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Colloquium
Seminar information archive ～03/06｜Next seminar｜Future seminars 03/07～
| Organizer(s) | ASUKE Taro, TERADA Itaru, HASEGAWA Ryu, MIYAMOTO Yasuhito (chair) |
|---|---|
| URL | https://www.ms.u-tokyo.ac.jp/seminar/colloquium_e/index_e.html |
Seminar information archive
2025/01/16
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
2024/12/20
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
2024/11/15
15:30-16:30 Room #大講義室 (Graduate School of Math. Sci. Bldg.)
Michael Pevzner (University of Reims / CNRS / The University of Tokyo)
Symmetry breaking for branching problems (ENGLISH)
https://forms.gle/DcsJVYS4fvMLfPEM8
Michael Pevzner (University of Reims / CNRS / The University of Tokyo)
Symmetry breaking for branching problems (ENGLISH)
[ Abstract ]
Restricting a group representation to its subgroups is a fundamental issue in Representation Theory. This process involves exploring how large symmetries can be broken down into smaller symmetries. Known as the branching problem, it provides a unifying framework for various seemingly disparate topics, including fusion rules, Clebsch-Gordan coefficients, Pieri rules for integral partitions, Plancherel-type formulas, Theta correspondence, and more recently, the Gross-Prasad-Gan conjectures.
Beyond analyzing abstract branching rules, constructing explicit operators that implement this symmetry breaking in concrete geometric models of infinite-dimensional representations of real reductive groups is a compelling and challenging problem. This field, located at the intersection of global analysis, Lie Theory, the geometry of homogeneous spaces, and algebraic representation theory, has attracted significant attention over the past decade. We will illustrate these concepts with key examples and provide an overview of the guiding principles that are shaping the emerging theory of symmetry breaking operators, along with original ideas related to holographic transforms and the associated generating operators.
[ Reference URL ]Restricting a group representation to its subgroups is a fundamental issue in Representation Theory. This process involves exploring how large symmetries can be broken down into smaller symmetries. Known as the branching problem, it provides a unifying framework for various seemingly disparate topics, including fusion rules, Clebsch-Gordan coefficients, Pieri rules for integral partitions, Plancherel-type formulas, Theta correspondence, and more recently, the Gross-Prasad-Gan conjectures.
Beyond analyzing abstract branching rules, constructing explicit operators that implement this symmetry breaking in concrete geometric models of infinite-dimensional representations of real reductive groups is a compelling and challenging problem. This field, located at the intersection of global analysis, Lie Theory, the geometry of homogeneous spaces, and algebraic representation theory, has attracted significant attention over the past decade. We will illustrate these concepts with key examples and provide an overview of the guiding principles that are shaping the emerging theory of symmetry breaking operators, along with original ideas related to holographic transforms and the associated generating operators.
https://forms.gle/DcsJVYS4fvMLfPEM8
2024/10/25
15:30-16:30 Room #大講義室(auditorium) (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.
Hokuto Konno (Graduate School of Mathematical Sciences, The University of Tokyo)
Diffeomorphism group and gauge theory (JAPANESE)
https://forms.gle/96tZtBr1GhdHi1tZ9
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.
Hokuto Konno (Graduate School of Mathematical Sciences, The University of Tokyo)
Diffeomorphism group and gauge theory (JAPANESE)
[ Abstract ]
The dimension 4 is special in the classification theory of manifolds, as it exhibits phenomena that occur exclusively in this dimension. It is now well-known that gauge theory, which involves the study of partial differential equations derived from physics on 4-dimensional manifolds, is a powerful tool for discovering and exploring such phenomena. On the other hand, in the topology of manifolds, the diffeomorphism group, which is the automorphism group of a given smooth manifold, is a fundamental object of interest. Even for higher-dimensional manifolds, whose classification was largely settled more than half a century ago, significant progress continues to be made, and this remains a major trend in recent topology. Nevertheless, the systematic study of the diffeomorphism groups of 4-dimensional manifolds, particularly from the perspective of gauge theory, had long remained underexplored, with only a few pioneering results. However, in recent years, there has been rapid progress in the "gauge theory for families", which is the application of gauge theory to families of 4-dimensional manifolds, leading to new insights into the diffeomorphism groups of 4-manifolds. Specifically, it has turned out that, similar to the classification theory of manifolds, the diffeomorphism groups of 4-manifolds exhibit phenomena that are unique to this dimension. In this talk, I will provide an overview of these recent developments.
[ Reference URL ]The dimension 4 is special in the classification theory of manifolds, as it exhibits phenomena that occur exclusively in this dimension. It is now well-known that gauge theory, which involves the study of partial differential equations derived from physics on 4-dimensional manifolds, is a powerful tool for discovering and exploring such phenomena. On the other hand, in the topology of manifolds, the diffeomorphism group, which is the automorphism group of a given smooth manifold, is a fundamental object of interest. Even for higher-dimensional manifolds, whose classification was largely settled more than half a century ago, significant progress continues to be made, and this remains a major trend in recent topology. Nevertheless, the systematic study of the diffeomorphism groups of 4-dimensional manifolds, particularly from the perspective of gauge theory, had long remained underexplored, with only a few pioneering results. However, in recent years, there has been rapid progress in the "gauge theory for families", which is the application of gauge theory to families of 4-dimensional manifolds, leading to new insights into the diffeomorphism groups of 4-manifolds. Specifically, it has turned out that, similar to the classification theory of manifolds, the diffeomorphism groups of 4-manifolds exhibit phenomena that are unique to this dimension. In this talk, I will provide an overview of these recent developments.
https://forms.gle/96tZtBr1GhdHi1tZ9
2024/07/26
15:30-16:30 Room #大講義室(auditorium) (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.
Juan Manfredi (University of Pittsburgh)
Mean value expansions for solutions to general elliptic and parabolic equations (English)
https://docs.google.com/forms/d/e/1FAIpQLSefp31yMulPlAUURVHuQK9p41IadOj9KN0l-dD-mpbapJ0K6w/viewform?usp=pp_url
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.
Juan Manfredi (University of Pittsburgh)
Mean value expansions for solutions to general elliptic and parabolic equations (English)
[ Abstract ]
Harmonic functions in Euclidean space are characterized by the mean value property and are also obtained as expectations of stopped Brownian motion processes. This equivalence has a long history with fundamental contributions by Doob, Hunt, Ito, Kakutani, Kolmogorov, L ́evy, and many others. In this lecture, I will present ways to extend this characterization to solutions of non-linear elliptic and parabolic equations.
The non-linearity of the equation requires that the rigid mean value property be replaced by asymptotic mean value expansions and the Brownian motion by stochastic games, but the main equivalence remains when formulated with the help of the theory of viscosity solutions. Moreover, this local equivalence also holds on more general ambient spaces like Riemannian manifolds and the Heisenberg group.
I will present examples related the Monge-Amp`ere and k-Hessian equations and to the p-Laplacian in Euclidean space and the Heisenberg group.
[ Reference URL ]Harmonic functions in Euclidean space are characterized by the mean value property and are also obtained as expectations of stopped Brownian motion processes. This equivalence has a long history with fundamental contributions by Doob, Hunt, Ito, Kakutani, Kolmogorov, L ́evy, and many others. In this lecture, I will present ways to extend this characterization to solutions of non-linear elliptic and parabolic equations.
The non-linearity of the equation requires that the rigid mean value property be replaced by asymptotic mean value expansions and the Brownian motion by stochastic games, but the main equivalence remains when formulated with the help of the theory of viscosity solutions. Moreover, this local equivalence also holds on more general ambient spaces like Riemannian manifolds and the Heisenberg group.
I will present examples related the Monge-Amp`ere and k-Hessian equations and to the p-Laplacian in Euclidean space and the Heisenberg group.
https://docs.google.com/forms/d/e/1FAIpQLSefp31yMulPlAUURVHuQK9p41IadOj9KN0l-dD-mpbapJ0K6w/viewform?usp=pp_url
2024/06/21
15:30-16:30 Room #大講義室(auditorium) (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.
Mircea Mustaţă (The University of Michigan)
The minimal exponent of hypersurface singularities (English)
https://docs.google.com/forms/d/e/1FAIpQLSdUrEZYZ4fvi8So3pUVkxF08M2jbVdo7hTew_B1S5l-opFyzg/viewform?usp=sharing
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.
Mircea Mustaţă (The University of Michigan)
The minimal exponent of hypersurface singularities (English)
[ Abstract ]
The log canonical threshold of a hypersurface is an invariant of singularities that plays an important role in birational geometry, but which arises in many other contexts and admits different characterizations. A refinement of this invariant is Saito's minimal exponent, whose definition relies on the theory of b-functions, an important concept in D-module theory. The new information (by comparison with the log canonical threshold) provides a numerical measure of rational singularities. In this talk I will give an introduction to minimal exponents, highlighting recent progress and open questions.
[ Reference URL ]The log canonical threshold of a hypersurface is an invariant of singularities that plays an important role in birational geometry, but which arises in many other contexts and admits different characterizations. A refinement of this invariant is Saito's minimal exponent, whose definition relies on the theory of b-functions, an important concept in D-module theory. The new information (by comparison with the log canonical threshold) provides a numerical measure of rational singularities. In this talk I will give an introduction to minimal exponents, highlighting recent progress and open questions.
https://docs.google.com/forms/d/e/1FAIpQLSdUrEZYZ4fvi8So3pUVkxF08M2jbVdo7hTew_B1S5l-opFyzg/viewform?usp=sharing
2024/05/31
15:30-16:30 Room #大講義室(auditorium) (Graduate School of Math. Sci. Bldg.)
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at [Reference URL].
Hiroshi Sakai (Graduate School of Mathematical Sciences, The University of Tokyo)
Introduction to large cardinals (JAPANESE)
https://forms.gle/ZmHhZW6bxUyKewro8
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at [Reference URL].
Hiroshi Sakai (Graduate School of Mathematical Sciences, The University of Tokyo)
Introduction to large cardinals (JAPANESE)
[ Abstract ]
Set theory is a branch of mathematics which studies infinite sets, and various infinite cardinals are considered in set theory. Among them, large cardinals are uncountable cardinals which have some transcendental properties to smaller cardinals. So far, many large cardinals are formulated by set theorists. They are so large that their existences are not provable in the standard axiom system ZFC of set theory. The axioms asserting their existences are called large cardinal axioms. One of interesting points of large cardinals is that, while large cardinals are much larger than the cardinality of the set of real numbers, we can prove various facts on sets of real numbers using large cardinal axioms. In this talk, I will explain outline of large cardinal theory. I will also talk about large cardinal properties of small uncountable cardinals, which I am interested in.
[ Reference URL ]Set theory is a branch of mathematics which studies infinite sets, and various infinite cardinals are considered in set theory. Among them, large cardinals are uncountable cardinals which have some transcendental properties to smaller cardinals. So far, many large cardinals are formulated by set theorists. They are so large that their existences are not provable in the standard axiom system ZFC of set theory. The axioms asserting their existences are called large cardinal axioms. One of interesting points of large cardinals is that, while large cardinals are much larger than the cardinality of the set of real numbers, we can prove various facts on sets of real numbers using large cardinal axioms. In this talk, I will explain outline of large cardinal theory. I will also talk about large cardinal properties of small uncountable cardinals, which I am interested in.
https://forms.gle/ZmHhZW6bxUyKewro8
2024/04/26
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.
2024/03/14
14:30-17:00 Room #大講義室(auditorium) (Graduate School of Math. Sci. Bldg.)
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at [Reference URL].
Toshiyasu Arai (Graduate School of Mathematical Sciences, The University of Tokyo) 14:30-15:30
Many years from now (JAPANESE)
https://forms.gle/m38f1KRi67ECuA7MA
Masahiro Yamamoto (Graduate School of Mathematical Sciences, The University of Tokyo) 16:00-17:00
Mathematics, which I eventually found that I like: from the viewpoint of some marginal areas (JAPANESE)
https://forms.gle/m38f1KRi67ECuA7MA
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at [Reference URL].
Toshiyasu Arai (Graduate School of Mathematical Sciences, The University of Tokyo) 14:30-15:30
Many years from now (JAPANESE)
[ Abstract ]
I have been studying proof theory since the 1980's. In this talk I will talk about what happened to me in these 40 years, and let me report the latest result on ordinal analysis.
[ Reference URL ]I have been studying proof theory since the 1980's. In this talk I will talk about what happened to me in these 40 years, and let me report the latest result on ordinal analysis.
https://forms.gle/m38f1KRi67ECuA7MA
Masahiro Yamamoto (Graduate School of Mathematical Sciences, The University of Tokyo) 16:00-17:00
Mathematics, which I eventually found that I like: from the viewpoint of some marginal areas (JAPANESE)
[ Abstract ]
Looking back on my experiences over 40 years, I have been convinced that I have been loving my own mathematics among others.
After all, I can sum up as that all my mathematics are concerned with the three topics: control theories, inverse problems and time-fractional partial differential equations. Some of these research fields has already developed to major topics, while others keep still minor interests.
When I started studies on inverse problems in 1980's, there were very few population of mathematicians as specialists in Japan. In particular, inverse problems did not call great attention of mathematicians and were understood as marginal mathematical topics in spite of practical significance and demands On the other hand, possibly available methodologies and ideas have been exploited and integrated gradually. As consequence, main research partners have been outside Japan.
I have been enjoying not only the research contents, but also such wider collaboration.
Aiming at non-meaningless reference for the youngers, and trying not to be too retrospective, I will describe how I have done in mathematics as well as my research contents.
[ Reference URL ]Looking back on my experiences over 40 years, I have been convinced that I have been loving my own mathematics among others.
After all, I can sum up as that all my mathematics are concerned with the three topics: control theories, inverse problems and time-fractional partial differential equations. Some of these research fields has already developed to major topics, while others keep still minor interests.
When I started studies on inverse problems in 1980's, there were very few population of mathematicians as specialists in Japan. In particular, inverse problems did not call great attention of mathematicians and were understood as marginal mathematical topics in spite of practical significance and demands On the other hand, possibly available methodologies and ideas have been exploited and integrated gradually. As consequence, main research partners have been outside Japan.
I have been enjoying not only the research contents, but also such wider collaboration.
Aiming at non-meaningless reference for the youngers, and trying not to be too retrospective, I will describe how I have done in mathematics as well as my research contents.
https://forms.gle/m38f1KRi67ECuA7MA
2024/01/19
15:30-16:30 Room #大講義室(auditorium) (Graduate School of Math. Sci. Bldg.)
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at [Reference URL].
Kenji Fukaya (Simons Center for Geometry and Physics)
Lagrangian correspondence and Floer theory (JAPANESE)
https://forms.gle/7T6ewXWtrVEKM9dY7
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at [Reference URL].
Kenji Fukaya (Simons Center for Geometry and Physics)
Lagrangian correspondence and Floer theory (JAPANESE)
[ Abstract ]
It was proposed by Weinstein that the morphism of the `category’ of symplectic manifold should be a Lagrangian correspondence (a Lagrangian submanifold of the direct product).
Gromov-Witten invariant is not functorial for this functor.
However Lagrangian Floer theory is functorial.
I will explain present status of the study of this functoriality and a few of its applications.
[ Reference URL ]It was proposed by Weinstein that the morphism of the `category’ of symplectic manifold should be a Lagrangian correspondence (a Lagrangian submanifold of the direct product).
Gromov-Witten invariant is not functorial for this functor.
However Lagrangian Floer theory is functorial.
I will explain present status of the study of this functoriality and a few of its applications.
https://forms.gle/7T6ewXWtrVEKM9dY7
2023/12/15
15:30-16:30 Room #大講義室(auditorium) (Graduate School of Math. Sci. Bldg.)
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at [Reference URL].
Mikiya Masuda (Osaka Central Advanced Mathematical Institute, Osaka Metropolitan University)
Hessenberg varieties and Stanley-Stembridge conjecture in graph theory (JAPANESE)
https://forms.gle/42wEF5c2pqsqrHqR7
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at [Reference URL].
Mikiya Masuda (Osaka Central Advanced Mathematical Institute, Osaka Metropolitan University)
Hessenberg varieties and Stanley-Stembridge conjecture in graph theory (JAPANESE)
[ Abstract ]
Hessenberg varieties, a family of subvarieties of flag varieties, includes Springer fibers in geometric representation theory, Peterson varieties related to the quantum cohomology of flag varieties, and permutohedral varieties which are nonsingular toric varieties. Hessenberg varieties are also related to the QR algorithm for matrix eigenvalues and to hyperplane arrangements. Recently, Hessenberg varieties have attracted attention because of their connection to the Stanley-Stembridge conjecture on symmetric functions in graph theory. In this talk, I will explain how Hessenberg varieties are related to this conjecture.
[ Reference URL ]Hessenberg varieties, a family of subvarieties of flag varieties, includes Springer fibers in geometric representation theory, Peterson varieties related to the quantum cohomology of flag varieties, and permutohedral varieties which are nonsingular toric varieties. Hessenberg varieties are also related to the QR algorithm for matrix eigenvalues and to hyperplane arrangements. Recently, Hessenberg varieties have attracted attention because of their connection to the Stanley-Stembridge conjecture on symmetric functions in graph theory. In this talk, I will explain how Hessenberg varieties are related to this conjecture.
https://forms.gle/42wEF5c2pqsqrHqR7
2023/10/27
15:30-16:30 Room #大講義室(auditorium) (Graduate School of Math. Sci. Bldg.)
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at [Reference URL].
Jenn-Nan Wang (National Taiwan University)
Increasing stability and decreasing instability estimates for an inverse boundary value problem (English)
https://forms.gle/9xDcHfHXFFHPfsKW6
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at [Reference URL].
Jenn-Nan Wang (National Taiwan University)
Increasing stability and decreasing instability estimates for an inverse boundary value problem (English)
[ Abstract ]
According to Hadamard’s definition, a well-posed problem satisfies three criteria: existence, uniqueness, and continuous dependence on the data. Most of forward problems (e.g., the boundary value problem or Calderón’s problem) can be proved to be well-posed. However, many inverse problems are known to be ill-posed, for example, the inverse boundary value problem in which one would like to determine unknown parameters from the boundary measurements. The failure of the continuous dependence on the data in Hadamard’s sense makes the feasible determination of unknown parameters rather difficult in practice. However, if one restricts the unknown parameters in a suitable subspace, one can restore the continuous dependence or stability. Nonetheless, the ill-posedness nature of the inverse problem may give rise a logarithmic type modulus of continuity. For Calderón’s problem, such logarithmic stability estimate was derived by Alessandrini and Mandache showed that this estimate is optimal by proving an instability estimate of exponential type. When we consider the time-harmonic equation, it was first proved by Isakov that the stability increases as the frequency increases. In this talk, I would like to discuss a refinement of Mandache’s idea aiming to derive explicitly the dependence of the instability estimate on the frequency. If time allows, I also want to discuss the increasing stability phenomenon from the statistical viewpoint based on the Bayes approach. The aim is to show that the posterior distribution contracts around the true parameter at a rate closely related to the decreasing instability estimate derived above.
[ Reference URL ]According to Hadamard’s definition, a well-posed problem satisfies three criteria: existence, uniqueness, and continuous dependence on the data. Most of forward problems (e.g., the boundary value problem or Calderón’s problem) can be proved to be well-posed. However, many inverse problems are known to be ill-posed, for example, the inverse boundary value problem in which one would like to determine unknown parameters from the boundary measurements. The failure of the continuous dependence on the data in Hadamard’s sense makes the feasible determination of unknown parameters rather difficult in practice. However, if one restricts the unknown parameters in a suitable subspace, one can restore the continuous dependence or stability. Nonetheless, the ill-posedness nature of the inverse problem may give rise a logarithmic type modulus of continuity. For Calderón’s problem, such logarithmic stability estimate was derived by Alessandrini and Mandache showed that this estimate is optimal by proving an instability estimate of exponential type. When we consider the time-harmonic equation, it was first proved by Isakov that the stability increases as the frequency increases. In this talk, I would like to discuss a refinement of Mandache’s idea aiming to derive explicitly the dependence of the instability estimate on the frequency. If time allows, I also want to discuss the increasing stability phenomenon from the statistical viewpoint based on the Bayes approach. The aim is to show that the posterior distribution contracts around the true parameter at a rate closely related to the decreasing instability estimate derived above.
https://forms.gle/9xDcHfHXFFHPfsKW6
2023/07/21
15:30-16:30 Room #大講義室(auditorium) (Graduate School of Math. Sci. Bldg.)
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at [Reference URL].
Masahito Yamazaki (Kavli Institute for the Physics and Mathematics of the Uniiverse, the University of Tokyo)
Quantum Field Theory in Mathematics (JAPANESE)
https://forms.gle/igR5ZB5AwginXBt49
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at [Reference URL].
Masahito Yamazaki (Kavli Institute for the Physics and Mathematics of the Uniiverse, the University of Tokyo)
Quantum Field Theory in Mathematics (JAPANESE)
[ Abstract ]
While quantum field theory has primarily been a theory in physics, it has also been a source of new ideas in mathematics, and has facilitated interactions between different branches of mathematics. There have also been many attempts to formulate quantum field theories themselves rigorously in mathematics. In this lecture we will discuss some examples of research in knot invariants and integrable models, to illustrate the impact of quantum field theories and string theory in modern mathematics.
[ Reference URL ]While quantum field theory has primarily been a theory in physics, it has also been a source of new ideas in mathematics, and has facilitated interactions between different branches of mathematics. There have also been many attempts to formulate quantum field theories themselves rigorously in mathematics. In this lecture we will discuss some examples of research in knot invariants and integrable models, to illustrate the impact of quantum field theories and string theory in modern mathematics.
https://forms.gle/igR5ZB5AwginXBt49
2023/06/30
15:30-16:30 Room #大講義室(auditorium) (Graduate School of Math. Sci. Bldg.)
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at https://forms.gle/z22nKn1NUrT41qiR7
Guy Henniart (Université Paris-Saclay)
Did you say $p$-adic? (English)
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at https://forms.gle/z22nKn1NUrT41qiR7
Guy Henniart (Université Paris-Saclay)
Did you say $p$-adic? (English)
[ Abstract ]
I am a Number Theorist and $p$ is a prime number. The $p$-adic numbers are obtained by pushing to the limit a simple idea. Suppose that you want to know which integers are sums of two squares. If an integer $x$ is odd, its square has the form $8k+1$; if $x$ is even, its square is a multiple of $4$. So the sum of two squares has the form $4k$, $4k+1$ or $4k+2$, never $4k+3$ ! More generally if a polynomial equation with integer coefficients has no integer solution if you work «modulo $N$» that is you neglect all multiples of an integer $N$, then a fortiori it has no integer solution. By the Chinese Remainder Theorem, working modulo $N$ is the same as working modulo $p^r$ where $p$ runs through prime divisors of $N$ and $p^r$ is the highest power of $p$ dividing $N$. Now work modulo $p$, modulo $p^2$, modulo $p^3$, etc. You have invented the $p$-adic integers, which are, I claim, as real as the real numbers and (nearly) as useful!
I am a Number Theorist and $p$ is a prime number. The $p$-adic numbers are obtained by pushing to the limit a simple idea. Suppose that you want to know which integers are sums of two squares. If an integer $x$ is odd, its square has the form $8k+1$; if $x$ is even, its square is a multiple of $4$. So the sum of two squares has the form $4k$, $4k+1$ or $4k+2$, never $4k+3$ ! More generally if a polynomial equation with integer coefficients has no integer solution if you work «modulo $N$» that is you neglect all multiples of an integer $N$, then a fortiori it has no integer solution. By the Chinese Remainder Theorem, working modulo $N$ is the same as working modulo $p^r$ where $p$ runs through prime divisors of $N$ and $p^r$ is the highest power of $p$ dividing $N$. Now work modulo $p$, modulo $p^2$, modulo $p^3$, etc. You have invented the $p$-adic integers, which are, I claim, as real as the real numbers and (nearly) as useful!
2023/06/05
15:30-16:30 Online
Curtis T McMullen (Harvard University)
Billiards and Moduli Spaces (ENGLISH)
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZMkfu2grj4sE9ycW-1MmIQ-768hTpobQKAD
Curtis T McMullen (Harvard University)
Billiards and Moduli Spaces (ENGLISH)
[ Abstract ]
The moduli space M_g of compact Riemann surface of genus g has been studied from diverse mathematical viewpoints for more than a century.
In this talk, intended for a general audience, we will discuss moduli space from a dynamical perspective. We will present general rigidity results, provide a glimpse of the remarkable curves and surfaces in M_g discovered during the last two decades, and explain how these algebraic varieties are related to the dynamics of billiards in regular polygons, L-shaped tables and quadrilaterals.
A variety of open problems will be mentioned along the way.
[ Reference URL ]The moduli space M_g of compact Riemann surface of genus g has been studied from diverse mathematical viewpoints for more than a century.
In this talk, intended for a general audience, we will discuss moduli space from a dynamical perspective. We will present general rigidity results, provide a glimpse of the remarkable curves and surfaces in M_g discovered during the last two decades, and explain how these algebraic varieties are related to the dynamics of billiards in regular polygons, L-shaped tables and quadrilaterals.
A variety of open problems will be mentioned along the way.
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZMkfu2grj4sE9ycW-1MmIQ-768hTpobQKAD
2023/05/19
15:30-16:30 Room #大講義室 (Graduate School of Math. Sci. Bldg.)
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at https://forms.gle/J4Wo8N6CbLmYiprUA.
Hiroki Masuda (Graduate School of Mathematical Sciences, the University of Tokyo)
Locally stable regression (日本語)
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please apply from the form at https://forms.gle/J4Wo8N6CbLmYiprUA.
Hiroki Masuda (Graduate School of Mathematical Sciences, the University of Tokyo)
Locally stable regression (日本語)
[ Abstract ]
A non-ergodic model structure naturally emerges in estimating a stochastic process model observed at high frequency over a fixed period. The probability structure of the driving noise determines whether or not the characteristics of the model can be statistically estimated. However, it is difficult to describe the possible phenomena in general when the noise is non-Gaussian. Building on such backgrounds, we will present some recent results on non-ergodic regression modeling driven by a locally stable Lévy process: the construction of an explicit non-Gaussian quasi-maximum likelihood and the asymptotic distribution of the corresponding estimator. We will also present a method for relative model comparison and its theoretical property.
A non-ergodic model structure naturally emerges in estimating a stochastic process model observed at high frequency over a fixed period. The probability structure of the driving noise determines whether or not the characteristics of the model can be statistically estimated. However, it is difficult to describe the possible phenomena in general when the noise is non-Gaussian. Building on such backgrounds, we will present some recent results on non-ergodic regression modeling driven by a locally stable Lévy process: the construction of an explicit non-Gaussian quasi-maximum likelihood and the asymptotic distribution of the corresponding estimator. We will also present a method for relative model comparison and its theoretical property.
2023/04/28
15:30-16:30 Hybrid
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please take part online [Reference URL]
Kazuo Habiro (Graduate School of Mathematical Sciences, the University of Tokyo)
On quantum topology (日本語)
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZIkc-Cvrz4oHNXj_kafJqhU6ZFWCABqgojM
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please take part online [Reference URL]
Kazuo Habiro (Graduate School of Mathematical Sciences, the University of Tokyo)
On quantum topology (日本語)
[ Abstract ]
I started my research from surgery theory of knots and 3-manifolds. This is related to finite type invariants, which was studied intensively at that time. I obtained a result which characterises the information that is carried by finite type invariants in terms of clasper surgery. After that, I have studied quantum invariants of integral homology spheres, Kirby calculus of framed links, quantum invariants of bottom tangles, functorialization of Le-Murakami-Ohtsuki invariants, quantum fundamental groups and quantum representation variety of 3-manifolds, traces of categorified quantum groups, etc. I would like to reflect on these studies and also discuss future prospects.
[ Reference URL ]I started my research from surgery theory of knots and 3-manifolds. This is related to finite type invariants, which was studied intensively at that time. I obtained a result which characterises the information that is carried by finite type invariants in terms of clasper surgery. After that, I have studied quantum invariants of integral homology spheres, Kirby calculus of framed links, quantum invariants of bottom tangles, functorialization of Le-Murakami-Ohtsuki invariants, quantum fundamental groups and quantum representation variety of 3-manifolds, traces of categorified quantum groups, etc. I would like to reflect on these studies and also discuss future prospects.
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZIkc-Cvrz4oHNXj_kafJqhU6ZFWCABqgojM
2023/03/13
13:00-17:00 Hybrid
Registration for online participation: [Reference URL], Application for onsite participation: https://forms.gle/2eDKDtNsTounyoXw6 (Update: Mar. 5)
Masahiko Kanai ( Graduate School of Mathematical Sciences, the University of Tokyo) 13:00-14:00
(JAPANESE)
[ Reference URL ]
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZElcO2oqTgoG9a1JSawX0kFRMSFheEptcaA
Hisashi Inaba (Graduate School of Mathematical Sciences, the University of Tokyo) 14:30-15:30
(JAPANESE)
[ Reference URL ]
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZIkceigrj4tEt0AydbnE8PVJmIS6xLanDAe
Shuji Saito ( Graduate School of Mathematical Sciences, the University of Tokyo) 16:00-17:00
From higher dimensional class field theory to a new theory of motives (ENGLISH)
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZAqf-ioqz8jG9BWefiIf_zTJ1t7R7VG1beV
Registration for online participation: [Reference URL], Application for onsite participation: https://forms.gle/2eDKDtNsTounyoXw6 (Update: Mar. 5)
Masahiko Kanai ( Graduate School of Mathematical Sciences, the University of Tokyo) 13:00-14:00
(JAPANESE)
[ Reference URL ]
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZElcO2oqTgoG9a1JSawX0kFRMSFheEptcaA
Hisashi Inaba (Graduate School of Mathematical Sciences, the University of Tokyo) 14:30-15:30
(JAPANESE)
[ Reference URL ]
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZIkceigrj4tEt0AydbnE8PVJmIS6xLanDAe
Shuji Saito ( Graduate School of Mathematical Sciences, the University of Tokyo) 16:00-17:00
From higher dimensional class field theory to a new theory of motives (ENGLISH)
[ Abstract ]
My first research was on Higher Dimensional Class Theory done in collaboration with Kazuya Kato. That was 40 years ago. The classical class field theory is a theory that controls the Galois group of the maximal abelian extension of a number field (a finite extension of the field of rational numbers) using only information intrinsic to the field (e.g., its ideal class group). Higher dimensional class field theory is an extension of this theory to the case of finitely generated fields over the field of rational numbers or a finite field. It is formulated as an arithmetic algebro-geometric problem using scheme theory.
In this talk, I will start with a review of the classical class field theory that can be understood by undergraduates and explain how higher dimensional class field theory is formulated in a way that is easy to understand even for non-specialists. I will also briefly explain an improvement of Kato-Saito's higher-dimensional class field theory that I made with Moritz Kerz in 2016, and how it triggered a recent new development of theory of motive. In particular, I will discuss the relationship between the new theory and ramification theory (of which Takeshi Saito is a world leader), which until now has had no interaction with theory of motives.
[ Reference URL ]My first research was on Higher Dimensional Class Theory done in collaboration with Kazuya Kato. That was 40 years ago. The classical class field theory is a theory that controls the Galois group of the maximal abelian extension of a number field (a finite extension of the field of rational numbers) using only information intrinsic to the field (e.g., its ideal class group). Higher dimensional class field theory is an extension of this theory to the case of finitely generated fields over the field of rational numbers or a finite field. It is formulated as an arithmetic algebro-geometric problem using scheme theory.
In this talk, I will start with a review of the classical class field theory that can be understood by undergraduates and explain how higher dimensional class field theory is formulated in a way that is easy to understand even for non-specialists. I will also briefly explain an improvement of Kato-Saito's higher-dimensional class field theory that I made with Moritz Kerz in 2016, and how it triggered a recent new development of theory of motive. In particular, I will discuss the relationship between the new theory and ramification theory (of which Takeshi Saito is a world leader), which until now has had no interaction with theory of motives.
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZAqf-ioqz8jG9BWefiIf_zTJ1t7R7VG1beV
2023/01/20
15:30-16:30 Hybrid
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please take part online [Reference URL].
Mikhail Bershtein (HSE University, Skoltech)
Kyiv formula and its applications (ENGLISH)
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZUrduioqjouG9wBfhl35VPxN_K92oa1wB4P
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please take part online [Reference URL].
Mikhail Bershtein (HSE University, Skoltech)
Kyiv formula and its applications (ENGLISH)
[ Abstract ]
The Kyiv formula gives the generic tau function of Painleve' equation (and more generally isomonodromy deformation equations) in terms of conformal blocks or Nekrasov partition function. I will explain the statement, examples and different approaches to the proof. If time permits, I will discuss some applications of this formula.
[ Reference URL ]The Kyiv formula gives the generic tau function of Painleve' equation (and more generally isomonodromy deformation equations) in terms of conformal blocks or Nekrasov partition function. I will explain the statement, examples and different approaches to the proof. If time permits, I will discuss some applications of this formula.
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZUrduioqjouG9wBfhl35VPxN_K92oa1wB4P
2022/11/25
15:30-16:30 Hybrid
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please take part online [Reference URL].
Shane Kelly (Graduate School of Mathematical Sciences, the University of Tokyo)
Motivic cohomology: theory and applications
(ENGLISH)
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZErcumupjouGdXpOac2j3rcFFN545yAuoSb
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please take part online [Reference URL].
Shane Kelly (Graduate School of Mathematical Sciences, the University of Tokyo)
Motivic cohomology: theory and applications
(ENGLISH)
[ Abstract ]
The motive of a smooth projective algebraic variety was originally envisaged by Grothendieck in the 60's as a generalisation of the Jacobian of a curve, and formed part of a strategy to prove the Weil conjectures. In the 90s, following conjectures of Beilinson on special values of L-functions, Voevodsky, together with Friedlander, Morel, Suslin, and others, generalised this to the A^1-homotopy type of a general algebraic variety. This A^1-homotopy theory lead to a proof of the Block-Kato conjecture (and a Fields Medal for Voevodsky).
One consequence of making things A^1-invariant is that unipotent groups (as well as wild ramification, irregular singularities, nilpotents including higher nilpotents in the sense of derived algebraic geometry, certain parts of K-theory, etc) become invisible and the last decade has seen a number of candidates for a non-A^1-invariant theory.
In this talk I will give an introduction to the classical theory and discuss some current and future research directions.
[ Reference URL ]The motive of a smooth projective algebraic variety was originally envisaged by Grothendieck in the 60's as a generalisation of the Jacobian of a curve, and formed part of a strategy to prove the Weil conjectures. In the 90s, following conjectures of Beilinson on special values of L-functions, Voevodsky, together with Friedlander, Morel, Suslin, and others, generalised this to the A^1-homotopy type of a general algebraic variety. This A^1-homotopy theory lead to a proof of the Block-Kato conjecture (and a Fields Medal for Voevodsky).
One consequence of making things A^1-invariant is that unipotent groups (as well as wild ramification, irregular singularities, nilpotents including higher nilpotents in the sense of derived algebraic geometry, certain parts of K-theory, etc) become invisible and the last decade has seen a number of candidates for a non-A^1-invariant theory.
In this talk I will give an introduction to the classical theory and discuss some current and future research directions.
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZErcumupjouGdXpOac2j3rcFFN545yAuoSb
2022/10/21
15:30-16:30 Room #オンライン (Graduate School of Math. Sci. Bldg.)
If you wish to join this colloquium, please register via [Reference URL] of MS Colloquium page.
Neal Bez (Graduate School of Science and Engineering, Saitama University)
The Fourier restriction conjecture (English)
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZcudO-srjMvHtUzVhQQZF9JhDSvy-Oxu2j2
If you wish to join this colloquium, please register via [Reference URL] of MS Colloquium page.
Neal Bez (Graduate School of Science and Engineering, Saitama University)
The Fourier restriction conjecture (English)
[ Abstract ]
The Fourier restriction conjecture is a central problem in modern harmonic analysis which traces back to deep observations of Elias M. Stein in the 1960s. The conjecture enjoys some remarkable connections to areas such as geometric measure theory, PDE, and number theory. In this talk, I will introduce the conjecture and discuss a few of these connections.
[ Reference URL ]The Fourier restriction conjecture is a central problem in modern harmonic analysis which traces back to deep observations of Elias M. Stein in the 1960s. The conjecture enjoys some remarkable connections to areas such as geometric measure theory, PDE, and number theory. In this talk, I will introduce the conjecture and discuss a few of these connections.
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZcudO-srjMvHtUzVhQQZF9JhDSvy-Oxu2j2
2022/07/22
15:30-16:30 Hybrid
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please take part online [Reference URL].
Ryo Takada (Graduate School of Mathematical Sciences, the University of Tokyo)
Mathematical analysis of dispersion and anisotropy in rotating stably stratified fluids (JAPANESE)
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZYtf-iorDIiGNXBzovQXlHZjH4iXVS6QB4t
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please take part online [Reference URL].
Ryo Takada (Graduate School of Mathematical Sciences, the University of Tokyo)
Mathematical analysis of dispersion and anisotropy in rotating stably stratified fluids (JAPANESE)
[ Abstract ]
In this talk, we consider the partial differential equations describing the motion of rotating stably stratified fluids. We will survey our recent results on the dispersive estimates for the linear propagators, and the strongly stratified limit for the inviscid Boussinesq equations.
[ Reference URL ]In this talk, we consider the partial differential equations describing the motion of rotating stably stratified fluids. We will survey our recent results on the dispersive estimates for the linear propagators, and the strongly stratified limit for the inviscid Boussinesq equations.
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZYtf-iorDIiGNXBzovQXlHZjH4iXVS6QB4t
2022/06/24
15:30-16:30 Hybrid
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please take part online [Reference URL].
Yoshiki Oshima (Graduate School of Mathematical Sciences, the University of Tokyo)
Unitary representations of real reductive Lie groups and the method of coadjoint orbits (JAPANESE)
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZIldu-vqD8tHtE0Vyl29MXHFfzp2NcC0MzR
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please take part online [Reference URL].
Yoshiki Oshima (Graduate School of Mathematical Sciences, the University of Tokyo)
Unitary representations of real reductive Lie groups and the method of coadjoint orbits (JAPANESE)
[ Abstract ]
The orbit method aims to study unitary representations of Lie groups by relating them to coadjoint actions. It is known that for unipotent groups there exists a one-to-one correspondence between the unitary representations and the coadjoint orbits. For reductive groups it has been observed that one is a good approximation of the other. In this talk, we would like to discuss some results on induction and restriction for reductive Lie groups from the viewpoint of orbit method.
[ Reference URL ]The orbit method aims to study unitary representations of Lie groups by relating them to coadjoint actions. It is known that for unipotent groups there exists a one-to-one correspondence between the unitary representations and the coadjoint orbits. For reductive groups it has been observed that one is a good approximation of the other. In this talk, we would like to discuss some results on induction and restriction for reductive Lie groups from the viewpoint of orbit method.
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZIldu-vqD8tHtE0Vyl29MXHFfzp2NcC0MzR
2022/05/20
15:30-16:30 Hybrid
The colloquium scheduled on May/20/2022 has been postponed in accordance with the speaker's convenience.
Ryo Takada (Graduate School of Mathematical Sciences, the University of Tokyo)
Mathematical analysis of dispersion and anisotropy in rotating stably stratified fluids (JAPANESE)
The colloquium scheduled on May/20/2022 has been postponed in accordance with the speaker's convenience.
Ryo Takada (Graduate School of Mathematical Sciences, the University of Tokyo)
Mathematical analysis of dispersion and anisotropy in rotating stably stratified fluids (JAPANESE)
[ Abstract ]
In this talk, we consider the partial differential equations describing the motion of rotating stably stratified fluids. We will survey our recent results on the dispersive estimates for the linear propagators, and the strongly stratified limit for the inviscid Boussinesq equations.
In this talk, we consider the partial differential equations describing the motion of rotating stably stratified fluids. We will survey our recent results on the dispersive estimates for the linear propagators, and the strongly stratified limit for the inviscid Boussinesq equations.
2022/04/22
15:30-16:30 Online
If you wish to join this colloquium, please register via [Reference URL] of MS Colloquium page.
Yukinobu Toda (Kavli IPMU, The University of Tokyo)
Curve counting theories and categorification
(JAPANESE)
If you wish to join this colloquium, please register via [Reference URL] of MS Colloquium page.
Yukinobu Toda (Kavli IPMU, The University of Tokyo)
Curve counting theories and categorification
(JAPANESE)
[ Abstract ]
There exist several curve counting theories on Calabi-Yau 3-folds such as Gromov-Witten invariants, Donaldson-Thomas invariants, Pandharipande-Thomas invariants and Gopakumar-Vafa invariants. These invariants are expected to be related each other, but most of them are still conjectural. In this talk, I will survey the recent developments of the study of these curve counting theories. If time permits, I will also explain my recent works on categorification of curve counting theories.
There exist several curve counting theories on Calabi-Yau 3-folds such as Gromov-Witten invariants, Donaldson-Thomas invariants, Pandharipande-Thomas invariants and Gopakumar-Vafa invariants. These invariants are expected to be related each other, but most of them are still conjectural. In this talk, I will survey the recent developments of the study of these curve counting theories. If time permits, I will also explain my recent works on categorification of curve counting theories.
