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Seminar information archive
Seminar information archive ～12/24｜Today's seminar 12/25 | Future seminars 12/26～
thesis presentations
11:00-12:15 Room #126 (Graduate School of Math. Sci. Bldg.)
BABA Tomoya (Graduate School of Mathematical Sciences University of Tokyo)
Log-rank test with nonparametric matching
(ノンパラメトリックなマッチングを用いたログランク検定）
BABA Tomoya (Graduate School of Mathematical Sciences University of Tokyo)
Log-rank test with nonparametric matching
(ノンパラメトリックなマッチングを用いたログランク検定）
thesis presentations
13:00-14:15 Room #126 (Graduate School of Math. Sci. Bldg.)
KURISAKI Masahiro (Graduate School of Mathematical Sciences University of Tokyo)
A New Proof for the Linear Filtering and Smoothing Equations, and Asymptotic Expansion of Nonlinear Filtering
(線形フィルタリングおよび平滑化方程式の新たな証明と、非線形フィルターの漸近展開)
KURISAKI Masahiro (Graduate School of Mathematical Sciences University of Tokyo)
A New Proof for the Linear Filtering and Smoothing Equations, and Asymptotic Expansion of Nonlinear Filtering
(線形フィルタリングおよび平滑化方程式の新たな証明と、非線形フィルターの漸近展開)
thesis presentations
14:45-16:00 Room #126 (Graduate School of Math. Sci. Bldg.)
SAKUMA Masaki (Graduate School of Mathematical Sciences University of Tokyo)
Extensions of the concentration compactness principle and their applications to critical p-fractional Choquard-type equations
(凝集コンパクト性原理の拡張と臨界p-非整数階Choquard 型方程式への応用)
SAKUMA Masaki (Graduate School of Mathematical Sciences University of Tokyo)
Extensions of the concentration compactness principle and their applications to critical p-fractional Choquard-type equations
(凝集コンパクト性原理の拡張と臨界p-非整数階Choquard 型方程式への応用)
thesis presentations
11:00-12:15 Room #128 (Graduate School of Math. Sci. Bldg.)
SAITO Yuta (Graduate School of Mathematical Sciences University of Tokyo)
Lubin-Tate (φ, Γ)-modules and generalization of their coefficient rings
(Lubin-Tate (φ, Γ) 加群とその係数環の一般化）
SAITO Yuta (Graduate School of Mathematical Sciences University of Tokyo)
Lubin-Tate (φ, Γ)-modules and generalization of their coefficient rings
(Lubin-Tate (φ, Γ) 加群とその係数環の一般化）
thesis presentations
13:00-14:15 Room #128 (Graduate School of Math. Sci. Bldg.)
BANDO Katsuyuki (Graduate School of Mathematical Sciences University of Tokyo)
Derived Satake category and Affine Hecke category in mixed characteristics
(混標数の導来佐武圏とアファインヘッケ圏）
BANDO Katsuyuki (Graduate School of Mathematical Sciences University of Tokyo)
Derived Satake category and Affine Hecke category in mixed characteristics
(混標数の導来佐武圏とアファインヘッケ圏）
thesis presentations
14:45-16:00 Room #128 (Graduate School of Math. Sci. Bldg.)
WANG PEIDUO (Graduate School of Mathematical Sciences University of Tokyo)
On generalized Fuchs theorem over relative p-adic polyannuli
(p進相対多重穴あき円板上の一般化フックス定理について）
WANG PEIDUO (Graduate School of Mathematical Sciences University of Tokyo)
On generalized Fuchs theorem over relative p-adic polyannuli
(p進相対多重穴あき円板上の一般化フックス定理について）
2025/01/23
thesis presentations
13:00-14:15 Room #118 (Graduate School of Math. Sci. Bldg.)
MATSUDA Koji (Graduate School of Mathematical Sciences University of Tokyo)
Rational points and Brauer–Manin obstruction on Shimura varieties classifying abelian varieties with quaternionic multiplication
(四元数乗法を持つアーベル多様体を分類する志村多様体の有理点とブラウアー-マニン障害)
MATSUDA Koji (Graduate School of Mathematical Sciences University of Tokyo)
Rational points and Brauer–Manin obstruction on Shimura varieties classifying abelian varieties with quaternionic multiplication
(四元数乗法を持つアーベル多様体を分類する志村多様体の有理点とブラウアー-マニン障害)
thesis presentations
14:45-16:00 Room #118 (Graduate School of Math. Sci. Bldg.)
SASAKI Yuya (Graduate School of Mathematical Sciences University of Tokyo)
On naturality of automorphisms of Hilbert schemes of points of some simple abelian varieties
(単純アーベル多様体の点のヒルベルトスキームの自己同型の自然性について)
SASAKI Yuya (Graduate School of Mathematical Sciences University of Tokyo)
On naturality of automorphisms of Hilbert schemes of points of some simple abelian varieties
(単純アーベル多様体の点のヒルベルトスキームの自己同型の自然性について)
thesis presentations
13:00-14:15 Room #122 (Graduate School of Math. Sci. Bldg.)
NATORI Masaki (Graduate School of Mathematical Sciences University of Tokyo)
A proof of Bott periodicity via Quot schemes and bulk-edge correspondence
(Quotスキームを用いたBott周期性の別証明とバルクエッジ対応)
NATORI Masaki (Graduate School of Mathematical Sciences University of Tokyo)
A proof of Bott periodicity via Quot schemes and bulk-edge correspondence
(Quotスキームを用いたBott周期性の別証明とバルクエッジ対応)
thesis presentations
14:45-16:00 Room #122 (Graduate School of Math. Sci. Bldg.)
YOSHIOKA Leo (Graduate School of Mathematical Sciences University of Tokyo)
Some non-trivial cycles of the space of long embeddings detected by configuration space integral invariants using g-loop graphs
( g ループグラフを用いた配置空間積分不変量で検出される埋め込みの空間の非自明なサイクルについて)
YOSHIOKA Leo (Graduate School of Mathematical Sciences University of Tokyo)
Some non-trivial cycles of the space of long embeddings detected by configuration space integral invariants using g-loop graphs
( g ループグラフを用いた配置空間積分不変量で検出される埋め込みの空間の非自明なサイクルについて)
thesis presentations
11:00-12:15 Room #126 (Graduate School of Math. Sci. Bldg.)
Liu Peijiang (Graduate School of Mathematical Sciences University of Tokyo)
Weak admissibility of exponentially twisted cohomology associated with some nondegenerate functions
(非退化関数に付随する捻じれコホモロジーの弱許容性について)
Liu Peijiang (Graduate School of Mathematical Sciences University of Tokyo)
Weak admissibility of exponentially twisted cohomology associated with some nondegenerate functions
(非退化関数に付随する捻じれコホモロジーの弱許容性について)
thesis presentations
14:45-16:00 Room #126 (Graduate School of Math. Sci. Bldg.)
MUKOUHARA Miho (Graduate School of Mathematical Sciences University of Tokyo)
On a Galois correspondence for compact group actions on simple C*-algebras
(単純C*環へのコンパクト群作用に対するガロア対応について)
MUKOUHARA Miho (Graduate School of Mathematical Sciences University of Tokyo)
On a Galois correspondence for compact group actions on simple C*-algebras
(単純C*環へのコンパクト群作用に対するガロア対応について)
thesis presentations
11:00-12:15 Room #128 (Graduate School of Math. Sci. Bldg.)
KEN Eitetsu (Graduate School of Mathematical Sciences University of Tokyo)
Games with backtracking options corresponding to the ordinal analysis of PA
(ペアノ算術の順序数解析に対応する、撤回を許したゲーム）
KEN Eitetsu (Graduate School of Mathematical Sciences University of Tokyo)
Games with backtracking options corresponding to the ordinal analysis of PA
(ペアノ算術の順序数解析に対応する、撤回を許したゲーム）
thesis presentations
14:45-16:00 Room #128 (Graduate School of Math. Sci. Bldg.)
YAMAMOTO Yuta (Graduate School of Mathematical Sciences University of Tokyo)
Two-dimensional structure of the duality of values and continuations
(値と継続の双対性の持つ2次元的構造)
YAMAMOTO Yuta (Graduate School of Mathematical Sciences University of Tokyo)
Two-dimensional structure of the duality of values and continuations
(値と継続の双対性の持つ2次元的構造)
thesis presentations
13:00-14:15 Room #126 (Graduate School of Math. Sci. Bldg.)
ISOBE Noboru (Graduate School of Mathematical Sciences University of Tokyo)
Mathematical Analysis for Evolution Equations Arising in Deep Learning Theory
(深層学習理論に現れる発展方程式の数理解析）
ISOBE Noboru (Graduate School of Mathematical Sciences University of Tokyo)
Mathematical Analysis for Evolution Equations Arising in Deep Learning Theory
(深層学習理論に現れる発展方程式の数理解析）
2025/01/22
Algebraic Geometry Seminar
13:30-15:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Hiromu Tanaka (The University of Tokyo)
Liftability and vanishing theorems for Fano threefolds in positive characteristic (日本語)
Hiromu Tanaka (The University of Tokyo)
Liftability and vanishing theorems for Fano threefolds in positive characteristic (日本語)
[ Abstract ]
Smooth Fano threefolds in positive characteristic satisfy Kodaira vanishing and lift to characteristic zero. This is joint work with Tatsuro Kawakami.
Smooth Fano threefolds in positive characteristic satisfy Kodaira vanishing and lift to characteristic zero. This is joint work with Tatsuro Kawakami.
2025/01/21
Tuesday Seminar on Topology
17:00-18:00 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Ryotaro Kosuge (The University of Tokyo)
Rational abelianizations of Chillingworth subgroups of mapping class groups and automorphism groups of free groups (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Ryotaro Kosuge (The University of Tokyo)
Rational abelianizations of Chillingworth subgroups of mapping class groups and automorphism groups of free groups (JAPANESE)
[ Abstract ]
The Chillingworth subgroup of the mapping class group of a surface is defined as the subgroup consisting of elements that preserve nonsingular vector fields up to homotopy. The action of the mapping class group on the set of homotopy classes of nonsingular vector fields is described using the concept of the winding number. By employing a cohomological approach, we extend the notion of the winding number to general manifolds, introducing the definition of the Chillingworth subgroup for both the mapping class group of general manifolds and the automorphism group of a free group. In this work, we determine the rational abelianization of the Chillingworth subgroup of the mapping class group of a surface and, under a certain assumption, also determine the rational abelianization of the Chillingworth subgroup for the automorphism group of a free group.
[ Reference URL ]The Chillingworth subgroup of the mapping class group of a surface is defined as the subgroup consisting of elements that preserve nonsingular vector fields up to homotopy. The action of the mapping class group on the set of homotopy classes of nonsingular vector fields is described using the concept of the winding number. By employing a cohomological approach, we extend the notion of the winding number to general manifolds, introducing the definition of the Chillingworth subgroup for both the mapping class group of general manifolds and the automorphism group of a free group. In this work, we determine the rational abelianization of the Chillingworth subgroup of the mapping class group of a surface and, under a certain assumption, also determine the rational abelianization of the Chillingworth subgroup for the automorphism group of a free group.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2025/01/20
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.
Arka Adhikari (University of Maryland)
Spectral measure for uniform d-regular digraphs
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Arka Adhikari (University of Maryland)
Spectral measure for uniform d-regular digraphs
[ Abstract ]
Consider the matrix $\sfA_\GG$ chosen uniformly at random from the finite
set of all $N$-dimensional matrices of zero main-diagonal and binary entries,
having each row and column of $\sfA_\GG$ sum to $d$.
That is, the adjacency matrix for the uniformly random
$d$-regular simple digraph $\GG$. Fixing $d \ge 3$, it has long been conjectured
that as $N \to \infty$ the corresponding empirical eigenvalue distributions converge
weakly, in probability, to an explicit non-random limit,
given by the Brown measure of the free sum of $d$ Haar unitary operators.
We reduce this conjecture to bounding the decay in $N$ of the probability that
the minimal singular value of the shifted matrix $\sfA(w) = \sfA_\GG - w \sfI$
is very small. While the latter remains a challenging task, the required bound is
comparable to the recently established control on the singularity of $\sfA_\GG$.
The reduction is achieved here by sharp estimates
on the behavior at large $N$, near the real line, of the Green's function (aka resolvent)
of the Hermitization of $\sfA(w)$, which is of independent interest.
Joint w/ A. Dembo
Consider the matrix $\sfA_\GG$ chosen uniformly at random from the finite
set of all $N$-dimensional matrices of zero main-diagonal and binary entries,
having each row and column of $\sfA_\GG$ sum to $d$.
That is, the adjacency matrix for the uniformly random
$d$-regular simple digraph $\GG$. Fixing $d \ge 3$, it has long been conjectured
that as $N \to \infty$ the corresponding empirical eigenvalue distributions converge
weakly, in probability, to an explicit non-random limit,
given by the Brown measure of the free sum of $d$ Haar unitary operators.
We reduce this conjecture to bounding the decay in $N$ of the probability that
the minimal singular value of the shifted matrix $\sfA(w) = \sfA_\GG - w \sfI$
is very small. While the latter remains a challenging task, the required bound is
comparable to the recently established control on the singularity of $\sfA_\GG$.
The reduction is achieved here by sharp estimates
on the behavior at large $N$, near the real line, of the Green's function (aka resolvent)
of the Hermitization of $\sfA(w)$, which is of independent interest.
Joint w/ A. Dembo
2025/01/16
Colloquium
15:30-16:30 Room #大講義室(Large Lecture Room) (Graduate School of Math. Sci. Bldg.)
In order to contact you in case of an outbreak of infections, we appreciate your regitration by following the link in the [Reference URL] field below.
Junkai Chen (National Taiwan University)
On classification of threefolds of general type (English)
https://docs.google.com/forms/d/e/1FAIpQLSfuEUNS92y5dTPoEANkgieuPhmDDQLB_fI4d-GT2p0VkT8KOg/viewform?usp=header
In order to contact you in case of an outbreak of infections, we appreciate your regitration by following the link in the [Reference URL] field below.
Junkai Chen (National Taiwan University)
On classification of threefolds of general type (English)
[ Abstract ]
In higher dimensional algebraic geometry, the following three types of varieties are considered to be the building blocks: Fano varieties, Calabi-Yau varieties, and varieties of general type. In the study of varieties of general type, one usually works on "good models" inside birationally equivalent classes. Minimal models and canonical models are natural choices of good models.
In the first part of the talk, we will try to introduce some aspects of the geography problem for threefolds of general type, which aim to study the distribution of birational invariants of threefolds of general type. In the second part of the talk, we will explore more geometric properties of those threefolds on or near the boundary. Some explicit examples will be described and we will compare various different models explicitly. If time permits, we also try to talk about their moduli spaces from different points of view.
[ Reference URL ]In higher dimensional algebraic geometry, the following three types of varieties are considered to be the building blocks: Fano varieties, Calabi-Yau varieties, and varieties of general type. In the study of varieties of general type, one usually works on "good models" inside birationally equivalent classes. Minimal models and canonical models are natural choices of good models.
In the first part of the talk, we will try to introduce some aspects of the geography problem for threefolds of general type, which aim to study the distribution of birational invariants of threefolds of general type. In the second part of the talk, we will explore more geometric properties of those threefolds on or near the boundary. Some explicit examples will be described and we will compare various different models explicitly. If time permits, we also try to talk about their moduli spaces from different points of view.
https://docs.google.com/forms/d/e/1FAIpQLSfuEUNS92y5dTPoEANkgieuPhmDDQLB_fI4d-GT2p0VkT8KOg/viewform?usp=header
Infinite Analysis Seminar Tokyo
15:30-16:30 Room #オンライン開催 (Graduate School of Math. Sci. Bldg.)
Please make contact to the following address if you want to attend the seminar.
Jean-Emile Bourgine (SIMIS (Shanghai Institute for Mathematics and Interdisciplinary Sciences))
Free field representations of quantum groups and q-deformed W-algebras through cluster algebras (ENGLISH)
Please make contact to the following address if you want to attend the seminar.
Jean-Emile Bourgine (SIMIS (Shanghai Institute for Mathematics and Interdisciplinary Sciences))
Free field representations of quantum groups and q-deformed W-algebras through cluster algebras (ENGLISH)
[ Abstract ]
Following the development of the AGT correspondence, new relations between free field representations of quantum groups and W-algebras were obtained. The simplest one is the homomorphism between the level $(N,0)$ horizontal representation of the quantum toroidal gl(1) algebra and (dressed) q-deformed $W_N$ algebras. In this talk, I will explain how to extend this type of relations to the Wakimoto representations of quantum affine sl(N) algebras using the 'surface defect' deformation of the quantum toroidal sl(N) algebra.
Following the development of the AGT correspondence, new relations between free field representations of quantum groups and W-algebras were obtained. The simplest one is the homomorphism between the level $(N,0)$ horizontal representation of the quantum toroidal gl(1) algebra and (dressed) q-deformed $W_N$ algebras. In this talk, I will explain how to extend this type of relations to the Wakimoto representations of quantum affine sl(N) algebras using the 'surface defect' deformation of the quantum toroidal sl(N) algebra.
2025/01/14
Tuesday Seminar of Analysis
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
SUZUKI Kanako (Ibaraki University)
Existence and stability of discontinuous stationary solutions to reaction-diffusion-ODE systems (Japanese)
https://forms.gle/GtA4bpBuy5cNzsyX8
SUZUKI Kanako (Ibaraki University)
Existence and stability of discontinuous stationary solutions to reaction-diffusion-ODE systems (Japanese)
[ Abstract ]
We consider reaction-diffusion-ODE systems, which consists of a single reaction-diffusion equation coupled with ordinary differential equations. Such systems arise, for example, from modeling of interactions between cellular processes and diffusing growth factors.
Reaction-diffusion-ODE systems in a bounded domain with Neumann boundary condition may have two types of stationary solutions, regular and discontinuous. We can show that all regular stationary solutions are unstable. This implies that reaction-diffusion-ODE systems cannot exhibit spatial patterns, and possible stable stationary solutions must be singular or discontinuous. In this talk, we present sufficient conditions for the existence and stability of discontinuous stationary solutions.
This talk is based on joint works with A. Marciniak-Czochra (Heidelberg University), G. Karch (University of Wroclaw) and S. Cygan (University of Wroclaw).
[ Reference URL ]We consider reaction-diffusion-ODE systems, which consists of a single reaction-diffusion equation coupled with ordinary differential equations. Such systems arise, for example, from modeling of interactions between cellular processes and diffusing growth factors.
Reaction-diffusion-ODE systems in a bounded domain with Neumann boundary condition may have two types of stationary solutions, regular and discontinuous. We can show that all regular stationary solutions are unstable. This implies that reaction-diffusion-ODE systems cannot exhibit spatial patterns, and possible stable stationary solutions must be singular or discontinuous. In this talk, we present sufficient conditions for the existence and stability of discontinuous stationary solutions.
This talk is based on joint works with A. Marciniak-Czochra (Heidelberg University), G. Karch (University of Wroclaw) and S. Cygan (University of Wroclaw).
https://forms.gle/GtA4bpBuy5cNzsyX8
Tuesday Seminar on Topology
17:00-18:00 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Leo Yoshioka (The University of Tokyo)
Some non-trivial cycles of the space of long embeddings detected by configuration space integral invariants using g-loop graphs (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Leo Yoshioka (The University of Tokyo)
Some non-trivial cycles of the space of long embeddings detected by configuration space integral invariants using g-loop graphs (JAPANESE)
[ Abstract ]
In this talk, we give some non-trivial cocycles and cycles of the space of long embeddings R^j --> R^n modulo immersions. First, we construct a cocycle through configuration space integrals with the simplest 2-loop graph cocycle of the Bott-Cattaneo-Rossi graph complex for odd n and j. Then, we give a cycle from a chord diagram on oriented lines, which is associated with the simplest 2-loop hairy graph. We show the non-triviality of this (co)cycle by pairing argument, which is reduced to pairing of graphs with the chord diagram. This construction of cycles and the pairing argument to show the non-triviality is also applied to general 2-loop (co)cycles of top degree. If time permits, we introduce a modified graph complex and configuration space integrals to give more general cocycles. This new graph complex is quasi-isomorphic to both the hairy graph complex and the graph complex introduced in embedding calculus by Arone and Turchin. With these modified cocycles, our pairing argument provides an alternative proof of the non-finite generation of the (j-1)-th rational homotopy group of the space of long j-knots R^j -->R^{j+2}, which Budney-Gabai and Watanabe first established.
[ Reference URL ]In this talk, we give some non-trivial cocycles and cycles of the space of long embeddings R^j --> R^n modulo immersions. First, we construct a cocycle through configuration space integrals with the simplest 2-loop graph cocycle of the Bott-Cattaneo-Rossi graph complex for odd n and j. Then, we give a cycle from a chord diagram on oriented lines, which is associated with the simplest 2-loop hairy graph. We show the non-triviality of this (co)cycle by pairing argument, which is reduced to pairing of graphs with the chord diagram. This construction of cycles and the pairing argument to show the non-triviality is also applied to general 2-loop (co)cycles of top degree. If time permits, we introduce a modified graph complex and configuration space integrals to give more general cocycles. This new graph complex is quasi-isomorphic to both the hairy graph complex and the graph complex introduced in embedding calculus by Arone and Turchin. With these modified cocycles, our pairing argument provides an alternative proof of the non-finite generation of the (j-1)-th rational homotopy group of the space of long j-knots R^j -->R^{j+2}, which Budney-Gabai and Watanabe first established.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
2025/01/06
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yongpan Zou (Univ. of Tokyo)
Positivity of twisted direct image sheaves (English)
https://u-tokyo-ac-jp.zoom.us/j/87229568765
Yongpan Zou (Univ. of Tokyo)
Positivity of twisted direct image sheaves (English)
[ Abstract ]
For a projective surjective morphism $f: X \to Y$ of complex manifolds with connected fibers, let $L$ be a line bundle on $X$. We are interested in the direct image $f_*(K_{X/Y} \otimes L)$. In general, the positivity of the bundle $L$ induces positivity in the direct image sheaves. Specifically, when $L$ is a big and nef line bundle, the vector bundle $f_*(K_{X/Y} \otimes L)$ is big. This is joint work with Y. Watanabe.
[ Reference URL ]For a projective surjective morphism $f: X \to Y$ of complex manifolds with connected fibers, let $L$ be a line bundle on $X$. We are interested in the direct image $f_*(K_{X/Y} \otimes L)$. In general, the positivity of the bundle $L$ induces positivity in the direct image sheaves. Specifically, when $L$ is a big and nef line bundle, the vector bundle $f_*(K_{X/Y} \otimes L)$ is big. This is joint work with Y. Watanabe.
https://u-tokyo-ac-jp.zoom.us/j/87229568765
2024/12/26
Discrete mathematical modelling seminar
15:00-17:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Wookyung KIM (Graduate School of Mathematical Sciences)
Integrable deformation of cluster map associated to finite type Dynkin diagram
Wookyung KIM (Graduate School of Mathematical Sciences)
Integrable deformation of cluster map associated to finite type Dynkin diagram
[ Abstract ]
An integrable deformation of a cluster map is an integrable Poisson map which is composed of a sequence of deformed cluster mutations, namely, parametric birational maps preserving the presymplectic form but destroying the Laurent property, which is a necessary part of the structure of a cluster algebra. However, this does not imply that the deformed map does not arise from a cluster map: one can use so-called Laurentification, which is a lifting of the map into a higher-dimensional space where the Laurent property is recovered, and thus the deformed map can be generated from elements in a cluster algebra. This deformation theory was introduced recently by Hone and Kouloukas, who presented several examples, including deformed integrable cluster maps associated with Dynkin types A_2,A_3 and A_4. In this talk, we will consider the deformation of integrable cluster map corresponding to the general even dimensional case, Dynkin type A_{2N}. If time permits, we will review the deformation of the cluster maps of other finite type cases such as type C and D. This is joint work with Grabowski, Hone and Mase.
An integrable deformation of a cluster map is an integrable Poisson map which is composed of a sequence of deformed cluster mutations, namely, parametric birational maps preserving the presymplectic form but destroying the Laurent property, which is a necessary part of the structure of a cluster algebra. However, this does not imply that the deformed map does not arise from a cluster map: one can use so-called Laurentification, which is a lifting of the map into a higher-dimensional space where the Laurent property is recovered, and thus the deformed map can be generated from elements in a cluster algebra. This deformation theory was introduced recently by Hone and Kouloukas, who presented several examples, including deformed integrable cluster maps associated with Dynkin types A_2,A_3 and A_4. In this talk, we will consider the deformation of integrable cluster map corresponding to the general even dimensional case, Dynkin type A_{2N}. If time permits, we will review the deformation of the cluster maps of other finite type cases such as type C and D. This is joint work with Grabowski, Hone and Mase.
2024/12/24
Tuesday Seminar of Analysis
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
KAKEHI Tomoyuki (University of Tsukuba)
Snapshot problems for the wave equation and for the Euler-Poisson-Darboux equation (Japanese)
https://forms.gle/2otzqXYVD6DqM11S8
KAKEHI Tomoyuki (University of Tsukuba)
Snapshot problems for the wave equation and for the Euler-Poisson-Darboux equation (Japanese)
[ Abstract ]
In this talk, we deal with snapshot problems for the wave equation and for the Euler-Poisson-Darboux equation. For simplicity, let us consider the wave equation $\partial_t^2 u - \Delta u =0$ on $\mathbb{R}^n$ with the condition $u|_{t=t_1} =f_1, \cdots, u|_{t=t_m} =f_m$. It is natural to ask when the above equation has a unique solution. We call the above problem the snapshot problem for the wave equation, and the set of $m$ functions $\{ f_1, \cdots, f_m \}$ the snapshot data. Roughly speaking, one of our main results is as follows.
Theorem. We assume that $m=3$ and $(t_3-t_1)/(t_2 -t_1)$ is irrational and not a Liouville number. In addition, we assume a certain compatibility condition on the snapshot data $\{ f_1, f_2, f_3 \}$. Then the snapshot problem for the wave equation has a unique solution.
We also consider a similar snapshot problem for the Euler-Poisson-Darboux equation. This is a joint work with Jens Christensen, Fulton Gonzalez, and Jue Wang.
[ Reference URL ]In this talk, we deal with snapshot problems for the wave equation and for the Euler-Poisson-Darboux equation. For simplicity, let us consider the wave equation $\partial_t^2 u - \Delta u =0$ on $\mathbb{R}^n$ with the condition $u|_{t=t_1} =f_1, \cdots, u|_{t=t_m} =f_m$. It is natural to ask when the above equation has a unique solution. We call the above problem the snapshot problem for the wave equation, and the set of $m$ functions $\{ f_1, \cdots, f_m \}$ the snapshot data. Roughly speaking, one of our main results is as follows.
Theorem. We assume that $m=3$ and $(t_3-t_1)/(t_2 -t_1)$ is irrational and not a Liouville number. In addition, we assume a certain compatibility condition on the snapshot data $\{ f_1, f_2, f_3 \}$. Then the snapshot problem for the wave equation has a unique solution.
We also consider a similar snapshot problem for the Euler-Poisson-Darboux equation. This is a joint work with Jens Christensen, Fulton Gonzalez, and Jue Wang.
https://forms.gle/2otzqXYVD6DqM11S8
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