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Seminar information archive
Seminar information archive ～05/15｜Today's seminar 05/16 | Future seminars 05/17～
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
2024/12/23
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Junjiro Noguchi (The Univ. of Tokyo)
Hyperbolicity and sections in a ramified cover over abelian varieties
with trace zero (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
Junjiro Noguchi (The Univ. of Tokyo)
Hyperbolicity and sections in a ramified cover over abelian varieties
with trace zero (Japanese)
[ Abstract ]
We discuss a higher dimensional generalization of the Manin-Grauert Theorem ('63/'65) in relation with the function field analogue of Lang's conjecture on the finiteness of rational points in a Kobayashi hyperbolic algebraic variety over a number field. Let $B$ be a possibly open algebraic curve over $\mathbf{C}$, and let $\pi:X \to B$ be a smooth or normal projective fiber space. In '81 I proved such theorems for $\dim \geq 1$, assuming the ampleness of the cotangent bundle $T^*(X_t)$, and in '85 the Kobayashi hyperbolicity of $X_t$ with some boundary condition (BC) (hyperbolic embedding condition relative over $\bar{B}$).
It is interesting to study if (BC) is really necessary or not. If $\dim X_t=1$, (BC) is automatically satisfied, and if $T^*(X_t)$ is ample, (BC) is not necessary; thus in those cases, (BC) is unnecessary. Lately, Xie-Yuan in arXiv '23 obtained such a result without (BC) for $X$ which is a hyperbolic finite cover of an abelian variety $A/B$.
The aim of this talk is to present a simplified treatment of the Xie-Yuan theorem from the viewpoint of Kobayashi hyperbolic geometry. In particular, if the $K/\mathbf{C}$-trace $Tr(A/B)=0$ with $K=\mathbf{C}(B)$, there are only finitely many $X(K)$-points or sections in $X \to B$. In this case, Bartsch-Javanpeykar in arXiv '24 gave another proof based on Parshin's topological rigidity theorem ('90). We will discuss the proof which is based on the Kobayashi hyperbolicity.
[ Reference URL ]We discuss a higher dimensional generalization of the Manin-Grauert Theorem ('63/'65) in relation with the function field analogue of Lang's conjecture on the finiteness of rational points in a Kobayashi hyperbolic algebraic variety over a number field. Let $B$ be a possibly open algebraic curve over $\mathbf{C}$, and let $\pi:X \to B$ be a smooth or normal projective fiber space. In '81 I proved such theorems for $\dim \geq 1$, assuming the ampleness of the cotangent bundle $T^*(X_t)$, and in '85 the Kobayashi hyperbolicity of $X_t$ with some boundary condition (BC) (hyperbolic embedding condition relative over $\bar{B}$).
It is interesting to study if (BC) is really necessary or not. If $\dim X_t=1$, (BC) is automatically satisfied, and if $T^*(X_t)$ is ample, (BC) is not necessary; thus in those cases, (BC) is unnecessary. Lately, Xie-Yuan in arXiv '23 obtained such a result without (BC) for $X$ which is a hyperbolic finite cover of an abelian variety $A/B$.
The aim of this talk is to present a simplified treatment of the Xie-Yuan theorem from the viewpoint of Kobayashi hyperbolic geometry. In particular, if the $K/\mathbf{C}$-trace $Tr(A/B)=0$ with $K=\mathbf{C}(B)$, there are only finitely many $X(K)$-points or sections in $X \to B$. In this case, Bartsch-Javanpeykar in arXiv '24 gave another proof based on Parshin's topological rigidity theorem ('90). We will discuss the proof which is based on the Kobayashi hyperbolicity.
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/12/20
Colloquium
15:30-16:30 Room #大講義室 (Graduate School of Math. Sci. Bldg.)
Hideo Kozono (Waseda University / Tohoku University)
Helmholtz-Weyl decomposition and its application to the magnetohydrodynamic equations (日本語)
https://forms.gle/QNj3fohg3ZRMD8RHA
Hideo Kozono (Waseda University / Tohoku University)
Helmholtz-Weyl decomposition and its application to the magnetohydrodynamic equations (日本語)
[ Abstract ]
We consider the Helmoltz-Weyl decomosition for $L^r$-vector fields in 3D bounded domains with the smooth boundary. The de Rham-Hodge-Kodaira decomposition of the $p$-form on compact Riemannian manifolds are well-known. However, in the general $L^r$-setting, such a decomposition has been relatively recently studied by
Fujiwara-Morimoto. In this talk, we deal with the 3D case and characterize two kinds of the space of harmonic vector fields in terms of the boundary condition where the vector fields are tangential or perpendicular to the boundary. Then it is clarified that the $L^r$-vector field is decomposed as a direct sum into harmonic, rotational and gradient parts. In particular, we bring the structure of the space with vector potentials into focus. As an application, we prove the asymptotic stability of the equilibrium to the magnetoydrodynamic equations associated with the harmonic vector field in the domain with the non-zero second Betti number. This is based on the joint work with Prof. Senjo Shimizu(Kyoto Univ.) and Prof. Taku Yanagisawa(Nara Women Univ.).
[ Reference URL ]We consider the Helmoltz-Weyl decomosition for $L^r$-vector fields in 3D bounded domains with the smooth boundary. The de Rham-Hodge-Kodaira decomposition of the $p$-form on compact Riemannian manifolds are well-known. However, in the general $L^r$-setting, such a decomposition has been relatively recently studied by
Fujiwara-Morimoto. In this talk, we deal with the 3D case and characterize two kinds of the space of harmonic vector fields in terms of the boundary condition where the vector fields are tangential or perpendicular to the boundary. Then it is clarified that the $L^r$-vector field is decomposed as a direct sum into harmonic, rotational and gradient parts. In particular, we bring the structure of the space with vector potentials into focus. As an application, we prove the asymptotic stability of the equilibrium to the magnetoydrodynamic equations associated with the harmonic vector field in the domain with the non-zero second Betti number. This is based on the joint work with Prof. Senjo Shimizu(Kyoto Univ.) and Prof. Taku Yanagisawa(Nara Women Univ.).
https://forms.gle/QNj3fohg3ZRMD8RHA
Algebraic Geometry Seminar
13:30-15:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Makoto Enokizono (University of Tokyo)
Normal stable degenerations of Noether-Horikawa surfaces
Makoto Enokizono (University of Tokyo)
Normal stable degenerations of Noether-Horikawa surfaces
[ Abstract ]
Noether-Horikawa surfaces are surfaces of general type satisfying the equation K2=2pg−4, which represents the boundary of the Noether inequality K2≥2pg−4 for surfaces of general type. In the 1970s, Horikawa conducted a detailed study of smooth Noether-Horikawa surfaces, providing a classification of these surfaces and describing their moduli spaces.
In this talk, I will present an explicit classification of normal stable degenerations of Noether-Horikawa surfaces. Specifically, I will discuss the following results:
(1) A preliminary classification of Noether-Horikawa surfaces with Q-Gorenstein smoothable log canonical singularities.
(2) Several criteria for determining the (global) Q-Gorenstein smoothability of the surfaces described in (1).
(3) Deformation results for Q-Gorenstein smoothable normal stable Noether-Horikawa surfaces, along with a description of the KSBA moduli spaces for these surfaces.
This is joint work with Hiroto Akaike, Masafumi Hattori and Yuki Koto.
Noether-Horikawa surfaces are surfaces of general type satisfying the equation K2=2pg−4, which represents the boundary of the Noether inequality K2≥2pg−4 for surfaces of general type. In the 1970s, Horikawa conducted a detailed study of smooth Noether-Horikawa surfaces, providing a classification of these surfaces and describing their moduli spaces.
In this talk, I will present an explicit classification of normal stable degenerations of Noether-Horikawa surfaces. Specifically, I will discuss the following results:
(1) A preliminary classification of Noether-Horikawa surfaces with Q-Gorenstein smoothable log canonical singularities.
(2) Several criteria for determining the (global) Q-Gorenstein smoothability of the surfaces described in (1).
(3) Deformation results for Q-Gorenstein smoothable normal stable Noether-Horikawa surfaces, along with a description of the KSBA moduli spaces for these surfaces.
This is joint work with Hiroto Akaike, Masafumi Hattori and Yuki Koto.
Tokyo-Nagoya Algebra Seminar
17:00-18:30 Online
Simon Riche (Université Clermont Auvergne)
Semiinfinite sheaves on affine flag varieties (English)
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
Simon Riche (Université Clermont Auvergne)
Semiinfinite sheaves on affine flag varieties (English)
[ Abstract ]
We will explain how, generalizing a construction of Gaitsgory, one can define and study a category of sheaves on the affine flag variety of a complex reductive group that "models" sheaves on the corresponding semiinfinite flag variety, with coefficients in a field of positive characteristic, and which should provide a geometric model for a category of representations of the Langlands dual Lie algebra over the given coefficient field. As an application, we use this construction to compute the dimensions of stalks of the intersection cohomology complex on Drinfeld's compactification, with coefficients in any field of good characteristic. This is joint work with Pramod Achar and Gurbir Dhillon.
ミーティング ID: 882 1561 8969
パスコード: 531394
[ Reference URL ]We will explain how, generalizing a construction of Gaitsgory, one can define and study a category of sheaves on the affine flag variety of a complex reductive group that "models" sheaves on the corresponding semiinfinite flag variety, with coefficients in a field of positive characteristic, and which should provide a geometric model for a category of representations of the Langlands dual Lie algebra over the given coefficient field. As an application, we use this construction to compute the dimensions of stalks of the intersection cohomology complex on Drinfeld's compactification, with coefficients in any field of good characteristic. This is joint work with Pramod Achar and Gurbir Dhillon.
ミーティング ID: 882 1561 8969
パスコード: 531394
https://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html
2024/12/19
Infinite Analysis Seminar Tokyo
14:00-15:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Omar Kidwai (The Chinese University of Hong Kong)
Quadratic differentials and Donaldson-Thomas invariants (English)
Omar Kidwai (The Chinese University of Hong Kong)
Quadratic differentials and Donaldson-Thomas invariants (English)
[ Abstract ]
We recall the relation between quadratic differentials and spaces of stability conditions due to Bridgeland-Smith. We describe the calculation of (refined) Donaldson-Thomas invariants for stability conditions on a certain class of 3-Calabi-Yau triangulated categories studied by Christ-Haiden-Qiu. This category is slightly different from the usual one discussed by Bridgeland and Smith, which in particular allows us to recover a nonzero invariant in the case where the quadratic differential has a second-order pole, in agreement with predictions from the physics literature. Based on joint work with N. Williams.
We recall the relation between quadratic differentials and spaces of stability conditions due to Bridgeland-Smith. We describe the calculation of (refined) Donaldson-Thomas invariants for stability conditions on a certain class of 3-Calabi-Yau triangulated categories studied by Christ-Haiden-Qiu. This category is slightly different from the usual one discussed by Bridgeland and Smith, which in particular allows us to recover a nonzero invariant in the case where the quadratic differential has a second-order pole, in agreement with predictions from the physics literature. Based on joint work with N. Williams.
2024/12/18
Seminar on Mathematics for various disciplines
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
This seminar is held on Wednesday in Room 056 and online.
Amy Novick-Cohen (Technion - Israel Institute of Technology)
Diffusion: Some new results and approaches (English)
https://u-tokyo-ac-jp.zoom.us/j/83306203126?pwd=b92LqeuB5sLUkN2LKu7Mp8SQmoSbAU.1
This seminar is held on Wednesday in Room 056 and online.
Amy Novick-Cohen (Technion - Israel Institute of Technology)
Diffusion: Some new results and approaches (English)
[ Abstract ]
We first briefly review a variety of geometries where surface diffusion is meaningful in the context of the stability of thin solid state films. Afterwards, we discuss joint work with E.A. Carlen & L. Peres Hari (2024), which focuses on rigorously establishing a connection between surface diffusion and the deep quench obstacle problem with a suitable degenerate mobility. Our study begins by rigorously establishing a connection between certain steady states of the respective systems, and then outlines a method for connecting the respective evolutions via minimizing motion descriptions.
Please join the Zoom meeting at the [Reference URL] below.
Meeting ID: 833 0620 3126
Passcode: 223203
[ Reference URL ]We first briefly review a variety of geometries where surface diffusion is meaningful in the context of the stability of thin solid state films. Afterwards, we discuss joint work with E.A. Carlen & L. Peres Hari (2024), which focuses on rigorously establishing a connection between surface diffusion and the deep quench obstacle problem with a suitable degenerate mobility. Our study begins by rigorously establishing a connection between certain steady states of the respective systems, and then outlines a method for connecting the respective evolutions via minimizing motion descriptions.
Please join the Zoom meeting at the [Reference URL] below.
Meeting ID: 833 0620 3126
Passcode: 223203
https://u-tokyo-ac-jp.zoom.us/j/83306203126?pwd=b92LqeuB5sLUkN2LKu7Mp8SQmoSbAU.1
2024/12/17
Tuesday Seminar on Topology
17:00-18:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Emmanuel Graff (The University of Tokyo)
Is there torsion in the homotopy braid group? (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Emmanuel Graff (The University of Tokyo)
Is there torsion in the homotopy braid group? (ENGLISH)
[ Abstract ]
In the 'Kourovka notebook,' V. Lin questions the existence of a non-trivial epimorphism from the braid group onto a non-abelian torsion-free group. The homotopy braid group, studied by Goldsmith in 1974, naturally appears as a potential candidate. In 2001, Humphries showed that this homotopy braid group is torsion-free for less than six strands. In this presentation, we will see a new approach based on the broader concept of welded braids, along with algebraic techniques, to determine whether the homotopy braid group provides a complete answer to Lin’s question.
[ Reference URL ]In the 'Kourovka notebook,' V. Lin questions the existence of a non-trivial epimorphism from the braid group onto a non-abelian torsion-free group. The homotopy braid group, studied by Goldsmith in 1974, naturally appears as a potential candidate. In 2001, Humphries showed that this homotopy braid group is torsion-free for less than six strands. In this presentation, we will see a new approach based on the broader concept of welded braids, along with algebraic techniques, to determine whether the homotopy braid group provides a complete answer to Lin’s question.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Operator Algebra Seminars
16:45-18:15 Room #002 (Graduate School of Math. Sci. Bldg.)
Makoto Yamashita (Univ. Oslo)
Bimodule approach to quantum field theory and categorical structures
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Makoto Yamashita (Univ. Oslo)
Bimodule approach to quantum field theory and categorical structures
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
2024/12/16
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Laurent Stolovitch (Universite Cote d'Azur)
CR singularities and dynamical systems (English)
https://forms.gle/gTP8qNZwPyQyxjTj8
Laurent Stolovitch (Universite Cote d'Azur)
CR singularities and dynamical systems (English)
[ Abstract ]
In this talk, we'll survey some recent results done since the seminal work of Moser and Webster about smooth real analytic surfaces in $C^2$ which are totally real everywhere but at a point where the tangent space is a complex line. Such a point is called a singularity of the Cauchy-Riemann structure. We are interested in the holomorphic classification of these surface near the singularity. It happens that there is a deep connection with holomorphic classification of some holomorphic dynamical systems near a fixed point so that new results for the later provide new result for the former.
[ Reference URL ]In this talk, we'll survey some recent results done since the seminal work of Moser and Webster about smooth real analytic surfaces in $C^2$ which are totally real everywhere but at a point where the tangent space is a complex line. Such a point is called a singularity of the Cauchy-Riemann structure. We are interested in the holomorphic classification of these surface near the singularity. It happens that there is a deep connection with holomorphic classification of some holomorphic dynamical systems near a fixed point so that new results for the later provide new result for the former.
https://forms.gle/gTP8qNZwPyQyxjTj8
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.
Shu Kanazawa (Kyoto University)
Central limit theorem for linear eigenvalue statistics of the adjacency matrices of random simplicial complexes
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Shu Kanazawa (Kyoto University)
Central limit theorem for linear eigenvalue statistics of the adjacency matrices of random simplicial complexes
[ Abstract ]
We consider the (higher-dimensional) adjacency matrix of the Linial-Meshulam complex model, which is a higher-dimensional generalization of the Erdős-Rényi random graph model. Recently, Knowles and Rosenthal proved that the empirical spectral distribution
of the adjacency matrix is asymptotically given by Wigner's semicircle law in a diluted regime. In this talk, I will present a central limit theorem for the linear eigenvalue statistics for test functions of polynomial growth that is of class C2 on a closed
interval. The proof is based on higher-dimensional combinatorial enumerations and concentration properties of random symmetric matrices. Furthermore, when the test function is a polynomial function, we obtain the explicit formula for the variance of the limiting
Gaussian distribution. This is joint work with Khanh Duy Trinh (Waseda University).
We consider the (higher-dimensional) adjacency matrix of the Linial-Meshulam complex model, which is a higher-dimensional generalization of the Erdős-Rényi random graph model. Recently, Knowles and Rosenthal proved that the empirical spectral distribution
of the adjacency matrix is asymptotically given by Wigner's semicircle law in a diluted regime. In this talk, I will present a central limit theorem for the linear eigenvalue statistics for test functions of polynomial growth that is of class C2 on a closed
interval. The proof is based on higher-dimensional combinatorial enumerations and concentration properties of random symmetric matrices. Furthermore, when the test function is a polynomial function, we obtain the explicit formula for the variance of the limiting
Gaussian distribution. This is joint work with Khanh Duy Trinh (Waseda University).
2024/12/12
Algebraic Geometry Seminar
13:30-15:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Chenyang Xu (Princeton University)
Irreducible symplectic varieties with a large second Betti number
Chenyang Xu (Princeton University)
Irreducible symplectic varieties with a large second Betti number
[ Abstract ]
(joint with Yuchen Liu, Zhiyu Liu) We show that the Lagrangian fibration constructed by Iiiev-Manivel using intermediate Jacobians of cubic fivefolds containing a fixed cubic fourfold, admits a compactification as a terminal Q-factorial irreducible symplectic varieties. As far as I know, besides OG10, this is the second family of irreducible symplectic varieties with the second Betti number at least 24.
(joint with Yuchen Liu, Zhiyu Liu) We show that the Lagrangian fibration constructed by Iiiev-Manivel using intermediate Jacobians of cubic fivefolds containing a fixed cubic fourfold, admits a compactification as a terminal Q-factorial irreducible symplectic varieties. As far as I know, besides OG10, this is the second family of irreducible symplectic varieties with the second Betti number at least 24.
2024/12/11
Number Theory Seminar
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Ryosuke Ooe (University of Tokyo)
The characteristic cycle of an l-adic sheaf on a smooth variety (Japanese)
Ryosuke Ooe (University of Tokyo)
The characteristic cycle of an l-adic sheaf on a smooth variety (Japanese)
[ Abstract ]
The characteristic cycle of an l-adic sheaf on a smooth variety over a perfect field is defined by Saito as a cycle on the cotangent bundle and the intersection with the zero section computes the Euler number. On the other hand, the characteristic cycle of an l-adic sheaf on a regular scheme in mixed characteristic is not yet defined. In this talk, I define the F-characteristic cycle of a rank one sheaf on an arithmetic surface whose intersection with the zero section computes the Swan conductor of the cohomology of the generic fiber. The definition is based on the computation of the characteristic cycle in equal characteristic by Yatagawa. I explain the rationality and the integrality of the characteristic form of an abelian character, which are necessary for the definition of the F-characteristic cycle.
The characteristic cycle of an l-adic sheaf on a smooth variety over a perfect field is defined by Saito as a cycle on the cotangent bundle and the intersection with the zero section computes the Euler number. On the other hand, the characteristic cycle of an l-adic sheaf on a regular scheme in mixed characteristic is not yet defined. In this talk, I define the F-characteristic cycle of a rank one sheaf on an arithmetic surface whose intersection with the zero section computes the Swan conductor of the cohomology of the generic fiber. The definition is based on the computation of the characteristic cycle in equal characteristic by Yatagawa. I explain the rationality and the integrality of the characteristic form of an abelian character, which are necessary for the definition of the F-characteristic cycle.
2024/12/10
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.
Shun Wakatsuki (Nagoya University)
Computation of the magnitude homology as a derived functor (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Shun Wakatsuki (Nagoya University)
Computation of the magnitude homology as a derived functor (JAPANESE)
[ Abstract ]
Asao-Ivanov showed that the magnitude homology of a finite metric space is isomorphic to the derived functor Tor over some ring. In this talk, I will explain an application of the theory of minimal projective resolution to this derived functor. Especially in the case of a geodetic graph, torsion-freeness and a criterion for diagonality of the magnitude homology are established. Moreover, I will give computational examples including cyclic graphs. This is a joint work with Yasuhiko Asao.
[ Reference URL ]Asao-Ivanov showed that the magnitude homology of a finite metric space is isomorphic to the derived functor Tor over some ring. In this talk, I will explain an application of the theory of minimal projective resolution to this derived functor. Especially in the case of a geodetic graph, torsion-freeness and a criterion for diagonality of the magnitude homology are established. Moreover, I will give computational examples including cyclic graphs. This is a joint work with Yasuhiko Asao.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Operator Algebra Seminars
15:00-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Yoh Tanimoto (Univ. Rome, "Tor Vergata")
Introduction to Lean theorem prover
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Yoh Tanimoto (Univ. Rome, "Tor Vergata")
Introduction to Lean theorem prover
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Operator Algebra Seminars
16:45-18:15 Room #002 (Graduate School of Math. Sci. Bldg.)
Maria Stella Adamo (FAU Erlangen-Nürnberg)
Osterwalder-Schrader axioms for unitary full VOAs
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
Maria Stella Adamo (FAU Erlangen-Nürnberg)
Osterwalder-Schrader axioms for unitary full VOAs
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm
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