, Bartsch-Javanpeykar in arXiv '24 gave another proof based on Parshin's topological rigidity theorem ('90). We will discuss the proof which is based on the Kobayashi hyperbolicity.
https://forms.gle/gTP8qNZwPyQyxjTj8
2024年12月20日(金)
談話会・数理科学講演会
15:30-16:30 数理科学研究科棟(駒場) 大講義室号室
小薗英雄 氏 (早稲田大学基幹理工学部 / 東北大学数理科学共創社会センター)
Helmholtz-Weyl分解とその電磁流体力学方程式への応用 (日本語)
https://forms.gle/QNj3fohg3ZRMD8RHA
小薗英雄 氏 (早稲田大学基幹理工学部 / 東北大学数理科学共創社会センター)
Helmholtz-Weyl分解とその電磁流体力学方程式への応用 (日本語)
[ 講演概要 ]
3次元Euclid空間内の滑らかな境界をもつ有界領域における$L^r$-ベクトル場のHelmholtz-Weyl分解について紹介する．コンパクトRiemann多様体上の$p$-次微分形式に対するde Rham-Hodge-小平分解についてはよく知られているが，ベクトル場が滑らかとは限らないLebesgue空間に属する場合には，藤原ー森本等によって比較的最近に得られた．本講演では3次元有界領域の場合に限って，調和ベクトル場の空間を境界に接している場合と，直交している場合の２種類の境界条件によって特徴づけ，$L^r$-ベクトル場の直和分解について解説する．特に，ベクトルポテンシャルの回転によって張られる部分空間の特徴づけに焦点をあてる．応用として，第２Betti数がゼロではない領域上の電磁流体力学方程式の調和ベクトルに附随する平衡解が，漸近安定であることを明らかにする．本講演の内容は，清水扇丈氏（京都大学）と柳澤卓氏（奈良女子大学）との共同研究に基づいている．
[ 参考URL ]3次元Euclid空間内の滑らかな境界をもつ有界領域における$L^r$-ベクトル場のHelmholtz-Weyl分解について紹介する．コンパクトRiemann多様体上の$p$-次微分形式に対するde Rham-Hodge-小平分解についてはよく知られているが，ベクトル場が滑らかとは限らないLebesgue空間に属する場合には，藤原ー森本等によって比較的最近に得られた．本講演では3次元有界領域の場合に限って，調和ベクトル場の空間を境界に接している場合と，直交している場合の２種類の境界条件によって特徴づけ，$L^r$-ベクトル場の直和分解について解説する．特に，ベクトルポテンシャルの回転によって張られる部分空間の特徴づけに焦点をあてる．応用として，第２Betti数がゼロではない領域上の電磁流体力学方程式の調和ベクトルに附随する平衡解が，漸近安定であることを明らかにする．本講演の内容は，清水扇丈氏（京都大学）と柳澤卓氏（奈良女子大学）との共同研究に基づいている．
https://forms.gle/QNj3fohg3ZRMD8RHA
代数幾何学セミナー
13:30-15:00 数理科学研究科棟(駒場) 118号室
榎園誠 氏 (東京大学)
Normal stable degenerations of Noether-Horikawa surfaces
榎園誠 氏 (東京大学)
Normal stable degenerations of Noether-Horikawa surfaces
[ 講演概要 ]
Noether-Horikawa surfaces are surfaces of general type satisfying the equation K2=2pg−4, which represents the boundary of the Noether inequality K2≥2pg−4 for surfaces of general type. In the 1970s, Horikawa conducted a detailed study of smooth Noether-Horikawa surfaces, providing a classification of these surfaces and describing their moduli spaces.
In this talk, I will present an explicit classification of normal stable degenerations of Noether-Horikawa surfaces. Specifically, I will discuss the following results:
(1) A preliminary classification of Noether-Horikawa surfaces with Q-Gorenstein smoothable log canonical singularities.
(2) Several criteria for determining the (global) Q-Gorenstein smoothability of the surfaces described in (1).
(3) Deformation results for Q-Gorenstein smoothable normal stable Noether-Horikawa surfaces, along with a description of the KSBA moduli spaces for these surfaces.
This is joint work with Hiroto Akaike, Masafumi Hattori and Yuki Koto.
Noether-Horikawa surfaces are surfaces of general type satisfying the equation K2=2pg−4, which represents the boundary of the Noether inequality K2≥2pg−4 for surfaces of general type. In the 1970s, Horikawa conducted a detailed study of smooth Noether-Horikawa surfaces, providing a classification of these surfaces and describing their moduli spaces.
In this talk, I will present an explicit classification of normal stable degenerations of Noether-Horikawa surfaces. Specifically, I will discuss the following results:
(1) A preliminary classification of Noether-Horikawa surfaces with Q-Gorenstein smoothable log canonical singularities.
(2) Several criteria for determining the (global) Q-Gorenstein smoothability of the surfaces described in (1).
(3) Deformation results for Q-Gorenstein smoothable normal stable Noether-Horikawa surfaces, along with a description of the KSBA moduli spaces for these surfaces.
This is joint work with Hiroto Akaike, Masafumi Hattori and Yuki Koto.
東京名古屋代数セミナー
17:00-18:30 オンライン開催
Simon Riche 氏 (Université Clermont Auvergne)
Semiinfinite sheaves on affine flag varieties (English)
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Simon Riche 氏 (Université Clermont Auvergne)
Semiinfinite sheaves on affine flag varieties (English)
[ 講演概要 ]
We will explain how, generalizing a construction of Gaitsgory, one can define and study a category of sheaves on the affine flag variety of a complex reductive group that "models" sheaves on the corresponding semiinfinite flag variety, with coefficients in a field of positive characteristic, and which should provide a geometric model for a category of representations of the Langlands dual Lie algebra over the given coefficient field. As an application, we use this construction to compute the dimensions of stalks of the intersection cohomology complex on Drinfeld's compactification, with coefficients in any field of good characteristic. This is joint work with Pramod Achar and Gurbir Dhillon.
ミーティング ID: 882 1561 8969
パスコード: 531394
[ 参考URL ]We will explain how, generalizing a construction of Gaitsgory, one can define and study a category of sheaves on the affine flag variety of a complex reductive group that "models" sheaves on the corresponding semiinfinite flag variety, with coefficients in a field of positive characteristic, and which should provide a geometric model for a category of representations of the Langlands dual Lie algebra over the given coefficient field. As an application, we use this construction to compute the dimensions of stalks of the intersection cohomology complex on Drinfeld's compactification, with coefficients in any field of good characteristic. This is joint work with Pramod Achar and Gurbir Dhillon.
ミーティング ID: 882 1561 8969
パスコード: 531394
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2024年12月19日(木)
東京無限可積分系セミナー
14:00-15:30 数理科学研究科棟(駒場) 002号室
Omar Kidwai 氏 (The Chinese University of Hong Kong)
Quadratic differentials and Donaldson-Thomas invariants (English)
Omar Kidwai 氏 (The Chinese University of Hong Kong)
Quadratic differentials and Donaldson-Thomas invariants (English)
[ 講演概要 ]
We recall the relation between quadratic differentials and spaces of stability conditions due to Bridgeland-Smith. We describe the calculation of (refined) Donaldson-Thomas invariants for stability conditions on a certain class of 3-Calabi-Yau triangulated categories studied by Christ-Haiden-Qiu. This category is slightly different from the usual one discussed by Bridgeland and Smith, which in particular allows us to recover a nonzero invariant in the case where the quadratic differential has a second-order pole, in agreement with predictions from the physics literature. Based on joint work with N. Williams.
We recall the relation between quadratic differentials and spaces of stability conditions due to Bridgeland-Smith. We describe the calculation of (refined) Donaldson-Thomas invariants for stability conditions on a certain class of 3-Calabi-Yau triangulated categories studied by Christ-Haiden-Qiu. This category is slightly different from the usual one discussed by Bridgeland and Smith, which in particular allows us to recover a nonzero invariant in the case where the quadratic differential has a second-order pole, in agreement with predictions from the physics literature. Based on joint work with N. Williams.
2024年12月18日(水)
諸分野のための数学研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
通常の曜日と異なります。会場が122号室から056号室に変更になりました。オンラインでも開催されます。
Amy Novick-Cohen 氏 (Technion - Israel Institute of Technology)
Diffusion: Some new results and approaches (English)
https://u-tokyo-ac-jp.zoom.us/j/83306203126?pwd=b92LqeuB5sLUkN2LKu7Mp8SQmoSbAU.1
通常の曜日と異なります。会場が122号室から056号室に変更になりました。オンラインでも開催されます。
Amy Novick-Cohen 氏 (Technion - Israel Institute of Technology)
Diffusion: Some new results and approaches (English)
[ 講演概要 ]
We first briefly review a variety of geometries where surface diffusion is meaningful in the context of the stability of thin solid state films. Afterwards, we discuss joint work with E.A. Carlen & L. Peres Hari (2024), which focuses on rigorously establishing a connection between surface diffusion and the deep quench obstacle problem with a suitable degenerate mobility. Our study begins by rigorously establishing a connection between certain steady states of the respective systems, and then outlines a method for connecting the respective evolutions via minimizing motion descriptions.
下記の [参考URL] からZoomミーティングにご参加ください。
ミーティング ID: 833 0620 3126
パスコード: 223203
[ 参考URL ]We first briefly review a variety of geometries where surface diffusion is meaningful in the context of the stability of thin solid state films. Afterwards, we discuss joint work with E.A. Carlen & L. Peres Hari (2024), which focuses on rigorously establishing a connection between surface diffusion and the deep quench obstacle problem with a suitable degenerate mobility. Our study begins by rigorously establishing a connection between certain steady states of the respective systems, and then outlines a method for connecting the respective evolutions via minimizing motion descriptions.
下記の [参考URL] からZoomミーティングにご参加ください。
ミーティング ID: 833 0620 3126
パスコード: 223203
https://u-tokyo-ac-jp.zoom.us/j/83306203126?pwd=b92LqeuB5sLUkN2LKu7Mp8SQmoSbAU.1
2024年12月17日(火)
トポロジー火曜セミナー
17:00-18:30 数理科学研究科棟(駒場) hybrid/056号室
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
Emmanuel Graff 氏 (東京大学大学院数理科学研究科)
Is there torsion in the homotopy braid group? (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
Emmanuel Graff 氏 (東京大学大学院数理科学研究科)
Is there torsion in the homotopy braid group? (ENGLISH)
[ 講演概要 ]
In the 'Kourovka notebook,' V. Lin questions the existence of a non-trivial epimorphism from the braid group onto a non-abelian torsion-free group. The homotopy braid group, studied by Goldsmith in 1974, naturally appears as a potential candidate. In 2001, Humphries showed that this homotopy braid group is torsion-free for less than six strands. In this presentation, we will see a new approach based on the broader concept of welded braids, along with algebraic techniques, to determine whether the homotopy braid group provides a complete answer to Lin’s question.
[ 参考URL ]In the 'Kourovka notebook,' V. Lin questions the existence of a non-trivial epimorphism from the braid group onto a non-abelian torsion-free group. The homotopy braid group, studied by Goldsmith in 1974, naturally appears as a potential candidate. In 2001, Humphries showed that this homotopy braid group is torsion-free for less than six strands. In this presentation, we will see a new approach based on the broader concept of welded braids, along with algebraic techniques, to determine whether the homotopy braid group provides a complete answer to Lin’s question.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 002号室
作用素環賞受賞講演です．部屋がいつもと違います．
山下真 氏 (Univ. Oslo)
Bimodule approach to quantum field theory and categorical structures
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
作用素環賞受賞講演です．部屋がいつもと違います．
山下真 氏 (Univ. Oslo)
Bimodule approach to quantum field theory and categorical structures
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
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