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Future seminars
Seminar information archive ～03/06｜Today's seminar 03/07 | Future seminars 03/08～
2025/03/17
Operator Algebra Seminars
16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
The day of the week and the room are different from the usual ones.
Ingo Runkel (Univ. Hamburg)
Lattice models and topological symmetries from 2d conformal field theory
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
The day of the week and the room are different from the usual ones.
Ingo Runkel (Univ. Hamburg)
Lattice models and topological symmetries from 2d conformal field theory
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
2025/03/20
Lectures
13:00-14:30 Room #123 (Graduate School of Math. Sci. Bldg.)
Pre-registration is necessary to participate.
Mayuko Yamashita (Kyoto University)
場の理論と代数トポロジー:その可能性の中心
[ Reference URL ]
https://docs.google.com/forms/d/e/1FAIpQLSdFXVfYg9D7OgoUymOqhCiUJoGxk4x-bqyB1_odjH0QQBdfWw/viewform?usp=dialog
Pre-registration is necessary to participate.
Mayuko Yamashita (Kyoto University)
場の理論と代数トポロジー:その可能性の中心
[ Reference URL ]
https://docs.google.com/forms/d/e/1FAIpQLSdFXVfYg9D7OgoUymOqhCiUJoGxk4x-bqyB1_odjH0QQBdfWw/viewform?usp=dialog
2025/04/14
FJ-LMI Seminar
17:00-18:00 Room #Main Lecture Hall (Graduate School of Math. Sci. Bldg.)
FJ-LMI Distinguished Lecture
Pierre SCHAPIRA (IMJ - Sorbonne University)
Microlocal local sheaf theory and elliptic pairs (英語)
https://fj-lmi.cnrs.fr/wp-content/uploads/2025/02/Tokyo25Colloq.pdf
FJ-LMI Distinguished Lecture
Pierre SCHAPIRA (IMJ - Sorbonne University)
Microlocal local sheaf theory and elliptic pairs (英語)
[ Abstract ]
On a complex manifold $X$, an elliptic pair $(\mathcal{M},G)$ is the data of a coherent $\mathcal{M}_X$-module $\mathcal{M}$ and an $\mathbb R$-constructible sheaf $G$ with the property that the characteristic variety $\operatorname{char}(\mathcal{M})$ and the micro-support $\mathrm{SS}(G)$ do not intersect outside the zero-section of $T^*X$. We prove a regularity result which generalizes the classical case of hyperfunction solutions of elliptic systems and a finiteness theorem when assuming that the support of the pair is compact.
Then we introduce the microlocal Euler class of $\mathcal{M}$ and that of $G$ and calculate the Euler-Poincaré index of the complex of holomorphic solutions of the pair as the integral over $T^*X$ of the cup product of these two characteristic classes. This construction gives a new approach to the Riemann-Roch or the Atiyah-Singer theorems.
I will start by briefly recalling all necessary notions of microlocal sheaf theory and $\mathcal{D}$-module theory.
[ Reference URL ]On a complex manifold $X$, an elliptic pair $(\mathcal{M},G)$ is the data of a coherent $\mathcal{M}_X$-module $\mathcal{M}$ and an $\mathbb R$-constructible sheaf $G$ with the property that the characteristic variety $\operatorname{char}(\mathcal{M})$ and the micro-support $\mathrm{SS}(G)$ do not intersect outside the zero-section of $T^*X$. We prove a regularity result which generalizes the classical case of hyperfunction solutions of elliptic systems and a finiteness theorem when assuming that the support of the pair is compact.
Then we introduce the microlocal Euler class of $\mathcal{M}$ and that of $G$ and calculate the Euler-Poincaré index of the complex of holomorphic solutions of the pair as the integral over $T^*X$ of the cup product of these two characteristic classes. This construction gives a new approach to the Riemann-Roch or the Atiyah-Singer theorems.
I will start by briefly recalling all necessary notions of microlocal sheaf theory and $\mathcal{D}$-module theory.
https://fj-lmi.cnrs.fr/wp-content/uploads/2025/02/Tokyo25Colloq.pdf
2025/04/16
FJ-LMI Seminar
13:30-14:30 Room #TBA (Graduate School of Math. Sci. Bldg.)
Pierre SCHAPIRA (IMJ - Sorbonne University)
Sheaves for spacetime (英語)
https://fj-lmi.cnrs.fr/wp-content/uploads/2025/02/Tokyo25Sem.pdf
Pierre SCHAPIRA (IMJ - Sorbonne University)
Sheaves for spacetime (英語)
[ Abstract ]
We shall study the Cauchy problem on globally hyperbolic manifolds with the only tools of microlocal sheaf theory and the precise Cauchy-Kowalevski theorem.
A causal manifold is a manifold $M$ endowed with a closed convex proper cone $\lambda\subset T^*M$. On such a manifold, one defines the $\lambda$-topology and the associated notion of a causal pre-order. One introduces the notion of a G-causal manifold, those for which there exists a time function. On a G-manifold, sheaves satisfying a suitable condition on their micro-support and defined on a neighborhood of a Cauchy hypersurface extend to the whole space. When the sheaf is the complex of hyperfunction solutions of a hyperbolic $\mathcal D$-module, this proves that the Cauchy problem is globally well-posed.
We will also describe a ``shifted spacetime'' associated with the quantization of an Hamiltonian isotopy.
This talk is partly based on papers in collaboration with Benoît Jubin, Stéphane Guillermou and Masaki Kashiwara.
[ Reference URL ]We shall study the Cauchy problem on globally hyperbolic manifolds with the only tools of microlocal sheaf theory and the precise Cauchy-Kowalevski theorem.
A causal manifold is a manifold $M$ endowed with a closed convex proper cone $\lambda\subset T^*M$. On such a manifold, one defines the $\lambda$-topology and the associated notion of a causal pre-order. One introduces the notion of a G-causal manifold, those for which there exists a time function. On a G-manifold, sheaves satisfying a suitable condition on their micro-support and defined on a neighborhood of a Cauchy hypersurface extend to the whole space. When the sheaf is the complex of hyperfunction solutions of a hyperbolic $\mathcal D$-module, this proves that the Cauchy problem is globally well-posed.
We will also describe a ``shifted spacetime'' associated with the quantization of an Hamiltonian isotopy.
This talk is partly based on papers in collaboration with Benoît Jubin, Stéphane Guillermou and Masaki Kashiwara.
https://fj-lmi.cnrs.fr/wp-content/uploads/2025/02/Tokyo25Sem.pdf
