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Future seminars
Seminar information archive ～04/22｜Today's seminar 04/23 | Future seminars 04/24～
2024/04/24
Numerical Analysis Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Yuka Hashimoto (NTT Network Service Systems Laboratories)
Generalization analysis of neural networks based on Koopman operators
(Japanese)
[ Reference URL ]
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Yuka Hashimoto (NTT Network Service Systems Laboratories)
Generalization analysis of neural networks based on Koopman operators
(Japanese)
[ Reference URL ]
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
FJ-LMI Seminar
15:00-16:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Laurent Di Menza (Université de Reims Champagne-Ardenne, CNRS)
Some aspects of Schrödinger models (英語)
https://fj-lmi.cnrs.fr/seminars/
Laurent Di Menza (Université de Reims Champagne-Ardenne, CNRS)
Some aspects of Schrödinger models (英語)
[ Abstract ]
In this talk, we focus on basic facts about the Schrödinger equation that arises in various physical contexts, from quantum mechanics to gravita-tional systems. This kind of equation has been intensively studied in the literature and many properties are known, either from a qualitative and quantitative point of view. The goal of this presentation is to give basic properties of solutions in different regimes. A particular effort will be paid for the numerical computation of solitons that consist in solutions that propagate with shape invariance.
[ Reference URL ]In this talk, we focus on basic facts about the Schrödinger equation that arises in various physical contexts, from quantum mechanics to gravita-tional systems. This kind of equation has been intensively studied in the literature and many properties are known, either from a qualitative and quantitative point of view. The goal of this presentation is to give basic properties of solutions in different regimes. A particular effort will be paid for the numerical computation of solitons that consist in solutions that propagate with shape invariance.
https://fj-lmi.cnrs.fr/seminars/
Discrete mathematical modelling seminar
13:30-15:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Jaume Alonso (Technische Universität Berlin)
Dynamical degrees of birational maps from indices of polynomials with respect to blow-ups (English)
Jaume Alonso (Technische Universität Berlin)
Dynamical degrees of birational maps from indices of polynomials with respect to blow-ups (English)
[ Abstract ]
In this talk we propose a new method for the exact computation of the degree $\deg (f^n)$ of the iterates of a birational map $f:\mathbb{P}^n \dashrightarrow \mathbb{P}^n$. The method is based on two main ingredients. Firstly, the factorisation of a polynomial under the pull-back by $f$, based on local indices of a polynomial associated to blow-ups used to resolve the singularity. Secondly, the propagation of these indices along the orbits of $f$. We will illustrate the method in different examples, showing its flexibility, since it does not require the construction of an algebraically stable lift of $f$, unlike other methods based on the Picard group.
This is a joint work with Yuri Suris and Kangning Wei.
In this talk we propose a new method for the exact computation of the degree $\deg (f^n)$ of the iterates of a birational map $f:\mathbb{P}^n \dashrightarrow \mathbb{P}^n$. The method is based on two main ingredients. Firstly, the factorisation of a polynomial under the pull-back by $f$, based on local indices of a polynomial associated to blow-ups used to resolve the singularity. Secondly, the propagation of these indices along the orbits of $f$. We will illustrate the method in different examples, showing its flexibility, since it does not require the construction of an algebraically stable lift of $f$, unlike other methods based on the Picard group.
This is a joint work with Yuri Suris and Kangning Wei.
2024/04/26
Algebraic Geometry Seminar
14:00-15:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Tatsuro Kawakami (Kyoto University)
Frobenius stable Grauert-Riemenschneider vanishing fails (日本語)
Tatsuro Kawakami (Kyoto University)
Frobenius stable Grauert-Riemenschneider vanishing fails (日本語)
[ Abstract ]
We show that the Frobenius stable version of Grauert-Riemenschneider vanishing fails for a terminal 3-fold in characteristic 2. To prove this, we introduce the notion of $F_p$-rationality for singularities in positive characteristic, and prove that 3-dimensional klt singularities are $F_p$-rational. I will also talk about the vanishing of $F_p$-cohomologies of log Fano threefolds. This is joint work with Jefferson Baudin and Fabio Bernasconi.
We show that the Frobenius stable version of Grauert-Riemenschneider vanishing fails for a terminal 3-fold in characteristic 2. To prove this, we introduce the notion of $F_p$-rationality for singularities in positive characteristic, and prove that 3-dimensional klt singularities are $F_p$-rational. I will also talk about the vanishing of $F_p$-cohomologies of log Fano threefolds. This is joint work with Jefferson Baudin and Fabio Bernasconi.
Colloquium
15:30-16:30 Room #大講義室(auditorium) (Graduate School of Math. Sci. Bldg.)
Shouhei Honda (Graduate School of Mathematical Sciences, University of Tokyo)
Riemannian manifolds and their limit spaces (JAPANESE)
Shouhei Honda (Graduate School of Mathematical Sciences, University of Tokyo)
Riemannian manifolds and their limit spaces (JAPANESE)
[ Abstract ]
The Gromov-Hausdorff (GH) distance defines a distance on the set A of all isometry classes of Riemannian manifolds. Gromov established a precompactness result with respect to the GH distance, under assuming a lower bound on Ricci curvature. In particular we are able to discuss limit nonsmooth spaces of Riemannian manifolds with Ricci curvature bounded below. In this talk, we explain recent developments about this topic.
The Gromov-Hausdorff (GH) distance defines a distance on the set A of all isometry classes of Riemannian manifolds. Gromov established a precompactness result with respect to the GH distance, under assuming a lower bound on Ricci curvature. In particular we are able to discuss limit nonsmooth spaces of Riemannian manifolds with Ricci curvature bounded below. In this talk, we explain recent developments about this topic.
2024/04/30
Operator Algebra Seminars
16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
Harshit Yadav (Univ. Alberta)
Non-semisimple modular tensor categories via local modules
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Harshit Yadav (Univ. Alberta)
Non-semisimple modular tensor categories via local modules
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
2024/05/01
Number Theory Seminar
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Kojiro Matsumoto (University of Tokyo)
On the potential automorphy and the local-global compatibility for the monodromy operators at p ≠ l over CM fields. (日本語)
Kojiro Matsumoto (University of Tokyo)
On the potential automorphy and the local-global compatibility for the monodromy operators at p ≠ l over CM fields. (日本語)
[ Abstract ]
Let F be a totally real field or CM field, n be a positive integer, l be a prime, π be a cohomological cuspidal automorphic representation of GLn over F and v be a non-l-adic finite place of F. In 2014, Harris-Lan-Taylor-Thorne constructed the l-adic Galois representation corresponding to π. (Scholze also constructed this by another method.) The compatibility of this construction and the local Langlands correspondence at v was proved up to semisimplification by Ila Varma(2014), but the compatibility for the monodromy operators was known only in conjugate self-dual cases and some special 2-dimensional cases. In this talk, we will prove the local-global compatibility in some self-dual cases and sufficiently regular weight cases by using some new potential automorphy theorems. Moreover, if we have time, we will also prove the Ramanujan conjecture for the cohomological cuspidal automorphic representations of GL2 over F, which was proved in parallel weight cases by Boxer-Calegari-Gee-Newton-Thorne (2023).
Let F be a totally real field or CM field, n be a positive integer, l be a prime, π be a cohomological cuspidal automorphic representation of GLn over F and v be a non-l-adic finite place of F. In 2014, Harris-Lan-Taylor-Thorne constructed the l-adic Galois representation corresponding to π. (Scholze also constructed this by another method.) The compatibility of this construction and the local Langlands correspondence at v was proved up to semisimplification by Ila Varma(2014), but the compatibility for the monodromy operators was known only in conjugate self-dual cases and some special 2-dimensional cases. In this talk, we will prove the local-global compatibility in some self-dual cases and sufficiently regular weight cases by using some new potential automorphy theorems. Moreover, if we have time, we will also prove the Ramanujan conjecture for the cohomological cuspidal automorphic representations of GL2 over F, which was proved in parallel weight cases by Boxer-Calegari-Gee-Newton-Thorne (2023).
Discrete mathematical modelling seminar
13:00-15:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Jaume Alonso (Technische Universität Berlin)
Semitoric systems and their symplectic invariants (English)
Jaume Alonso (Technische Universität Berlin)
Semitoric systems and their symplectic invariants (English)
[ Abstract ]
Semitoric systems are a special class of completely integrable systems defined on four-dimensional symplectic manifolds. One of the reasons that make these systems interesting is their classification in terms of five symplectic invariants proposed by Pelayo and Vũ Ngọc. In the last years, many efforts have been made in order to extend this classification to broader settings, to generate more examples and to compute their invariants. In this talk we will discuss some of the most important properties of semitoric systems and introduce some families of systems with one and more focus-focus singularities. We will also show how the symplectic invariants of these systems change as we move the parameters of the families and how they can be computed using mathematical software.
This is a joint work with H. Dullin, S. Hohloch and J. Palmer.
Semitoric systems are a special class of completely integrable systems defined on four-dimensional symplectic manifolds. One of the reasons that make these systems interesting is their classification in terms of five symplectic invariants proposed by Pelayo and Vũ Ngọc. In the last years, many efforts have been made in order to extend this classification to broader settings, to generate more examples and to compute their invariants. In this talk we will discuss some of the most important properties of semitoric systems and introduce some families of systems with one and more focus-focus singularities. We will also show how the symplectic invariants of these systems change as we move the parameters of the families and how they can be computed using mathematical software.
This is a joint work with H. Dullin, S. Hohloch and J. Palmer.
2024/05/07
Tuesday Seminar on Topology
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Ingrid Irmer (Southern University of Science and Technology)
The Thurston spine and the Systole function of Teichmüller space (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Ingrid Irmer (Southern University of Science and Technology)
The Thurston spine and the Systole function of Teichmüller space (ENGLISH)
[ Abstract ]
The systole function $f_{sys}$ on Teichm\"uller space $\mathcal{T}_{g}$ of a closed genus $g$ surface is a piecewise-smooth map $\mathcal{T}_{g}\rightarrow \mathbb{R}$ whose value at any point is the length of the shortest geodesic on the corresponding hyperbolic surface. It is known that $f_{sys}$ gives a mapping class group-equivariant handle decomposition of $\mathcal{T}_{g}$ via an analogue of Morse Theory. This talk explains the relationship between this handle decomposition and the Thurston spine of $\mathcal{T}_{g}$.
[ Reference URL ]The systole function $f_{sys}$ on Teichm\"uller space $\mathcal{T}_{g}$ of a closed genus $g$ surface is a piecewise-smooth map $\mathcal{T}_{g}\rightarrow \mathbb{R}$ whose value at any point is the length of the shortest geodesic on the corresponding hyperbolic surface. It is known that $f_{sys}$ gives a mapping class group-equivariant handle decomposition of $\mathcal{T}_{g}$ via an analogue of Morse Theory. This talk explains the relationship between this handle decomposition and the Thurston spine of $\mathcal{T}_{g}$.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/05/08
Number Theory Seminar
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Xinyao Zhang (University of Tokyo)
The pro-modularity in the residually reducible case (English)
Xinyao Zhang (University of Tokyo)
The pro-modularity in the residually reducible case (English)
[ Abstract ]
For a continuous odd two dimensional Galois representation over a finite field of characteristic p, it is conjectured that its universal deformation ring is isomorphic to some p-adic big Hecke algebra, called the big R=T theorem. Recently, Deo explored the residually reducible case and proved a big R=T theorem for Q under the assumption of the cyclicity of some cohomology group. However, his method is unavailable for totally real fields since the assumption does not hold any longer. In this talk, we follow the strategy of the work from Skinner-Wiles and Pan on the Fontaine-Mazur conjecture and give a pro-modularity result for some totally real fields, which is an analogue to the big R=T theorem.
For a continuous odd two dimensional Galois representation over a finite field of characteristic p, it is conjectured that its universal deformation ring is isomorphic to some p-adic big Hecke algebra, called the big R=T theorem. Recently, Deo explored the residually reducible case and proved a big R=T theorem for Q under the assumption of the cyclicity of some cohomology group. However, his method is unavailable for totally real fields since the assumption does not hold any longer. In this talk, we follow the strategy of the work from Skinner-Wiles and Pan on the Fontaine-Mazur conjecture and give a pro-modularity result for some totally real fields, which is an analogue to the big R=T theorem.
2024/05/13
Tokyo Probability Seminar
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Shuwen Lou (University of Illinois)
TBD
Shuwen Lou (University of Illinois)
TBD
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yu Kawakami (Kanazawa Univ.)
(Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Yu Kawakami (Kanazawa Univ.)
(Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/05/14
Tuesday Seminar of Analysis
16:00-17:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Heinz Siedentop (LMU University of Munich)
The Energy of Heavy Atoms: Density Functionals (English)
https://forms.gle/ZEyVso6wa9QpNfxH7
Heinz Siedentop (LMU University of Munich)
The Energy of Heavy Atoms: Density Functionals (English)
[ Abstract ]
Since computing the energy of a system with $N$ particles requires solving a $4^N$ dimensional system of (pseudo-)differential equations in $3N$ independent variables, an analytic solution is practically impossible. Therefore density functionals, i.e., functionals that depend on the particle density (3 variables) only and yield the energy upon minimization, are of great interest.
This concept has been applied successfully in non-relativistic quantum mechanics. However, in relativistic quantum mechanics even the simple analogue of the Thomas-Fermi functional is not bounded from below for Coulomb potential. This problem was addressed eventually by Engel and Dreizler who derived a functional from QED. I will review some known mathematical properties of this functional and show that it yields basic features of physics, such as asymptotic correct energy, stability of matter, and boundedness of the excess charge.
[ Reference URL ]Since computing the energy of a system with $N$ particles requires solving a $4^N$ dimensional system of (pseudo-)differential equations in $3N$ independent variables, an analytic solution is practically impossible. Therefore density functionals, i.e., functionals that depend on the particle density (3 variables) only and yield the energy upon minimization, are of great interest.
This concept has been applied successfully in non-relativistic quantum mechanics. However, in relativistic quantum mechanics even the simple analogue of the Thomas-Fermi functional is not bounded from below for Coulomb potential. This problem was addressed eventually by Engel and Dreizler who derived a functional from QED. I will review some known mathematical properties of this functional and show that it yields basic features of physics, such as asymptotic correct energy, stability of matter, and boundedness of the excess charge.
https://forms.gle/ZEyVso6wa9QpNfxH7
Tuesday Seminar of Analysis
17:15-18:15 Room #128 (Graduate School of Math. Sci. Bldg.)
Robert Laister (University of the West of England)
Well-posedness for Semilinear Heat Equations in Orlicz Spaces (English)
https://forms.gle/ZEyVso6wa9QpNfxH7
Robert Laister (University of the West of England)
Well-posedness for Semilinear Heat Equations in Orlicz Spaces (English)
[ Abstract ]
We consider the local well-posedness of semilinear heat equations in Orlicz spaces, the latter prescribed via a Young function $\Phi$. Many existence-uniqueness results exist in the literature for power-like or exponential-like nonlinearities $f$, where the natural setting is an Orlicz space of corresponding type; i.e. if $f$ is power-like then $\Phi$ is power-like (Lebesgue space), if $f$ is exponential-like then $\Phi$ is exponential-like. However, the general problem of prescribing a suitable $\Phi$ for a given, otherwise arbitrary $f$ is open. Our goal is to provide a suitable framework to resolve this problem and I will present some recent results in this direction. The key is a new (to the best of our knowledge) smoothing estimate for the heat semigroup between two arbitrary Orlicz spaces. Existence then follows familiar lines via monotonicity or contraction mapping arguments. Global solutions are also presented under additional assumptions. This work is part of a collaborative project with Prof Kazuhiro Ishige, Dr Yohei Fujishima and Dr Kotaro Hisa.
[ Reference URL ]We consider the local well-posedness of semilinear heat equations in Orlicz spaces, the latter prescribed via a Young function $\Phi$. Many existence-uniqueness results exist in the literature for power-like or exponential-like nonlinearities $f$, where the natural setting is an Orlicz space of corresponding type; i.e. if $f$ is power-like then $\Phi$ is power-like (Lebesgue space), if $f$ is exponential-like then $\Phi$ is exponential-like. However, the general problem of prescribing a suitable $\Phi$ for a given, otherwise arbitrary $f$ is open. Our goal is to provide a suitable framework to resolve this problem and I will present some recent results in this direction. The key is a new (to the best of our knowledge) smoothing estimate for the heat semigroup between two arbitrary Orlicz spaces. Existence then follows familiar lines via monotonicity or contraction mapping arguments. Global solutions are also presented under additional assumptions. This work is part of a collaborative project with Prof Kazuhiro Ishige, Dr Yohei Fujishima and Dr Kotaro Hisa.
https://forms.gle/ZEyVso6wa9QpNfxH7
2024/05/15
Numerical Analysis Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Koya Sakakibara (Kanazawa University)
TBA (Japanese)
[ Reference URL ]
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Koya Sakakibara (Kanazawa University)
TBA (Japanese)
[ Reference URL ]
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
2024/05/20
Seminar on Geometric Complex Analysis
10:50-12:20 Room #128 (Graduate School of Math. Sci. Bldg.)
Lijie Sun (Yamaguchi Univ.)
Kähler metrics in the Siegel domain (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
Lijie Sun (Yamaguchi Univ.)
Kähler metrics in the Siegel domain (Japanese)
[ Abstract ]
The Siegel domain is endowed with an intrinsic Kähler structure, making it an exemplary model for the complex hyperbolic plane. Its boundary, characterized as the one-point compactification of the Heisenberg group, plays an important role in studying the geometry of the Siegel domain. In this talk, using the CR structure of the Heisenberg group we introduce a variety of Kähler structures within the Siegel domain. We conclude by demonstrating that all these metrics are PCR-Kähler equivalent, that is, essentially the same when confined to the CR structure. This talk is based on a joint work with Ioannis Platis and Joonhyung Kim.
[ Reference URL ]The Siegel domain is endowed with an intrinsic Kähler structure, making it an exemplary model for the complex hyperbolic plane. Its boundary, characterized as the one-point compactification of the Heisenberg group, plays an important role in studying the geometry of the Siegel domain. In this talk, using the CR structure of the Heisenberg group we introduce a variety of Kähler structures within the Siegel domain. We conclude by demonstrating that all these metrics are PCR-Kähler equivalent, that is, essentially the same when confined to the CR structure. This talk is based on a joint work with Ioannis Platis and Joonhyung Kim.
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/05/27
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Taiji Marugame (The Univ. of Electro-Communications)
TBA (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
Taiji Marugame (The Univ. of Electro-Communications)
TBA (Japanese)
[ Abstract ]
TBA
[ Reference URL ]TBA
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/05/29
Numerical Analysis Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Satoshi Hayakawa (Sony Group Corporation)
Random convex hulls and kernel quadrature (Japanese)
[ Reference URL ]
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
Satoshi Hayakawa (Sony Group Corporation)
Random convex hulls and kernel quadrature (Japanese)
[ Reference URL ]
https://sites.google.com/g.ecc.u-tokyo.ac.jp/utnas-bulletin-board/
