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過去の記録 ～10/15｜本日 10/16 | 今後の予定 10/17～
2026年10月13日(火)
トポロジー火曜セミナー
16:00-17:30 数理科学研究科棟(駒場) hybrid/123号室
LMI colloquium と合同開催。 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。
Léo Bénard 氏 (Aix-Marseille Université, FJ-LMI CNRS)
On a Langlands duality conjecture for character varieties of 3 manifolds (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
LMI colloquium と合同開催。 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。
Léo Bénard 氏 (Aix-Marseille Université, FJ-LMI CNRS)
On a Langlands duality conjecture for character varieties of 3 manifolds (ENGLISH)
[ 講演概要 ]
Inspired by a similar conjecture for skein modules of 3 manifolds formulated by Ben-Zvi, Gunningham, Jordan and Safronov, we conjecture that for G complex reductive group and L(G) its Langlands dual, for a 3 manifold M, if the character varieties X(M, G) and X(M, L(G)) are finite, then they have the same cardinality counted with multiplicity. We will discuss examples, non-examples, non-reduced points, and describe the cases where we can prove this statement. This is joint work with Renaud Detcherry (Dijon).
[ 参考URL ]Inspired by a similar conjecture for skein modules of 3 manifolds formulated by Ben-Zvi, Gunningham, Jordan and Safronov, we conjecture that for G complex reductive group and L(G) its Langlands dual, for a 3 manifold M, if the character varieties X(M, G) and X(M, L(G)) are finite, then they have the same cardinality counted with multiplicity. We will discuss examples, non-examples, non-reduced points, and describe the cases where we can prove this statement. This is joint work with Renaud Detcherry (Dijon).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
代数学コロキウム
17:00-18:00 数理科学研究科棟(駒場) 117号室
Dustin Clausen 氏 (IHES)
A refinement of Serre's conjecture
Dustin Clausen 氏 (IHES)
A refinement of Serre's conjecture
[ 講演概要 ]
Gaitsgory-Raskin proved a remarkable theorem: in the function field setting, a certain natural vector space of (everywhere unramified) automorphic forms for GL_n is isomorphic to the global sections of the dualizing sheaf on a natural stack of Langlands parameters. I will describe an attempt to translate the statement of this theorem to the number field context, in the setting of mod p automorphic forms. The resulting conjectural statement is a variant of conjectures of Emerton-Zhu; for GL_2 it is a refinement of Khare-Wintenberger's theorem (formerly, Serre's conjecture) relating modular forms and Galois representations mod p.
Gaitsgory-Raskin proved a remarkable theorem: in the function field setting, a certain natural vector space of (everywhere unramified) automorphic forms for GL_n is isomorphic to the global sections of the dualizing sheaf on a natural stack of Langlands parameters. I will describe an attempt to translate the statement of this theorem to the number field context, in the setting of mod p automorphic forms. The resulting conjectural statement is a variant of conjectures of Emerton-Zhu; for GL_2 it is a refinement of Khare-Wintenberger's theorem (formerly, Serre's conjecture) relating modular forms and Galois representations mod p.
2026年10月08日(木)
数値解析セミナー
16:30-18:00 数理科学研究科棟(駒場) 002号室
木曜日の開催になります。ご注意ください。
Marcus Grote 氏 (University of Basel)
Adaptive FEM with Explicit Time Integration For the Wave Equation
(English)
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
木曜日の開催になります。ご注意ください。
Marcus Grote 氏 (University of Basel)
Adaptive FEM with Explicit Time Integration For the Wave Equation
(English)
[ 講演概要 ]
Starting from a recent a posteriori error estimator for the finite element solution of the wave equation with explicit time integration [Grote, Lakkis, Santos, 2024], we devise a space-time adaptive strategy which includes both time evolving meshes and local time-stepping to overcome any overly stringent CFL stability restriction on the time-step due to local mesh refinement. Moreover, at each time-step the adaptive algorithm monitors the accuracy thanks to the error indicators and recomputes the current step on a refined mesh until the desired tolerance is met; meanwhile, the mesh is coarsened in regions of smaller errors. Leapfrog based local time-stepping is applied in all regions of local mesh refinement to incorporate adaptivity into fully explicit time integration with mesh change while retaining efficiency. Numerical results illustrate the optimal rate of convergence of the a posteriori error estimators on time evolving meshes.
[ 参考URL ]Starting from a recent a posteriori error estimator for the finite element solution of the wave equation with explicit time integration [Grote, Lakkis, Santos, 2024], we devise a space-time adaptive strategy which includes both time evolving meshes and local time-stepping to overcome any overly stringent CFL stability restriction on the time-step due to local mesh refinement. Moreover, at each time-step the adaptive algorithm monitors the accuracy thanks to the error indicators and recomputes the current step on a refined mesh until the desired tolerance is met; meanwhile, the mesh is coarsened in regions of smaller errors. Leapfrog based local time-stepping is applied in all regions of local mesh refinement to incorporate adaptivity into fully explicit time integration with mesh change while retaining efficiency. Numerical results illustrate the optimal rate of convergence of the a posteriori error estimators on time evolving meshes.
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
2026年10月06日(火)
数値解析セミナー
16:30-18:00 数理科学研究科棟(駒場) 002号室
Yohance Osborne 氏 (Durham University)
Numerical approximation of mean field games systems (English)
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Yohance Osborne 氏 (Durham University)
Numerical approximation of mean field games systems (English)
[ 講演概要 ]
Mean field games (MFG) are models for Nash equilibria of competitive differential games of optimal control involving a continuum of players. MFG equilibria are often described by systems of partial differential equations, where a Hamilton–Jacobi–Bellman (HJB) equation for the representative player’s value function is coupled nonlinearly with a Kolmogorov–Fokker–Planck (KFP) equation that determines the player distribution. MFG systems are particularly challenging to approximate computationally because they exhibit the following difficulties all at once: nonlinear couplings between the HJB and KFP equations, a temporal forward–backward structure, non-negativity of absolutely continuous player distributions, as well as potential nondifferentiability of the Hamiltonian. This talk addresses the numerical approximation of MFG systems for two classes of numerical schemes: (1) monotone stabilized finite element methods for second-order MFG systems with nondifferentiable Hamiltonians, and (2) particle methods for first-order MFG systems under displacement monotonicity. I will present theorems on the strong convergence of these numerical schemes and their rates of convergence, along with discussion of some numerical experiments.
[ 参考URL ]Mean field games (MFG) are models for Nash equilibria of competitive differential games of optimal control involving a continuum of players. MFG equilibria are often described by systems of partial differential equations, where a Hamilton–Jacobi–Bellman (HJB) equation for the representative player’s value function is coupled nonlinearly with a Kolmogorov–Fokker–Planck (KFP) equation that determines the player distribution. MFG systems are particularly challenging to approximate computationally because they exhibit the following difficulties all at once: nonlinear couplings between the HJB and KFP equations, a temporal forward–backward structure, non-negativity of absolutely continuous player distributions, as well as potential nondifferentiability of the Hamiltonian. This talk addresses the numerical approximation of MFG systems for two classes of numerical schemes: (1) monotone stabilized finite element methods for second-order MFG systems with nondifferentiable Hamiltonians, and (2) particle methods for first-order MFG systems under displacement monotonicity. I will present theorems on the strong convergence of these numerical schemes and their rates of convergence, along with discussion of some numerical experiments.
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
トポロジー火曜セミナー
16:00-17:30 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。
平良 晃一 氏 (東京大学大学院数理科学研究科)
Large eigenvalues and logarithmic Weyl law of the Connes-Moscovici operator (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。
平良 晃一 氏 (東京大学大学院数理科学研究科)
Large eigenvalues and logarithmic Weyl law of the Connes-Moscovici operator (JAPANESE)
[ 講演概要 ]
Bohr-Sommerfeldの量子化条件は，古典粒子系の閉軌道に沿う作用積分を用いて，対応する量子系の半古典的固有値を記述する法則である．Maslov indexを修正項として取り入れた量子化条件はKellerとMaslovにより独立に見出され，その後，ArnoldやHörmanderらによって数学的に厳密な枠組みが整備されてきた．一方，1次元のStrum-Liouville系では，適当な境界条件を課すことで，閉軌道に基づく通常のBohr-Sommerfeldの描像が直接適用できない場合にも離散固有値が現れることがある．本研究では，近年Connes-Moscoviciが導入したprolate 作用素に焦点を当てて，古典粒子系に閉軌道が存在しない場合にどのようにして固有値が生じ，その固有値を作用積分とMaslov indexによってどのように記述できるかを説明する．応用として，Connes-Moscoviciにより予想された，対数項を伴うWeyl則（固有値の数の漸近挙動）についての結果を紹介する．本研究はM. Willems氏（Utrecht大学）とM.Wrochna氏（Utrecht大学）との共同研究である．
[ 参考URL ]Bohr-Sommerfeldの量子化条件は，古典粒子系の閉軌道に沿う作用積分を用いて，対応する量子系の半古典的固有値を記述する法則である．Maslov indexを修正項として取り入れた量子化条件はKellerとMaslovにより独立に見出され，その後，ArnoldやHörmanderらによって数学的に厳密な枠組みが整備されてきた．一方，1次元のStrum-Liouville系では，適当な境界条件を課すことで，閉軌道に基づく通常のBohr-Sommerfeldの描像が直接適用できない場合にも離散固有値が現れることがある．本研究では，近年Connes-Moscoviciが導入したprolate 作用素に焦点を当てて，古典粒子系に閉軌道が存在しない場合にどのようにして固有値が生じ，その固有値を作用積分とMaslov indexによってどのように記述できるかを説明する．応用として，Connes-Moscoviciにより予想された，対数項を伴うWeyl則（固有値の数の漸近挙動）についての結果を紹介する．本研究はM. Willems氏（Utrecht大学）とM.Wrochna氏（Utrecht大学）との共同研究である．
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2026年10月05日(月)
作用素環セミナー
15:30-17:00 数理科学研究科棟(駒場) 126号室
森 孟彦 氏 (サレジオ工業高専)
The qx+r problem and the Cuntz algebra
森 孟彦 氏 (サレジオ工業高専)
The qx+r problem and the Cuntz algebra
複素解析幾何セミナー
10:30-12:00 数理科学研究科棟(駒場) 126号室
久本 智之 氏 (名古屋大学)
Miyaoka–Yau inequality, delta invariant, and the Calabi functional (Japanese)
https://forms.gle/8ERsVDLuKHwbVzm57
久本 智之 氏 (名古屋大学)
Miyaoka–Yau inequality, delta invariant, and the Calabi functional (Japanese)
[ 講演概要 ]
本講演は、岩井雅崇氏（大阪大学）との共同研究に基づく。我々は（K安定とは限らない）一般のFano多様体に対して、いわゆるδ不変量を組み込む形で宮岡-Yau型の不等式を確立した。この新しい不等式の等号成立条件、そしてCalabi汎関数との関係について紹介したい。
[ 参考URL ]本講演は、岩井雅崇氏（大阪大学）との共同研究に基づく。我々は（K安定とは限らない）一般のFano多様体に対して、いわゆるδ不変量を組み込む形で宮岡-Yau型の不等式を確立した。この新しい不等式の等号成立条件、そしてCalabi汎関数との関係について紹介したい。
https://forms.gle/8ERsVDLuKHwbVzm57
東京確率論セミナー
16:50-18:20 数理科学研究科棟(駒場) 122号室
教室は１２２です。今日はTea Time はありません。
田口 大 氏 (関西大学)
Euler–Maruyama scheme with unbounded Hölder drift
教室は１２２です。今日はTea Time はありません。
田口 大 氏 (関西大学)
Euler–Maruyama scheme with unbounded Hölder drift
[ 講演概要 ]
In this talk, we establish the strong rate of convergence of the Euler--Maruyama scheme for multidimensional stochastic differential equations with unbounded, uniformly locally Hölder continuous drift and multiplicative noise. Our approach relies on the Itô--Tanaka trick (Zvonkin-type transformation) adapted to unbounded drift. Furthermore, in order to apply the stochastic sewing lemma, we employ heat kernel estimates for the transition density of the Euler--Maruyama scheme. This talk is based on joint work with Tsukasa Moritoki (Okayama university).
In this talk, we establish the strong rate of convergence of the Euler--Maruyama scheme for multidimensional stochastic differential equations with unbounded, uniformly locally Hölder continuous drift and multiplicative noise. Our approach relies on the Itô--Tanaka trick (Zvonkin-type transformation) adapted to unbounded drift. Furthermore, in order to apply the stochastic sewing lemma, we employ heat kernel estimates for the transition density of the Euler--Maruyama scheme. This talk is based on joint work with Tsukasa Moritoki (Okayama university).
2026年10月02日(金)
代数幾何学セミナー
10:30-12:00 数理科学研究科棟(駒場) 122号室
いつもと時間帯・部屋が異なります。
JongHae Keum 氏 (KIAS)
Automorphisms of Fermat quartic surface
いつもと時間帯・部屋が異なります。
JongHae Keum 氏 (KIAS)
Automorphisms of Fermat quartic surface
[ 講演概要 ]
In 1944 Beniamino Segre proved that the Fermat quartic surface in the 3-dimensional projective space has infinitely many discrete automorphisms. It was the first example of an algebraic surface with infinite discrete automorphism group. Since then, it has long been an open problem to find generators of its automorphism group.
On the other hand, any other Fermat hypersurface of dimension > 1 and degree > 2 admits only projectively linear automorphisms, and has finite automorphism group.
With Keiji Oguiso and Xun Yu, we solve this problem, finding 16 geometric generators of finite order.
I will present this result, along with history of computation of automorphism groups of other K3 surfaces.
In 1944 Beniamino Segre proved that the Fermat quartic surface in the 3-dimensional projective space has infinitely many discrete automorphisms. It was the first example of an algebraic surface with infinite discrete automorphism group. Since then, it has long been an open problem to find generators of its automorphism group.
On the other hand, any other Fermat hypersurface of dimension > 1 and degree > 2 admits only projectively linear automorphisms, and has finite automorphism group.
With Keiji Oguiso and Xun Yu, we solve this problem, finding 16 geometric generators of finite order.
I will present this result, along with history of computation of automorphism groups of other K3 surfaces.
2026年09月28日(月)
東京確率論セミナー
14:00-17:30 数理科学研究科棟(駒場) 126号室
15:20〜 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。
Stefan Junk 氏 (Gakushuin University) 14:00-15:15
Some elements of the proof of equivalence of strong and very strong disorder for directed polymers (private seminar)
Dominik Schmid 氏 ( University of Augsburg) 16:00-17:30
The periodic directed landscape
15:20〜 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。
Stefan Junk 氏 (Gakushuin University) 14:00-15:15
Some elements of the proof of equivalence of strong and very strong disorder for directed polymers (private seminar)
Dominik Schmid 氏 ( University of Augsburg) 16:00-17:30
The periodic directed landscape
[ 講演概要 ]
The Kardar--Parisi--Zhang universality class is a central topic in mathematical physics and probability theory. In this talk, we discuss the conjectural scaling limit of periodic models in the Kardar--Parisi--Zhang universality class: the periodic directed landscape. We establish the convergence of periodic exponential last passage percolation to the periodic directed landscape and give a variational characterization of the periodic KPZ fixed point, recently constructed by Baik, Liao, and Liu. We also establish the convergence of periodic asymmetric simple exclusion processes to periodic KPZ fixed points, coupled through the same periodic directed landscape. A key ingredient is a gluing technique for combining overlapping directed landscapes, which may be of independent interest. This is based on joint work with Amol Aggarwal and Ivan Corwin.
The Kardar--Parisi--Zhang universality class is a central topic in mathematical physics and probability theory. In this talk, we discuss the conjectural scaling limit of periodic models in the Kardar--Parisi--Zhang universality class: the periodic directed landscape. We establish the convergence of periodic exponential last passage percolation to the periodic directed landscape and give a variational characterization of the periodic KPZ fixed point, recently constructed by Baik, Liao, and Liu. We also establish the convergence of periodic asymmetric simple exclusion processes to periodic KPZ fixed points, coupled through the same periodic directed landscape. A key ingredient is a gluing technique for combining overlapping directed landscapes, which may be of independent interest. This is based on joint work with Amol Aggarwal and Ivan Corwin.
2026年09月10日(木)
東京確率論セミナー
14:00-17:30 数理科学研究科棟(駒場) 126号室
講演の開始が早くなっています。
Sung-Soo Byun 氏 (Seoul National University) 14:00-15:30
Inhomogeneous Geometric Last Passage Percolation and the q-deformed Jacobi Unitary Ensemble
GIG random matrices and a Yang-Baxter extension of the Matsumoto-Yor property
講演の開始が早くなっています。
Sung-Soo Byun 氏 (Seoul National University) 14:00-15:30
Inhomogeneous Geometric Last Passage Percolation and the q-deformed Jacobi Unitary Ensemble
[ 講演概要 ]
Since the pioneering work of Johansson, geometric last passage percolation (LPP) has become one of the central models in integrable probability, with many remarkable properties established over the past two decades. Most existing results, particularly those admitting explicit formulae, however, concern homogeneous environments. In this talk, I will discuss geometric LPP in a particular inhomogeneous environment. Our approach is based on a duality with a q-deformed analogue of the classical Jacobi unitary ensemble. Exploiting recent developments in the asymptotic spectral analysis of this random matrix model, I will present recent results on the law of large numbers, an explicit characterisation of the shape function, and the fluctuation behaviour of the last passage time.
Jacek Wesolowski 氏 (Warsaw University of Technology) 16:00-17:30Since the pioneering work of Johansson, geometric last passage percolation (LPP) has become one of the central models in integrable probability, with many remarkable properties established over the past two decades. Most existing results, particularly those admitting explicit formulae, however, concern homogeneous environments. In this talk, I will discuss geometric LPP in a particular inhomogeneous environment. Our approach is based on a duality with a q-deformed analogue of the classical Jacobi unitary ensemble. Exploiting recent developments in the asymptotic spectral analysis of this random matrix model, I will present recent results on the law of large numbers, an explicit characterisation of the shape function, and the fluctuation behaviour of the last passage time.
GIG random matrices and a Yang-Baxter extension of the Matsumoto-Yor property
[ 講演概要 ]
A map is independence preserving (IP) if there exists a product probability measure which is transferred by this map into to a product probability measures. Many classical examples of such maps and related probability laws are known probably the best known is the map (x,y)\mapsto (x+y, x-y) is an IP map for product of normal laws. Sasada and Uozumi (2024) identified IP a new family of parametric Yang-Baxter maps on positive quadrant together with related probability laws. In particular, the map H_{III,B}^{(\alpha,\beta)}, of this family was connected to the IP property of the GIG distributions. This IP property appears also naturally in probabilistic integrable models of discrete Korteweg de Vries type, as observed by Croydon and Sasada (2020). In the case of (\alpha,\beta)=(1,0), remarkably, this IP property reduces to the classical Matsumoto-Yor property rooted in the conditional structure of functionals of exponential Brownian motion.
We will propose an extension of H_{III,B}^{(\alpha,\beta)} to a Yang-Baxter map on the cone of symmetric positive definite matrices of a fixed dimension. We will show that this extended map preserves independence of GIG random matrices. We will present a proof that the matrix GIG distribution is characterized by the IP property of this map.
A map is independence preserving (IP) if there exists a product probability measure which is transferred by this map into to a product probability measures. Many classical examples of such maps and related probability laws are known probably the best known is the map (x,y)\mapsto (x+y, x-y) is an IP map for product of normal laws. Sasada and Uozumi (2024) identified IP a new family of parametric Yang-Baxter maps on positive quadrant together with related probability laws. In particular, the map H_{III,B}^{(\alpha,\beta)}, of this family was connected to the IP property of the GIG distributions. This IP property appears also naturally in probabilistic integrable models of discrete Korteweg de Vries type, as observed by Croydon and Sasada (2020). In the case of (\alpha,\beta)=(1,0), remarkably, this IP property reduces to the classical Matsumoto-Yor property rooted in the conditional structure of functionals of exponential Brownian motion.
We will propose an extension of H_{III,B}^{(\alpha,\beta)} to a Yang-Baxter map on the cone of symmetric positive definite matrices of a fixed dimension. We will show that this extended map preserves independence of GIG random matrices. We will present a proof that the matrix GIG distribution is characterized by the IP property of this map.
東京無限可積分系セミナー
14:00-16:00 数理科学研究科棟(駒場) 123号室
村瀬元彦 氏 (UC Davis)
The SL(2) that relates Gaiotto's Conformal Limit and the Geometric Langlands Correspondence (English)
村瀬元彦 氏 (UC Davis)
The SL(2) that relates Gaiotto's Conformal Limit and the Geometric Langlands Correspondence (English)
[ 講演概要 ]
The purpose of this talk is to show that Gaiotto's "conformal limit" construction of opers via the non-Abelian Hodge correspondence gives the same map that appears in the Geometric Langlands Correspondence for the case of opers. The resulting map is a unique canonical biholomorphic map from the moduli space of G-spectral curves to the moduli space of LG-opers, both defined over a smooth complex projective curve X with a complex simple algebraic group G and its Langlands dual LG.
The Structure of the Talk:
In the first hour of the talk I will present the main theorem and explain motivational materials, including:
・The differential equations interpreting the stability conditions in algebraic geometry of moduli spaces;
・Simpson's NAH map between the moduli spaces of Higgs bundles and connections on X;
・The moduli space of opers that forms a Lagrangian in the moduli space of local systems on X;
・From a spectral curve to an oper as a quantization procedure; and
・The idea of Gaiotto on taking a scaling limit of NAH that changes a transcendental topological map into a calculable algebraic map.
In the second hour, I will talk about the following subjects:
・The Geometric Langlands Correspondence for the case of opers due to Beilinson-Drinfeld;
・Kostant's TDS;
・The proof of Gaiotto's conformal limit for the case of sl(2);
・GLC for sl(2);
・The parallelism of these proofs going from sl(2) to the general case through Kostant's TDS.
The purpose of this talk is to show that Gaiotto's "conformal limit" construction of opers via the non-Abelian Hodge correspondence gives the same map that appears in the Geometric Langlands Correspondence for the case of opers. The resulting map is a unique canonical biholomorphic map from the moduli space of G-spectral curves to the moduli space of LG-opers, both defined over a smooth complex projective curve X with a complex simple algebraic group G and its Langlands dual LG.
The Structure of the Talk:
In the first hour of the talk I will present the main theorem and explain motivational materials, including:
・The differential equations interpreting the stability conditions in algebraic geometry of moduli spaces;
・Simpson's NAH map between the moduli spaces of Higgs bundles and connections on X;
・The moduli space of opers that forms a Lagrangian in the moduli space of local systems on X;
・From a spectral curve to an oper as a quantization procedure; and
・The idea of Gaiotto on taking a scaling limit of NAH that changes a transcendental topological map into a calculable algebraic map.
In the second hour, I will talk about the following subjects:
・The Geometric Langlands Correspondence for the case of opers due to Beilinson-Drinfeld;
・Kostant's TDS;
・The proof of Gaiotto's conformal limit for the case of sl(2);
・GLC for sl(2);
・The parallelism of these proofs going from sl(2) to the general case through Kostant's TDS.
2026年09月09日(水)
日仏数学拠点FJ-LMIセミナー
11:15-12:00 数理科学研究科棟(駒場) 056号室
Léo BÉNARD 氏 (CNRS FJ-LMI)
Character varieties of knots, and the Reidemeister torsion function (英語)
https://fj-lmi.cnrs.fr/seminars
Léo BÉNARD 氏 (CNRS FJ-LMI)
Character varieties of knots, and the Reidemeister torsion function (英語)
[ 講演概要 ]
I will mainly motivate the study of Reidemeister torsion from a historical perspective, and highlight some recent related results and questions.
[ 参考URL ]I will mainly motivate the study of Reidemeister torsion from a historical perspective, and highlight some recent related results and questions.
https://fj-lmi.cnrs.fr/seminars
日仏数学拠点FJ-LMIセミナー
15:00-16:00 数理科学研究科棟(駒場) 126号室
Herbert GANGL 氏 (Durham University)
Introduction to polylogarithms, with connections to number theory and algebraic $K$-theory (英語)
https://fj-lmi.cnrs.fr/wp-content/uploads/2026/09/Warm_up_session_schedule_and_abstracts.pdf
Herbert GANGL 氏 (Durham University)
Introduction to polylogarithms, with connections to number theory and algebraic $K$-theory (英語)
[ 講演概要 ]
In this survey talk we discuss several basic properties of classical polylogarithms
$$ \mathrm{Li}_m(z)=\sum_{k\geq1}\frac{z^k}{k^m}
$$
in the unit disc, for $m \geq 1$, leading up to a beautiful connection to the algebraic $K$-theory of number
fields, motivated by an attempt to find a suitable generalisation of Dirichlet’s celebrated class number
formula. Bloch initiated this for the dilogarithm, and Zagier extended it to higher polylogarithms. It
turns out that an arguably even more suitable class of functions to describe this connection involves
multiple polylogarithms (MPLs = nested sums of classical ones, in several variables $z_1, \ldots , z_d)$. If time
allows, we will also try to give a glimpse of Goncharov’s highly relevant “depth reduction conjecture”
for MPLs and what is known about it.
[ 参考URL ]In this survey talk we discuss several basic properties of classical polylogarithms
$$ \mathrm{Li}_m(z)=\sum_{k\geq1}\frac{z^k}{k^m}
$$
in the unit disc, for $m \geq 1$, leading up to a beautiful connection to the algebraic $K$-theory of number
fields, motivated by an attempt to find a suitable generalisation of Dirichlet’s celebrated class number
formula. Bloch initiated this for the dilogarithm, and Zagier extended it to higher polylogarithms. It
turns out that an arguably even more suitable class of functions to describe this connection involves
multiple polylogarithms (MPLs = nested sums of classical ones, in several variables $z_1, \ldots , z_d)$. If time
allows, we will also try to give a glimpse of Goncharov’s highly relevant “depth reduction conjecture”
for MPLs and what is known about it.
https://fj-lmi.cnrs.fr/wp-content/uploads/2026/09/Warm_up_session_schedule_and_abstracts.pdf
日仏数学拠点FJ-LMIセミナー
16:15-17:15 数理科学研究科棟(駒場) 126号室
Luc PIRIO 氏 (CNRS FJ-LMI)
Polylogarithms and Webs
https://fj-lmi.cnrs.fr/wp-content/uploads/2026/09/Warm_up_session_schedule_and_abstracts.pdf
Luc PIRIO 氏 (CNRS FJ-LMI)
Polylogarithms and Webs
[ 講演概要 ]
In this rather informal talk, I will discuss how web geometry provides a geometric approach
to functional identities that are formally similar to those satisfied by polylogarithms.
[ 参考URL ]In this rather informal talk, I will discuss how web geometry provides a geometric approach
to functional identities that are formally similar to those satisfied by polylogarithms.
https://fj-lmi.cnrs.fr/wp-content/uploads/2026/09/Warm_up_session_schedule_and_abstracts.pdf
2026年08月21日(金)
代数幾何学セミナー
13:15-14:45 数理科学研究科棟(駒場) 128号室
（8/17更新）講演者の都合で中止となりました。
Heath Pearson 氏 (the University of Nottingham)
TBA
（8/17更新）講演者の都合で中止となりました。
Heath Pearson 氏 (the University of Nottingham)
TBA
[ 講演概要 ]
TBA
TBA
2026年08月04日(火)
博士論文発表会
16:15-17:30 数理科学研究科棟(駒場) 122号室
朝永 龍 氏 (東京大学大学院数理科学研究科)
d-Tilting bundles and applications to d-representation infinite algebras and non-commutative crepant resolutions
（d-傾束およびそのd-無限表現型代数と非可換クレパント特異点解消への応用）
朝永 龍 氏 (東京大学大学院数理科学研究科)
d-Tilting bundles and applications to d-representation infinite algebras and non-commutative crepant resolutions
（d-傾束およびそのd-無限表現型代数と非可換クレパント特異点解消への応用）
2026年07月31日(金)
代数幾何学セミナー
16:00-17:30 数理科学研究科棟(駒場) 118号室
Adrian Langer 氏 (University of Warsaw)
Fundamental group schemes in positive characteristic and its
applications
Adrian Langer 氏 (University of Warsaw)
Fundamental group schemes in positive characteristic and its
applications
[ 講演概要 ]
The main goal of this talk is to study analogues of the topological
fundamental group for (possibly singular) algebraic varieties in
positive characteristic. I will focus on one such analogue, whose
category of representations is given by crystals on so called stratified
site of a variety X.
This is motivated by Grothendieck's version of the Riemann-Hilbert
correspondence, which states that for a proper complex, possibly
singular, variety the category of representations of the topological
fundamental group of the analytification of X is equivalent to the
category of crystals on the stratified site of X. In positive
characteristic, crystals on the stratified site can equivalently be
described as F-divided bundles. For smooth varieties, these objects have
been studied extensively by, among others, D. Gieseker, J. P. dos
Santos, H. Esnault, V. Mehta and V. Srinivas. In this talk, I will
discuss several properties of the fundamental group that are familiar
from the complex setting and show that they continue to hold in positive
characteristic, even for singular varieties. As an application, I will
prove that simply connected, proper, normal varieties in positive
characteristic admit no nontrivial F-divided bundles. This generalizes
an earlier result of H. Esnault and V. Mehta concerning smooth
projective varieties, and settles Gieseker's conjecture in a more
general setting. If time permits I will also discuss the relative
version of Gieseker's conjecture. Most of this work is joint with Lei
Zhang (SYSU, Zhuhai).
The main goal of this talk is to study analogues of the topological
fundamental group for (possibly singular) algebraic varieties in
positive characteristic. I will focus on one such analogue, whose
category of representations is given by crystals on so called stratified
site of a variety X.
This is motivated by Grothendieck's version of the Riemann-Hilbert
correspondence, which states that for a proper complex, possibly
singular, variety the category of representations of the topological
fundamental group of the analytification of X is equivalent to the
category of crystals on the stratified site of X. In positive
characteristic, crystals on the stratified site can equivalently be
described as F-divided bundles. For smooth varieties, these objects have
been studied extensively by, among others, D. Gieseker, J. P. dos
Santos, H. Esnault, V. Mehta and V. Srinivas. In this talk, I will
discuss several properties of the fundamental group that are familiar
from the complex setting and show that they continue to hold in positive
characteristic, even for singular varieties. As an application, I will
prove that simply connected, proper, normal varieties in positive
characteristic admit no nontrivial F-divided bundles. This generalizes
an earlier result of H. Esnault and V. Mehta concerning smooth
projective varieties, and settles Gieseker's conjecture in a more
general setting. If time permits I will also discuss the relative
version of Gieseker's conjecture. Most of this work is joint with Lei
Zhang (SYSU, Zhuhai).
2026年07月27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
15:20〜 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。
坪谷 玲緒 氏 (京都大学)
Weak solution theory for the stochastic compressible Navier-Stokes equations with slip boundary conditions
15:20〜 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。
坪谷 玲緒 氏 (京都大学)
Weak solution theory for the stochastic compressible Navier-Stokes equations with slip boundary conditions
[ 講演概要 ]
Navier-Stokes方程式は、粘性のある流体の運動を記述する方程式であり、流体力学だけでなく非線形偏微分方程式論においても中心的な研究対象である。確率論の文脈では、外部からの不確実な影響や微視的な揺らぎを記述するため、ノイズを含む確率Navier-Stokes方程式が研究されている。非圧縮性流体の解析は古くから盛んに行われてきた一方で、気体のように密度変化を伴う圧縮性流体の解析は、特に確率論において比較的新しく、現在も多くの課題が残されている。さらに、流体の解析において境界条件の選択は重要な意味をもつ。近年では、流体が境界面に沿って滑ることを許す滑り境界条件が、物理的に自然な境界条件の一つとして注目を集めている。以上の背景を踏まえ、本講演では、まず確率圧縮性Navier-Stokes方程式の構造について概説し、その後、滑り境界条件のもとでの弱解理論について、講演者の結果を紹介する。
Navier-Stokes方程式は、粘性のある流体の運動を記述する方程式であり、流体力学だけでなく非線形偏微分方程式論においても中心的な研究対象である。確率論の文脈では、外部からの不確実な影響や微視的な揺らぎを記述するため、ノイズを含む確率Navier-Stokes方程式が研究されている。非圧縮性流体の解析は古くから盛んに行われてきた一方で、気体のように密度変化を伴う圧縮性流体の解析は、特に確率論において比較的新しく、現在も多くの課題が残されている。さらに、流体の解析において境界条件の選択は重要な意味をもつ。近年では、流体が境界面に沿って滑ることを許す滑り境界条件が、物理的に自然な境界条件の一つとして注目を集めている。以上の背景を踏まえ、本講演では、まず確率圧縮性Navier-Stokes方程式の構造について概説し、その後、滑り境界条件のもとでの弱解理論について、講演者の結果を紹介する。
2026年07月23日(木)
博士論文発表会
14:00-15:15 数理科学研究科棟(駒場) 122号室
髙谷 悠太 氏 (東京大学大学院数理科学研究科)
Moduli space of depth-zero level structures on local shtukas
（局所シュトゥーカの深度0レベル構造のモジュライ空間）
髙谷 悠太 氏 (東京大学大学院数理科学研究科)
Moduli space of depth-zero level structures on local shtukas
（局所シュトゥーカの深度0レベル構造のモジュライ空間）
2026年07月21日(火)
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
磯野優介 氏 (京大数理研)
Introduction to Tomita--Takesaki theory
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
磯野優介 氏 (京大数理研)
Introduction to Tomita--Takesaki theory
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
2026年07月17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) NISSAY Lecture Hall号室
松井宏樹 氏 (東京大学大学院数理科学研究科)
力学系から生じる位相充足群およびC*環について (日本語)
松井宏樹 氏 (東京大学大学院数理科学研究科)
力学系から生じる位相充足群およびC*環について (日本語)
[ 講演概要 ]
カントール集合上の極小な力学系から位相充足群と呼ばれる可算無限群を構成することができる。この群はその交換子群が単純になるという著しい性質を持ち、さまざまな力学系から興味深い性質を持つ無限群を与えることができる。1992年にSteinによって導入されたStein群を一つの題材として、最近の研究の進展を概観・紹介したい。時間が許す範囲で、力学系から構成されるC*環やそのK群、或いは力学系自身のホモロジー群との関連についても触れたい。
カントール集合上の極小な力学系から位相充足群と呼ばれる可算無限群を構成することができる。この群はその交換子群が単純になるという著しい性質を持ち、さまざまな力学系から興味深い性質を持つ無限群を与えることができる。1992年にSteinによって導入されたStein群を一つの題材として、最近の研究の進展を概観・紹介したい。時間が許す範囲で、力学系から構成されるC*環やそのK群、或いは力学系自身のホモロジー群との関連についても触れたい。
2026年07月15日(水)
代数学コロキウム
17:00-18:00 数理科学研究科棟(駒場) 117号室
福冨 直人 氏 (東京大学大学院数理科学研究科)
Localization and coalescence of condensed ringed spaces
福冨 直人 氏 (東京大学大学院数理科学研究科)
Localization and coalescence of condensed ringed spaces
[ 講演概要 ]
Gillam proved that the category of locally ringed spaces admits a fully faithful embedding into a certain category, which has a right adjoint that maps some simple objects to the spectra of rings. In this talk, we use condensed mathematics to define an analogous category and its coreflective full subcategories, and explain that one of their coreflections maps certain simple objects to the adic spectra of certain Huber pairs.
Gillam proved that the category of locally ringed spaces admits a fully faithful embedding into a certain category, which has a right adjoint that maps some simple objects to the spectra of rings. In this talk, we use condensed mathematics to define an analogous category and its coreflective full subcategories, and explain that one of their coreflections maps certain simple objects to the adic spectra of certain Huber pairs.
2026年07月14日(火)
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
安藤浩志 氏 (千葉大学)
Model theory and Connes' bicentralizer problem
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
安藤浩志 氏 (千葉大学)
Model theory and Connes' bicentralizer problem
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Lie群論・表現論セミナー
16:00-17:30 数理科学研究科棟(駒場) 056号室
トポロジー火曜セミナーと合同開催。
田中雄一郎 氏 (東大数理)
Visible actions of real reductive groups on complex algebraic varieties
トポロジー火曜セミナーと合同開催。
田中雄一郎 氏 (東大数理)
Visible actions of real reductive groups on complex algebraic varieties
[ 講演概要 ]
A unitary representation of a locally compact group is multiplicity-free if each irreducible representation appears at most once in its irreducible decomposition.
To provide a unified perspective on this property in the context of Lie group representations, T. Kobayashi introduced the theory of visible action for holomorphic actions of Lie groups on complex manifolds.
This approach enables us to understand many known examples uniformly and also leads to the discovery of new ones by utilizing Kobayashi’s propagation theorem of multiplicity-freeness property for visible actions.
In this talk, we will begin with the definition of visible action, illustrated with examples, and then explore some known results on classifications of visible actions and relationships among the coisotropicity, the sphericity and the visibility for group-actions on complex smooth algebraic varieties.
We will also discuss recent results based on unitary tricks for transferring properties of compact group-actions on complex flag manifolds to non-compact ones.
A unitary representation of a locally compact group is multiplicity-free if each irreducible representation appears at most once in its irreducible decomposition.
To provide a unified perspective on this property in the context of Lie group representations, T. Kobayashi introduced the theory of visible action for holomorphic actions of Lie groups on complex manifolds.
This approach enables us to understand many known examples uniformly and also leads to the discovery of new ones by utilizing Kobayashi’s propagation theorem of multiplicity-freeness property for visible actions.
In this talk, we will begin with the definition of visible action, illustrated with examples, and then explore some known results on classifications of visible actions and relationships among the coisotropicity, the sphericity and the visibility for group-actions on complex smooth algebraic varieties.
We will also discuss recent results based on unitary tricks for transferring properties of compact group-actions on complex flag manifolds to non-compact ones.
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