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過去の記録
過去の記録 ～08/15｜本日 08/16 | 今後の予定 08/17～
博士論文発表会
15:45-17:00 数理科学研究科棟(駒場) 126号室
片岡 武典 氏 (東京大学大学院数理科学研究科)
Equivariant Iwasawa theory for elliptic curves
(楕円曲線の同変岩澤理論）
(JAPANESE)
片岡 武典 氏 (東京大学大学院数理科学研究科)
Equivariant Iwasawa theory for elliptic curves
(楕円曲線の同変岩澤理論）
(JAPANESE)
博士論文発表会
17:15-18:30 数理科学研究科棟(駒場) 126号室
戸次 鵬人 氏 (東京大学大学院数理科学研究科)
Some arithmetic properties of geodesic cycles on locally symmetric spaces
(局所対称空間上の測地的サイクルの数論的性質についての研究）
(JAPANESE)
戸次 鵬人 氏 (東京大学大学院数理科学研究科)
Some arithmetic properties of geodesic cycles on locally symmetric spaces
(局所対称空間上の測地的サイクルの数論的性質についての研究）
(JAPANESE)
2019年01月30日(水)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 126号室
藤陽平 氏 (理研)
2次元共形場理論を用いたトポロジカル相のモデルの構成 (Japanese)
藤陽平 氏 (理研)
2次元共形場理論を用いたトポロジカル相のモデルの構成 (Japanese)
2019年01月29日(火)
代数幾何学セミナー
15:30-17:00 数理科学研究科棟(駒場) 122号室
三井健太郎 氏 (神戸)
Logarithmic good reduction and the index (TBA)
三井健太郎 氏 (神戸)
Logarithmic good reduction and the index (TBA)
[ 講演概要 ]
A proper smooth variety over a complete discrete valuation field is said to have (log) good reduction if it admits a proper (log) smooth model over the valuation ring (the log structure is given by the closed fiber). Monodromy criteria for good reduction and log good reduction have been studied. We study the log case by additional other conditions on geometric invariants such as the index of the variety (the minimal positive degree of a 0-cycle). In particular, we obtain a criterion for log good reduction of curves of genus one.
A proper smooth variety over a complete discrete valuation field is said to have (log) good reduction if it admits a proper (log) smooth model over the valuation ring (the log structure is given by the closed fiber). Monodromy criteria for good reduction and log good reduction have been studied. We study the log case by additional other conditions on geometric invariants such as the index of the variety (the minimal positive degree of a 0-cycle). In particular, we obtain a criterion for log good reduction of curves of genus one.
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
Salvatore Stuvard 氏 (The University of Texas at Austin)
The regularity of area minimizing currents modulo $p$ (English)
Salvatore Stuvard 氏 (The University of Texas at Austin)
The regularity of area minimizing currents modulo $p$ (English)
[ 講演概要 ]
The theory of integer rectifiable currents was introduced by Federer and Fleming in the early 1960s in order to provide a class of generalized surfaces where the classical Plateau problem could be solved by direct methods. Since then, a number of alternative spaces of surfaces have been developed in geometric measure theory, as required for theory and applications. In particular, Fleming introduced currents modulo $2$ to treat non-orientable surfaces, and currents modulo $p$ (where $p \geq 2$ is an integer) to study more general surfaces occurring as soap films.
It is easy to see that, in general, area minimizing currents modulo $p$ need not be smooth surfaces. In this talk, I will sketch the proof of the following result, which achieves the best possible estimate for the Hausdorff dimension of the singular set of an area minimizing current modulo $p$ in the most general hypotheses, thus answering a question of White from the 1980s: if $T$ is an area minimizing current modulo $p$ of dimension $m$ in $R^{m+n}$, then $T$ is smooth at all its interior points, except those belonging to a singular set of Hausdorff dimension at most $m-1$.
The theory of integer rectifiable currents was introduced by Federer and Fleming in the early 1960s in order to provide a class of generalized surfaces where the classical Plateau problem could be solved by direct methods. Since then, a number of alternative spaces of surfaces have been developed in geometric measure theory, as required for theory and applications. In particular, Fleming introduced currents modulo $2$ to treat non-orientable surfaces, and currents modulo $p$ (where $p \geq 2$ is an integer) to study more general surfaces occurring as soap films.
It is easy to see that, in general, area minimizing currents modulo $p$ need not be smooth surfaces. In this talk, I will sketch the proof of the following result, which achieves the best possible estimate for the Hausdorff dimension of the singular set of an area minimizing current modulo $p$ in the most general hypotheses, thus answering a question of White from the 1980s: if $T$ is an area minimizing current modulo $p$ of dimension $m$ in $R^{m+n}$, then $T$ is smooth at all its interior points, except those belonging to a singular set of Hausdorff dimension at most $m-1$.
2019年01月28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) 128号室
河本 陽介 氏 (福岡歯科大学)
ランダム行列に関する普遍的な点過程間の遷移関係とその力学版 (JAPANESE)
河本 陽介 氏 (福岡歯科大学)
ランダム行列に関する普遍的な点過程間の遷移関係とその力学版 (JAPANESE)
[ 講演概要 ]
ランダム行列に関する無限粒子系の点過程として、Bessel点過程、サイン点過程、Airy点過程がよく知られている。これらは最初、Gaussianランダム行列モデルの固有値のスケーリング極限として得られたが、その後様々なモデルのスケーリング極限としても得られるという普遍性が明らかになった。この意味で、上記3つの点過程はランダム行列に関する典型的なモデルといえる。さらに、この3つは互いにスケーリング極限で結びついており、Bessel点過程を親玉とした遷移関係が存在することが知られている。今回の講演では、この点過程間の遷移関係が、点過程に自然に付随する確率力学にも遺伝することを導き、確率力学のレベルにおいてもBessel干渉型確率微分方程式を親玉とする遷移関係があることを紹介する。また時間が許す限り証明についても述べたい。
ランダム行列に関する無限粒子系の点過程として、Bessel点過程、サイン点過程、Airy点過程がよく知られている。これらは最初、Gaussianランダム行列モデルの固有値のスケーリング極限として得られたが、その後様々なモデルのスケーリング極限としても得られるという普遍性が明らかになった。この意味で、上記3つの点過程はランダム行列に関する典型的なモデルといえる。さらに、この3つは互いにスケーリング極限で結びついており、Bessel点過程を親玉とした遷移関係が存在することが知られている。今回の講演では、この点過程間の遷移関係が、点過程に自然に付随する確率力学にも遺伝することを導き、確率力学のレベルにおいてもBessel干渉型確率微分方程式を親玉とする遷移関係があることを紹介する。また時間が許す限り証明についても述べたい。
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
大野乾太郎 氏 (東京大学)
Minimizing CM degree and slope stability of projective varieties (JAPANESE)
大野乾太郎 氏 (東京大学)
Minimizing CM degree and slope stability of projective varieties (JAPANESE)
[ 講演概要 ]
Chow-Mumford (CM) line bundle is considered to play an important role in moduli problem for K-stable Fano varieties. In this talk, we consider a minimization problem of the degree of the CM line bundle among all possible fillings of a polarized family over a punctured curve. We show that such minimization implies the slope semistability of the fiber if the central fiber is smooth.
Chow-Mumford (CM) line bundle is considered to play an important role in moduli problem for K-stable Fano varieties. In this talk, we consider a minimization problem of the degree of the CM line bundle among all possible fillings of a polarized family over a punctured curve. We show that such minimization implies the slope semistability of the fiber if the central fiber is smooth.
2019年01月22日(火)
解析学火曜セミナー
16:50-18:20 数理科学研究科棟(駒場) 128号室
加藤圭一 氏 (東京理科大学)
Construction of solutions to Schrodinger equations with sub-quadratic potential via wave packet transform (Japanese)
加藤圭一 氏 (東京理科大学)
Construction of solutions to Schrodinger equations with sub-quadratic potential via wave packet transform (Japanese)
[ 講演概要 ]
In this talk, we consider linear Schrodinger equations with sub-quadratic potentials, which can be transformed by the wave packet transform with time dependent wave packet to a PDE of first order with inhomogeneous terms including unknown function and second derivatives of the potential. If the second derivatives of the potentials are bounded, the homogenous term of the first oder equation gives a construction of solutions to Schrodinger equations with sub-quadratic potentials by the similar way as in D. Fujiwara's work for Feynman path integral. We will show numerical computations by using our construction, if we have enough time.
In this talk, we consider linear Schrodinger equations with sub-quadratic potentials, which can be transformed by the wave packet transform with time dependent wave packet to a PDE of first order with inhomogeneous terms including unknown function and second derivatives of the potential. If the second derivatives of the potentials are bounded, the homogenous term of the first oder equation gives a construction of solutions to Schrodinger equations with sub-quadratic potentials by the similar way as in D. Fujiwara's work for Feynman path integral. We will show numerical computations by using our construction, if we have enough time.
2019年01月21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
Nicholas James McCleerey 氏 (Northwestern University)
POLAR TRANSFORM AND LOCAL POSITIVITY FOR CURVES (ENGLISH)
Nicholas James McCleerey 氏 (Northwestern University)
POLAR TRANSFORM AND LOCAL POSITIVITY FOR CURVES (ENGLISH)
[ 講演概要 ]
Using the duality of positive cones, we show that applying the polar transform from convexanalysis to local positivity invariants for divisors gives interesting and new local positivity invariantsfor curves. These new invariants have nice properties similar to those for divisors. In particular, thisenables us to give a characterization of the divisorial components of the non-K¨ahler locus of a big class. This is joint worth with Jian Xiao.
Using the duality of positive cones, we show that applying the polar transform from convexanalysis to local positivity invariants for divisors gives interesting and new local positivity invariantsfor curves. These new invariants have nice properties similar to those for divisors. In particular, thisenables us to give a characterization of the divisorial components of the non-K¨ahler locus of a big class. This is joint worth with Jian Xiao.
2019年01月16日(水)
代数学コロキウム
18:00-19:00 数理科学研究科棟(駒場) 056号室
Lei Fu 氏 (Yau Mathematical Sciences Center, Tsinghua University)
p-adic Gelfand-Kapranov-Zelevinsky systems (ENGLISH)
Lei Fu 氏 (Yau Mathematical Sciences Center, Tsinghua University)
p-adic Gelfand-Kapranov-Zelevinsky systems (ENGLISH)
[ 講演概要 ]
Using Dwork's trace formula, we express the exponential sum associated to a Laurent polynomial as the trace of a chain map on a twisted de Rham complex for the torus over the p-adic field. Treating the coefficients of the polynomial as parameters, we obtain the p-adic Gelfand-Kapranov-Zelevinsky (GKZ) system, which is a complex of D^\dagger-modules with Frobenius structure.
（本講演は「東京北京パリ数論幾何セミナー」として，インターネットによる東大数理，Morningside Center of Mathematics と IHES の双方向同時中継で行います．今回は北京からの中継です．）
Using Dwork's trace formula, we express the exponential sum associated to a Laurent polynomial as the trace of a chain map on a twisted de Rham complex for the torus over the p-adic field. Treating the coefficients of the polynomial as parameters, we obtain the p-adic Gelfand-Kapranov-Zelevinsky (GKZ) system, which is a complex of D^\dagger-modules with Frobenius structure.
（本講演は「東京北京パリ数論幾何セミナー」として，インターネットによる東大数理，Morningside Center of Mathematics と IHES の双方向同時中継で行います．今回は北京からの中継です．）
2019年01月15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) 056号室
Tea: Common Room 16:30-17:00
久野 雄介 氏 (津田塾大学)
Generalized Dehn twists on surfaces and homology cylinders (JAPANESE)
Tea: Common Room 16:30-17:00
久野 雄介 氏 (津田塾大学)
Generalized Dehn twists on surfaces and homology cylinders (JAPANESE)
[ 講演概要 ]
This is a joint work with Gwénaël Massuyeau (University of Burgundy). Lickorish's trick describes Dehn twists along simple closed curves on an oriented surface in terms of surgery of 3-manifolds. We discuss one possible generalization of this description to the situation where the curve under consideration may have self-intersections. Our result generalizes previously known computations related to the Johnson homomorphisms for the mapping class groups and for homology cylinders. In particular, we obtain an alternative and direct proof of the surjectivity of the Johnson homomorphisms for homology cylinders, which was proved by Garoufalidis-Levine and Habegger.
This is a joint work with Gwénaël Massuyeau (University of Burgundy). Lickorish's trick describes Dehn twists along simple closed curves on an oriented surface in terms of surgery of 3-manifolds. We discuss one possible generalization of this description to the situation where the curve under consideration may have self-intersections. Our result generalizes previously known computations related to the Johnson homomorphisms for the mapping class groups and for homology cylinders. In particular, we obtain an alternative and direct proof of the surjectivity of the Johnson homomorphisms for homology cylinders, which was proved by Garoufalidis-Levine and Habegger.
2019年01月09日(水)
代数学コロキウム
17:00-18:00 数理科学研究科棟(駒場) 056号室
Laurent Berger 氏 (ENS de Lyon)
Formal groups and p-adic dynamical systems (ENGLISH)
Laurent Berger 氏 (ENS de Lyon)
Formal groups and p-adic dynamical systems (ENGLISH)
[ 講演概要 ]
A formal group gives rise to a p-adic dynamical system. I will discuss some results about formal groups that can be proved using this point of view. I will also discuss the theory of p-adic dynamical systems and some open questions.
A formal group gives rise to a p-adic dynamical system. I will discuss some results about formal groups that can be proved using this point of view. I will also discuss the theory of p-adic dynamical systems and some open questions.
2019年01月08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) 056号室
Tea: Common Room 16:30-17:00
Marek Kaluba 氏 (Adam Mickiewicz Univeristy)
On property (T) for $\mathrm{Aut}(F_n)$ and $\mathrm{SL}_n(\mathbb{Z})$ (ENGLISH)
Tea: Common Room 16:30-17:00
Marek Kaluba 氏 (Adam Mickiewicz Univeristy)
On property (T) for $\mathrm{Aut}(F_n)$ and $\mathrm{SL}_n(\mathbb{Z})$ (ENGLISH)
[ 講演概要 ]
We prove that $\mathrm{Aut}(F_n)$ has Kazhdan's property (T) for every $n \ge 6$. Together with a previous result of Kaluba, Nowak, and Ozawa, this gives the same statement for $n \ge 5$. We also provide explicit lower bounds for the Kazhdan constants of $\mathrm{SAut}(F_n)$ (with $n \ge 6$) and of $\mathrm{SL}_n(\mathbb{Z})$ (with $n \ge 3$) with respect to natural generating sets. In the latter case, these bounds improve upon previously known lower bounds whenever $n >6$.
We prove that $\mathrm{Aut}(F_n)$ has Kazhdan's property (T) for every $n \ge 6$. Together with a previous result of Kaluba, Nowak, and Ozawa, this gives the same statement for $n \ge 5$. We also provide explicit lower bounds for the Kazhdan constants of $\mathrm{SAut}(F_n)$ (with $n \ge 6$) and of $\mathrm{SL}_n(\mathbb{Z})$ (with $n \ge 3$) with respect to natural generating sets. In the latter case, these bounds improve upon previously known lower bounds whenever $n >6$.
2018年12月25日(火)
解析学火曜セミナー
16:50-18:20 数理科学研究科棟(駒場) 128号室
眞崎聡 氏 (大阪大学)
Modified scattering for nonlinear dispersive equations with critical non-polynomial nonlinearities (Japanese)
眞崎聡 氏 (大阪大学)
Modified scattering for nonlinear dispersive equations with critical non-polynomial nonlinearities (Japanese)
[ 講演概要 ]
In this talk, I will introduce resent progress on modified scattering for Schrodinger equation and Klein-Gordon equation with a non-polynomial nonlinearity. We use Fourier series expansion technique to find the resonant part of the nonlinearity which produces phase correction factor.
In this talk, I will introduce resent progress on modified scattering for Schrodinger equation and Klein-Gordon equation with a non-polynomial nonlinearity. We use Fourier series expansion technique to find the resonant part of the nonlinearity which produces phase correction factor.
東京無限可積分系セミナー
16:00-17:00 数理科学研究科棟(駒場) 002号室
武部尚志 氏 (National Research University Higher School of Economics (Moscow))
Q-operators for generalised eight vertex models associated
to the higher spin representations of the Sklyanin algebra. (ENGLISH)
武部尚志 氏 (National Research University Higher School of Economics (Moscow))
Q-operators for generalised eight vertex models associated
to the higher spin representations of the Sklyanin algebra. (ENGLISH)
[ 講演概要 ]
The Q-operator was first introduced by Baxter in 1972 as a
tool to solve the eight vertex model and recently attracts
attention from the representation theoretical viewpoint. In
this talk, we show that Baxter's apparently quite ad hoc and
technical construction can be generalised to the model
associated to the higher spin representations of the
Sklyanin algebra. If everybody in the audience understands Japanese, the talk
will be in Japanese.
The Q-operator was first introduced by Baxter in 1972 as a
tool to solve the eight vertex model and recently attracts
attention from the representation theoretical viewpoint. In
this talk, we show that Baxter's apparently quite ad hoc and
technical construction can be generalised to the model
associated to the higher spin representations of the
Sklyanin algebra. If everybody in the audience understands Japanese, the talk
will be in Japanese.
2018年12月21日(金)
代数幾何学セミナー
10:30-11:30 数理科学研究科棟(駒場) 123号室
Mattias Jonsson 氏 (Michigan)
Degenerations of p-adic volume forms (English)
Mattias Jonsson 氏 (Michigan)
Degenerations of p-adic volume forms (English)
[ 講演概要 ]
Let X be an n-dimensional smooth projective variety over a non-Archimedean local field K. Also fix a regular n-form on X. This data induces a positive measure on the space of K'-rational points for any finite extension K' of K. We describe the asymptotics, as K' runs through towers of finite extensions of K, in terms of Berkovich analytic geometry. This is joint work with Johannes Nicaise.
Let X be an n-dimensional smooth projective variety over a non-Archimedean local field K. Also fix a regular n-form on X. This data induces a positive measure on the space of K'-rational points for any finite extension K' of K. We describe the asymptotics, as K' runs through towers of finite extensions of K, in terms of Berkovich analytic geometry. This is joint work with Johannes Nicaise.
2018年12月20日(木)
トポロジー火曜セミナー
13:00-14:30 数理科学研究科棟(駒場) 056号室
開催日時にご注意下さい
Anderson Vera 氏 (Université de Strasbourg)
Johnson-type homomorphisms and the LMO functor (ENGLISH)
開催日時にご注意下さい
Anderson Vera 氏 (Université de Strasbourg)
Johnson-type homomorphisms and the LMO functor (ENGLISH)
[ 講演概要 ]
One of the main objects associated to a surface S is the mapping class group MCG(S). This group plays an important role in the study of 3-manifolds. Reciprocally, the topological invariants of 3-manifolds can be used to obtain interesting representations of MCG(S).
One possible approach to the study of MCG(S) is to consider its action on the fundamental group P of the surface or on some subgroups of P. This way, we can obtain some kind of filtrations of MCG(S) and homomorphisms, called Johnson type homomorphisms, which take values in certain spaces of diagrams. These spaces of diagrams are quotients of the target space of the LMO functor. Hence it is natural to ask what is the relation between the Johnson type homomorphisms and the LMO functor. The answer is well known in the case of the Torelli group and the usual Johnson homomorphisms. In this talk we consider two other different filtrations of MCG(S) introduced by Levine and Habiro-Massuyeau. We show that the respective Johnson homomorphisms can also be deduced from the LMO functor.
One of the main objects associated to a surface S is the mapping class group MCG(S). This group plays an important role in the study of 3-manifolds. Reciprocally, the topological invariants of 3-manifolds can be used to obtain interesting representations of MCG(S).
One possible approach to the study of MCG(S) is to consider its action on the fundamental group P of the surface or on some subgroups of P. This way, we can obtain some kind of filtrations of MCG(S) and homomorphisms, called Johnson type homomorphisms, which take values in certain spaces of diagrams. These spaces of diagrams are quotients of the target space of the LMO functor. Hence it is natural to ask what is the relation between the Johnson type homomorphisms and the LMO functor. The answer is well known in the case of the Torelli group and the usual Johnson homomorphisms. In this talk we consider two other different filtrations of MCG(S) introduced by Levine and Habiro-Massuyeau. We show that the respective Johnson homomorphisms can also be deduced from the LMO functor.
2018年12月19日(水)
作用素環セミナー
16:45-18:15 数理科学研究科棟(駒場) 126号室
水田黎 氏 (東大数理)
Polynomial Time Algorithm for Computing N-th Moments of a Self-Adjoint Operator in Algebra Generated by Free Independent Semicircular Elements
水田黎 氏 (東大数理)
Polynomial Time Algorithm for Computing N-th Moments of a Self-Adjoint Operator in Algebra Generated by Free Independent Semicircular Elements
代数学コロキウム
17:30-18:30 数理科学研究科棟(駒場) 056号室
Jean-Stefan Koskivirta 氏 (東京大学数理科学研究科)
Cohomology vanishing for automorphic vector bundles (ENGLISH)
Jean-Stefan Koskivirta 氏 (東京大学数理科学研究科)
Cohomology vanishing for automorphic vector bundles (ENGLISH)
[ 講演概要 ]
A Shimura variety carries naturally a family of vector bundles parametrized by the characters of a maximal torus in the attached group. We want to determine which of these vector bundles are ample, and also show cohomology vanishing results. For this we use generalized Hasse invariants on the stack of G-zips of Moonen-Pink-Wedhorn-Ziegler. It is a group-theoretical counterpart of the Shimura variety and carries a similar family of vector bundles. This is joint work with Y.Brunebarbe, W.Goldring and B.Stroh.
A Shimura variety carries naturally a family of vector bundles parametrized by the characters of a maximal torus in the attached group. We want to determine which of these vector bundles are ample, and also show cohomology vanishing results. For this we use generalized Hasse invariants on the stack of G-zips of Moonen-Pink-Wedhorn-Ziegler. It is a group-theoretical counterpart of the Shimura variety and carries a similar family of vector bundles. This is joint work with Y.Brunebarbe, W.Goldring and B.Stroh.
2018年12月18日(火)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
In-Jee Jeong 氏 (Korea Institute for Advanced Study (KIAS))
Dynamics of singular vortex patches (English)
In-Jee Jeong 氏 (Korea Institute for Advanced Study (KIAS))
Dynamics of singular vortex patches (English)
[ 講演概要 ]
Vortex patches are solutions to the 2D Euler equations that are given by the characteristic function of a bounded domain that moves with time. It is well-known that if initially the boundary of the domain is smooth, the boundary remains smooth for all time. On the other hand, we consider patches with corner singularities. It turns out that, depending on whether the initial patch satisfies an appropriate rotational symmetry condition or not, the corner structure may propagate for all time or lost immediately. In the rotationally symmetric case, we are able to construct patches with interesting dynamical behavior as time goes to infinity. When the symmetry is absent, we present a simple yet formal evolution equation which describes the dynamics of the boundary. It suggests that the angle cusps instantaneously for $t > 0$.
This is joint work with Tarek Elgindi.
Vortex patches are solutions to the 2D Euler equations that are given by the characteristic function of a bounded domain that moves with time. It is well-known that if initially the boundary of the domain is smooth, the boundary remains smooth for all time. On the other hand, we consider patches with corner singularities. It turns out that, depending on whether the initial patch satisfies an appropriate rotational symmetry condition or not, the corner structure may propagate for all time or lost immediately. In the rotationally symmetric case, we are able to construct patches with interesting dynamical behavior as time goes to infinity. When the symmetry is absent, we present a simple yet formal evolution equation which describes the dynamics of the boundary. It suggests that the angle cusps instantaneously for $t > 0$.
This is joint work with Tarek Elgindi.
トポロジー火曜セミナー
17:30-18:30 数理科学研究科棟(駒場) 056号室
Tea: Common Room 17:00-17:30
鳥居 猛 氏 (岡山大学)
離散GスペクトラムとK(n)局所安定ホモトピー圏のモデルについて (JAPANESE)
Tea: Common Room 17:00-17:30
鳥居 猛 氏 (岡山大学)
離散GスペクトラムとK(n)局所安定ホモトピー圏のモデルについて (JAPANESE)
[ 講演概要 ]
K(n)局所安定ホモトピー圏はスペクトラムの安定ホモトピー圏の基本構成単位と考えられる。この講演ではMorava E理論とその安定化群との関係が明確になるようなK(n)局所安定ホモトピー圏のモデルを構成する。そのために、Behrens-Davisにより研究された副有限群Gに対する離散対称Gスペクトラムについて考える。そして、K(n)局所安定ホモトピー圏が、離散対称G_nスペクトラムの圏におけるE_nの離散モデル上の加群のホモトピー圏の中に実現されることを示す。
K(n)局所安定ホモトピー圏はスペクトラムの安定ホモトピー圏の基本構成単位と考えられる。この講演ではMorava E理論とその安定化群との関係が明確になるようなK(n)局所安定ホモトピー圏のモデルを構成する。そのために、Behrens-Davisにより研究された副有限群Gに対する離散対称Gスペクトラムについて考える。そして、K(n)局所安定ホモトピー圏が、離散対称G_nスペクトラムの圏におけるE_nの離散モデル上の加群のホモトピー圏の中に実現されることを示す。
2018年12月17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
神本丈 氏 (九州大学)
Newton polyhedra and order of contact on real hypersurfaces (JAPANESE)
神本丈 氏 (九州大学)
Newton polyhedra and order of contact on real hypersurfaces (JAPANESE)
[ 講演概要 ]
This talk will concern some issues on order of contact on real hypersurfaces, which was introduced by D'Angelo. To be more precise, a sufficient condition for the equality of regular type and singular type is given. This condition is written by using the Newton polyhedron of a defining function. Our result includes earlier known results concerning convex domains, pseudoconvex Reinhardt domains and pseudoconvex domains whose regular types are 4. Furthermore, under the above condition, the values of the types can be directly seen in a simple geometrical information from the Newton polyhedron.
The technique of using Newton polyhedra has many significant applications in singularity theory. In particular, this technique has been great success in the study of the Lojasiewicz exponent. Our study about the types is analogous to some works on the Lojasiewicz exponent.
This talk will concern some issues on order of contact on real hypersurfaces, which was introduced by D'Angelo. To be more precise, a sufficient condition for the equality of regular type and singular type is given. This condition is written by using the Newton polyhedron of a defining function. Our result includes earlier known results concerning convex domains, pseudoconvex Reinhardt domains and pseudoconvex domains whose regular types are 4. Furthermore, under the above condition, the values of the types can be directly seen in a simple geometrical information from the Newton polyhedron.
The technique of using Newton polyhedra has many significant applications in singularity theory. In particular, this technique has been great success in the study of the Lojasiewicz exponent. Our study about the types is analogous to some works on the Lojasiewicz exponent.
2018年12月14日(金)
代数幾何学セミナー
10:30-11:30 数理科学研究科棟(駒場) 123号室
Zhi Jiang 氏 (Fudan)
On the birationality of quint-canonical systems of irregular threefolds of general type (English)
Zhi Jiang 氏 (Fudan)
On the birationality of quint-canonical systems of irregular threefolds of general type (English)
[ 講演概要 ]
It is well-known that the quint-canonical map of a surface of general type is birational.
We will show that the same result holds for irregular threefolds of general type. The proof is based on
a careful study of the positivity of the pushforwards of pluricanonical bundles on abelian varieties and Severi
type inequalities. This is a joint work with J.A. Chen, J.Chen, and M.Chen.
It is well-known that the quint-canonical map of a surface of general type is birational.
We will show that the same result holds for irregular threefolds of general type. The proof is based on
a careful study of the positivity of the pushforwards of pluricanonical bundles on abelian varieties and Severi
type inequalities. This is a joint work with J.A. Chen, J.Chen, and M.Chen.
2018年12月12日(水)
代数学コロキウム
18:00-19:00 数理科学研究科棟(駒場) 056号室
Gaëtan Chenevier 氏 (CNRS, Université Paris-Sud)
A higher weight (and automorphic) generalization of the Hermite-Minkowski theorem (ENGLISH)
Gaëtan Chenevier 氏 (CNRS, Université Paris-Sud)
A higher weight (and automorphic) generalization of the Hermite-Minkowski theorem (ENGLISH)
[ 講演概要 ]
I will show that for any integer N, there are only finitely many cuspidal algebraic automorphic representations of GL_m over Q whose Artin conductor is N and whose "weights" are in the interval {0,...,23} (with m varying). Via the conjectural yoga between geometric Galois representations (or motives) and algebraic automorphic forms, this statement may be viewed as a generalization of the classical Hermite-Minkowski theorem in algebraic number theory. I will also discuss variants of these results when the base field Q is replaced by an arbitrary number field.
（本講演は「東京北京パリ数論幾何セミナー」として，インターネットによる東大数理，Morningside Center of Mathematics と IHES の双方向同時中継で行います．今回はパリからの中継です．）
I will show that for any integer N, there are only finitely many cuspidal algebraic automorphic representations of GL_m over Q whose Artin conductor is N and whose "weights" are in the interval {0,...,23} (with m varying). Via the conjectural yoga between geometric Galois representations (or motives) and algebraic automorphic forms, this statement may be viewed as a generalization of the classical Hermite-Minkowski theorem in algebraic number theory. I will also discuss variants of these results when the base field Q is replaced by an arbitrary number field.
（本講演は「東京北京パリ数論幾何セミナー」として，インターネットによる東大数理，Morningside Center of Mathematics と IHES の双方向同時中継で行います．今回はパリからの中継です．）
2018年12月11日(火)
PDE実解析研究会
10:30-11:30 数理科学研究科棟(駒場) 056号室
Marek Fila 氏 (Comenius University in Bratislava)
Solutions with moving singularities for equations of porous medium type (English)
Marek Fila 氏 (Comenius University in Bratislava)
Solutions with moving singularities for equations of porous medium type (English)
[ 講演概要 ]
We construct positive solutions of equations of porous medium type with a singularity which moves in time along a prescribed curve and keeps the spatial profile of singular stationary solutions. It turns out that there appears a critical exponent for the existence of such solutions. This is a joint work with Jin Takahashi and Eiji Yanagida.
We construct positive solutions of equations of porous medium type with a singularity which moves in time along a prescribed curve and keeps the spatial profile of singular stationary solutions. It turns out that there appears a critical exponent for the existence of such solutions. This is a joint work with Jin Takahashi and Eiji Yanagida.
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