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Seminar information archive
Seminar information archive ～12/08｜Today's seminar 12/09 | Future seminars 12/10～
2024/05/14
Tuesday Seminar of Analysis
16:00-18:15 Room #128 (Graduate School of Math. Sci. Bldg.)
Heinz Siedentop (LMU University of Munich) 16:00-17:00
The Energy of Heavy Atoms: Density Functionals (English)
https://forms.gle/ZEyVso6wa9QpNfxH7
Robert Laister (University of the West of England) 17:15-18:15
Well-posedness for Semilinear Heat Equations in Orlicz Spaces (English)
https://forms.gle/ZEyVso6wa9QpNfxH7
Heinz Siedentop (LMU University of Munich) 16:00-17:00
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
Robert Laister (University of the West of England) 17:15-18:15
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
Tuesday Seminar on Topology
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Noriyuki Hamada (Institute of Mathematics for Industry, Kyushu University)
Exotic 4-manifolds with signature zero (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Noriyuki Hamada (Institute of Mathematics for Industry, Kyushu University)
Exotic 4-manifolds with signature zero (JAPANESE)
[ Abstract ]
We will talk about our novel examples of symplectic 4-manifolds, which are homeomorphic but not diffeomorphic to the standard simply-connected closed 4-manifolds with signature zero. In particular, they provide such examples with the smallest Euler characteristics known to date. Our method employs the time-honored approach of reverse-engineering, while the key new ingredients are the model manifolds that we build from scratch as Lefschetz fibrations. Notably, our method greatly simplifies pi_1 calculations, typically the most intricate aspect in existing literature.
This is joint work with Inanc Baykur (University of Massachusetts Amherst).
[ Reference URL ]We will talk about our novel examples of symplectic 4-manifolds, which are homeomorphic but not diffeomorphic to the standard simply-connected closed 4-manifolds with signature zero. In particular, they provide such examples with the smallest Euler characteristics known to date. Our method employs the time-honored approach of reverse-engineering, while the key new ingredients are the model manifolds that we build from scratch as Lefschetz fibrations. Notably, our method greatly simplifies pi_1 calculations, typically the most intricate aspect in existing literature.
This is joint work with Inanc Baykur (University of Massachusetts Amherst).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Operator Algebra Seminars
16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
Ziyun Xu (Univ. Tokyo)
Completely rational conformal nets and modular tensor categories
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Ziyun Xu (Univ. Tokyo)
Completely rational conformal nets and modular tensor categories
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
2024/05/13
Tokyo Probability Seminar
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Shuwen Lou (University of Illinois)
Brownian motion with darning and its related open problem (English)
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Shuwen Lou (University of Illinois)
Brownian motion with darning and its related open problem (English)
[ Abstract ]
In this talk, I will discuss some existing results about Brownian motion with darning, including its HKE and discrete approximate by random walks, along with an open problem: What is the relationship between (a) subordinated BM with darning, and (b) the process obtained by darning together two subordinated reflected BM. This is an ongoing collaboration with Zhen-Qing Chen.
In this talk, I will discuss some existing results about Brownian motion with darning, including its HKE and discrete approximate by random walks, along with an open problem: What is the relationship between (a) subordinated BM with darning, and (b) the process obtained by darning together two subordinated reflected BM. This is an ongoing collaboration with Zhen-Qing Chen.
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
2024/05/08
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.
2024/05/07
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
Operator Algebra Seminars
16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
Kohki Sakamoto (Univ. Tokyo)
Harmonic measures in percolation clusters on hyperbolic groups
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Kohki Sakamoto (Univ. Tokyo)
Harmonic measures in percolation clusters on hyperbolic groups
[ 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.
2024/04/30
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
2024/04/26
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.
2024/04/24
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.
2024/04/23
Tuesday Seminar on Topology
17:00-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Tatsumasa Suzuki (Meiji University)
Pochette surgery on 4-manifolds and the Ozsváth--Szabó $d$-invariants of Brieskorn homology 3-spheres (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Tatsumasa Suzuki (Meiji University)
Pochette surgery on 4-manifolds and the Ozsváth--Szabó $d$-invariants of Brieskorn homology 3-spheres (JAPANESE)
[ Abstract ]
This talk consists of the following two research contents:
I. The boundary sum of $S^1 \times D^3$ and $D^2 \times S^2$ is called a pochette. The pochette surgery, which is a generalization of Gluck surgery and a special case of torus surgery, was discovered by Zjuñici Iwase and Yukio Matsumoto in 2004. For a pochette $P$ embedded in a 4-manifold $X$, a pochette surgery on $X$ is the operation of removing the interior of $P$ and gluing $P$ by a diffeomorphism of the boundary of $P$. In this talk, we focus on the fact that pochette surgery is a surgery with a cord and the 2-sphere $S^2$, and attempt to classify the diffeomorphism type of pochette surgery on the 4-sphere $S^4$.
II. In 2003, Peter Ozsváth and Zoltán Szabó introduced a homology cobordism invariant for homology 3-spheres called a $d$-invariant. In this talk, we present new computable examples by refining the Karakurt--Şavk formula for any Brieskorn homology 3-sphere $\Sigma(p,q,r)$ with $p$ is odd and $pq+pr-qr=1$. Furthermore, by refining the Can--Karakurt formula for the $d$-invariant of any $\Sigma(p,q,r)$, we also introduce the relationship with the $d$-invariant of $\Sigma(p,q,r)$ and those of lens spaces.
This talk includes contents of joint work with Motoo Tange (University of Tsukuba).
[ Reference URL ]This talk consists of the following two research contents:
I. The boundary sum of $S^1 \times D^3$ and $D^2 \times S^2$ is called a pochette. The pochette surgery, which is a generalization of Gluck surgery and a special case of torus surgery, was discovered by Zjuñici Iwase and Yukio Matsumoto in 2004. For a pochette $P$ embedded in a 4-manifold $X$, a pochette surgery on $X$ is the operation of removing the interior of $P$ and gluing $P$ by a diffeomorphism of the boundary of $P$. In this talk, we focus on the fact that pochette surgery is a surgery with a cord and the 2-sphere $S^2$, and attempt to classify the diffeomorphism type of pochette surgery on the 4-sphere $S^4$.
II. In 2003, Peter Ozsváth and Zoltán Szabó introduced a homology cobordism invariant for homology 3-spheres called a $d$-invariant. In this talk, we present new computable examples by refining the Karakurt--Şavk formula for any Brieskorn homology 3-sphere $\Sigma(p,q,r)$ with $p$ is odd and $pq+pr-qr=1$. Furthermore, by refining the Can--Karakurt formula for the $d$-invariant of any $\Sigma(p,q,r)$, we also introduce the relationship with the $d$-invariant of $\Sigma(p,q,r)$ and those of lens spaces.
This talk includes contents of joint work with Motoo Tange (University of Tsukuba).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2024/04/22
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Takayuki Koike (Osaka Metropolitan Univ.)
Neighborhood of a compact curve whose intersection matrix has a positive eigenvalue (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Takayuki Koike (Osaka Metropolitan Univ.)
Neighborhood of a compact curve whose intersection matrix has a positive eigenvalue (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/04/17
Number Theory Seminar
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Ahmed Abbes (Institut des Hautes Études Scientifiques, University of Tokyo)
Functoriality of the p-adic Simpson correspondence by proper push forward (English)
Ahmed Abbes (Institut des Hautes Études Scientifiques, University of Tokyo)
Functoriality of the p-adic Simpson correspondence by proper push forward (English)
[ Abstract ]
Faltings initiated in 2005 a p-adic analogue of the (complex) Simpson correspondence whose construction has been taken up by various authors, according to several approaches. After recalling the one initiated by myself with Michel Gros, I will present our initial result on the functoriality of the p-adic Simpson correspondence by proper push forward, leading to a generalization of the relative Hodge-Tate spectral sequence. If time permits, I will give a brief overview of an ongoing project with Michel Gros and Takeshi Tsuji, aimed at establishing a more robust framework for achieving broader functoriality results of the p-adic Simpson correspondence, by both proper push forward and pullback.
Faltings initiated in 2005 a p-adic analogue of the (complex) Simpson correspondence whose construction has been taken up by various authors, according to several approaches. After recalling the one initiated by myself with Michel Gros, I will present our initial result on the functoriality of the p-adic Simpson correspondence by proper push forward, leading to a generalization of the relative Hodge-Tate spectral sequence. If time permits, I will give a brief overview of an ongoing project with Michel Gros and Takeshi Tsuji, aimed at establishing a more robust framework for achieving broader functoriality results of the p-adic Simpson correspondence, by both proper push forward and pullback.
Discrete mathematical modelling seminar
13:30-15:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Jaume Alonso (Technische Universität Berlin)
Discrete Painlevé equations and pencils of quadrics in 3D (English)
Jaume Alonso (Technische Universität Berlin)
Discrete Painlevé equations and pencils of quadrics in 3D (English)
[ Abstract ]
In this talk we propose a new geometric interpretation of discrete Painlevé equations. From this point of view, the equations are birational transformations of $\mathbb{P}^3$ that preserve a pencil of quadrics and map each quadric of the pencil to a different one, according to a Möbius transformation of the pencil parameter. This allows for a classification of discrete Painlevé equations based on the classification of pencils of quadrics in $\mathbb{P}^3$. In this scheme, discrete Painlevé equations are obtained as deformations of the 3D QRT maps introduced in the previous talk, which consist of the composition of two involutions along the generators of the quadrics of a pencil of quadrics until they meet a second pencil. The deformation is then a birational (often linear) transformation in $\mathbb{P}^3$ under which the pencil remains invariant, but the individual quadrics do not.
This is a joint work with Yuri Suris and Kangning Wei.
In this talk we propose a new geometric interpretation of discrete Painlevé equations. From this point of view, the equations are birational transformations of $\mathbb{P}^3$ that preserve a pencil of quadrics and map each quadric of the pencil to a different one, according to a Möbius transformation of the pencil parameter. This allows for a classification of discrete Painlevé equations based on the classification of pencils of quadrics in $\mathbb{P}^3$. In this scheme, discrete Painlevé equations are obtained as deformations of the 3D QRT maps introduced in the previous talk, which consist of the composition of two involutions along the generators of the quadrics of a pencil of quadrics until they meet a second pencil. The deformation is then a birational (often linear) transformation in $\mathbb{P}^3$ under which the pencil remains invariant, but the individual quadrics do not.
This is a joint work with Yuri Suris and Kangning Wei.
2024/04/16
Tuesday Seminar on Topology
17:00-18:00 Online
Pre-registration required. See our seminar webpage.
Hiroaki Karuo (Gakushuin University)
Skein algebras and quantum tori in view of pants decompositions (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Hiroaki Karuo (Gakushuin University)
Skein algebras and quantum tori in view of pants decompositions (JAPANESE)
[ Abstract ]
To understand the algebraic structures of skein algebras and their generalizations, we usually try to embed these algebras into quantum tori using ideal triangulations of a surface and the splitting map. However, such a construction does not work for the skein algebras of closed surfaces and the Roger--Yang skein algebras of punctured surfaces.
In the talk, we define filtrations on these algebras using pants decompositions and embed the associated graded algebras into quantum tori. As a consequence, Roger--Yang skein algebras are quantizations of decorated Teichmuller spaces. This talk is based on a joint work with Wade Bloomquist (Morningside University) and Thang Le (Georgia Institute of Technology).
[ Reference URL ]To understand the algebraic structures of skein algebras and their generalizations, we usually try to embed these algebras into quantum tori using ideal triangulations of a surface and the splitting map. However, such a construction does not work for the skein algebras of closed surfaces and the Roger--Yang skein algebras of punctured surfaces.
In the talk, we define filtrations on these algebras using pants decompositions and embed the associated graded algebras into quantum tori. As a consequence, Roger--Yang skein algebras are quantizations of decorated Teichmuller spaces. This talk is based on a joint work with Wade Bloomquist (Morningside University) and Thang Le (Georgia Institute of Technology).
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Operator Algebra Seminars
16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
Jean Roydor (Sorbonne Université)
Perturbations of von Neumann algebras
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Jean Roydor (Sorbonne Université)
Perturbations of von Neumann algebras
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
2024/04/15
Tokyo Probability Seminar
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Tomohiro Aya (Kyoto University)
Quantitative stochastic homogenization of elliptic equations with unbounded coefficients (日本語)
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Tomohiro Aya (Kyoto University)
Quantitative stochastic homogenization of elliptic equations with unbounded coefficients (日本語)
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yuya Takeuchi (Tsukuba Univ.)
Kohn-Rossi cohomology of spherical CR manifolds (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Yuya Takeuchi (Tsukuba Univ.)
Kohn-Rossi cohomology of spherical CR manifolds (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/04/11
Applied Analysis
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Jan Haskovec (KAUST, Saudi Arabia)
Non-Markovian models of collective motion (English)
https://forms.gle/5cZ4WzqBjhsXrxgU6
Jan Haskovec (KAUST, Saudi Arabia)
Non-Markovian models of collective motion (English)
[ Abstract ]
I will give an overview of recent results for models of collective behavior governed by functional differential equations with non-Markovian structure. The talk will focus on models of interacting agents with applications in biology (flocking, swarming), social sciences (opinion formation) and engineering (swarm robotics), where latency (delay) plays a significant role. I will characterize two main sources of delay - inter-agent communications ("transmission delay") and information processing ("reaction delay") - and discuss their impacts on the group dynamics. I will give an overview of analytical methods for studying the asymptotic behavior of the models in question and their mean-field limits. In particular, I will show that the transmission vs. reaction delay leads to fundamentally different mathematical structures and requires appropriate choice of analytical tools. Finally, motivated by situations where finite speed of information propagation is significant, I will introduce an interesting class of problems where the delay depends nontrivially and nonlinearly on the state of the system, and discuss the available analytical results and open problems here.
[ Reference URL ]I will give an overview of recent results for models of collective behavior governed by functional differential equations with non-Markovian structure. The talk will focus on models of interacting agents with applications in biology (flocking, swarming), social sciences (opinion formation) and engineering (swarm robotics), where latency (delay) plays a significant role. I will characterize two main sources of delay - inter-agent communications ("transmission delay") and information processing ("reaction delay") - and discuss their impacts on the group dynamics. I will give an overview of analytical methods for studying the asymptotic behavior of the models in question and their mean-field limits. In particular, I will show that the transmission vs. reaction delay leads to fundamentally different mathematical structures and requires appropriate choice of analytical tools. Finally, motivated by situations where finite speed of information propagation is significant, I will introduce an interesting class of problems where the delay depends nontrivially and nonlinearly on the state of the system, and discuss the available analytical results and open problems here.
https://forms.gle/5cZ4WzqBjhsXrxgU6
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