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Seminar information archive
Seminar information archive ～12/07｜Today's seminar 12/08 | Future seminars 12/09～
2017/11/14
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Meng Chen (Fudan)
A characterization of the birationality of 4-canonical maps of minimal 3-folds (English)
Meng Chen (Fudan)
A characterization of the birationality of 4-canonical maps of minimal 3-folds (English)
[ Abstract ]
We explain the following theorem: For any minimal 3-fold X of general type with p_g>4, the 4-canonical map is non-birational if and only if X is birationally fibred by a pencil of (1,2) surfaces. The statement fails in the case of p_g=4.
We explain the following theorem: For any minimal 3-fold X of general type with p_g>4, the 4-canonical map is non-birational if and only if X is birationally fibred by a pencil of (1,2) surfaces. The statement fails in the case of p_g=4.
Numerical Analysis Seminar
16:50-18:20 Room #002 (Graduate School of Math. Sci. Bldg.)
Ai Ishikawa (Kobe University)
Energy-preserving numerical method based on the variational principle and application to unconstrained optimization problems (Japanese)
Ai Ishikawa (Kobe University)
Energy-preserving numerical method based on the variational principle and application to unconstrained optimization problems (Japanese)
2017/11/13
Tokyo Probability Seminar
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Masaki Wada (Faculty of Human Development and Culture, Fukushima University)
(JAPANESE)
Masaki Wada (Faculty of Human Development and Culture, Fukushima University)
(JAPANESE)
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Georg Schumacher (Philipps-Universität Marburg)
Relative Canonical Bundles for Families of Calabi-Yau Manifolds
Georg Schumacher (Philipps-Universität Marburg)
Relative Canonical Bundles for Families of Calabi-Yau Manifolds
[ Abstract ]
We consider holomorphic families of Calabi-Yau manifolds (here being defined by the vanishing of the first real Chern class). We study induced hermitian metrics on the relative canonical bundle, which are related to the Weil-Petersson form on the base. Under a certain condition the total space possesses a Kähler form, whose restriction to fibers are equal to the Ricci flat metrics. Furthermore we prove an extension theorem for the Weil-Petersson form and give applications.
We consider holomorphic families of Calabi-Yau manifolds (here being defined by the vanishing of the first real Chern class). We study induced hermitian metrics on the relative canonical bundle, which are related to the Weil-Petersson form on the base. Under a certain condition the total space possesses a Kähler form, whose restriction to fibers are equal to the Ricci flat metrics. Furthermore we prove an extension theorem for the Weil-Petersson form and give applications.
Operator Algebra Seminars
16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
Juan Orendain (UNAM)
Globularily generated double categories: On the problem of existence of internalizations for decorated bicategories (English)
Juan Orendain (UNAM)
Globularily generated double categories: On the problem of existence of internalizations for decorated bicategories (English)
2017/11/10
Infinite Analysis Seminar Tokyo
17:00-18:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Fabio Novaes (International Institute of Physics (UFRN))
Chern-Simons, gravity and integrable systems. (ENGLISH)
http://www.iip.ufrn.br/eventslecturer?inf==0EVRpXTR1TP
Fabio Novaes (International Institute of Physics (UFRN))
Chern-Simons, gravity and integrable systems. (ENGLISH)
[ Abstract ]
It is known since the 80's that pure three-dimensional gravity is classically equivalent to a Chern-Simons theory with gauge group SL(2,R) x SL(2,R). For a given set of boundary conditions, the asymptotic classical phase space has a central extension in terms of two copies of Virasoro algebra. In particular, this gives a conformal field theory representation of black hole solutions in 3d gravity, also known as BTZ black holes. The BTZ black hole entropy can then be recovered using CFT. In this talk, we review this story and discuss recent results on how to relax the BTZ boundary conditions to obtain the KdV hierarchy at the boundary. More generally, this shows that Chern-Simons theory can represent virtually any integrable system at the boundary, given some consistency conditions. We also briefly discuss how this formulation can be useful to describe non-relativistic systems.
[ Reference URL ]It is known since the 80's that pure three-dimensional gravity is classically equivalent to a Chern-Simons theory with gauge group SL(2,R) x SL(2,R). For a given set of boundary conditions, the asymptotic classical phase space has a central extension in terms of two copies of Virasoro algebra. In particular, this gives a conformal field theory representation of black hole solutions in 3d gravity, also known as BTZ black holes. The BTZ black hole entropy can then be recovered using CFT. In this talk, we review this story and discuss recent results on how to relax the BTZ boundary conditions to obtain the KdV hierarchy at the boundary. More generally, this shows that Chern-Simons theory can represent virtually any integrable system at the boundary, given some consistency conditions. We also briefly discuss how this formulation can be useful to describe non-relativistic systems.
http://www.iip.ufrn.br/eventslecturer?inf==0EVRpXTR1TP
2017/11/09
Kavli IPMU Komaba Seminar
13:30-14:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Edouard Brezin (lpt ens, Paris)
Various applications of supersymmetry in statistical physics (English)
Edouard Brezin (lpt ens, Paris)
Various applications of supersymmetry in statistical physics (English)
[ Abstract ]
Supersymmetry is a fundamental concept in particle physics (although it has not been seen experimentally so far). But it is although a powerful tool in a number of problems arising in quantum mechanics and statistical physics. It has been widely used in the theory of disordered systems (Efetov et al.), it led to dimensional reduction for branched polymers (Parisi-Sourlas), for the susy classical gas (Brydges and Imbrie), for Landau levels with impurities. If has also many powerful applications in the theory of random matrices. I will briefly review some of these topics.
Supersymmetry is a fundamental concept in particle physics (although it has not been seen experimentally so far). But it is although a powerful tool in a number of problems arising in quantum mechanics and statistical physics. It has been widely used in the theory of disordered systems (Efetov et al.), it led to dimensional reduction for branched polymers (Parisi-Sourlas), for the susy classical gas (Brydges and Imbrie), for Landau levels with impurities. If has also many powerful applications in the theory of random matrices. I will briefly review some of these topics.
2017/11/08
Number Theory Seminar
18:00-19:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Xin Wan (Morningside Center for Mathematics)
Iwasawa theory and Bloch-Kato conjecture for modular forms (ENGLISH)
Xin Wan (Morningside Center for Mathematics)
Iwasawa theory and Bloch-Kato conjecture for modular forms (ENGLISH)
[ Abstract ]
Bloch and Kato formulated conjectures relating sizes of p-adic Selmer groups with special values of L-functions. Iwasawa theory is a useful tool for studying these conjectures and BSD conjecture for elliptic curves. For example the Iwasawa main conjecture for modular forms formulated by Kato implies the Tamagawa number formula for modular forms of analytic rank 0.
In this talk I'll first briefly review the above theory. Then we will focus on a different Iwasawa theory approach for this problem. The starting point is a recent joint work with Jetchev and Skinner proving the BSD formula for elliptic curves of analytic rank 1. We will discuss how such results are generalized to modular forms. If time allowed we may also explain the possibility to use it to deduce Bloch-Kato conjectures in both analytic rank 0 and 1 cases. In certain aspects such approach should be more powerful than classical Iwasawa theory, and has some potential to attack cases with bad ramification at p.
Bloch and Kato formulated conjectures relating sizes of p-adic Selmer groups with special values of L-functions. Iwasawa theory is a useful tool for studying these conjectures and BSD conjecture for elliptic curves. For example the Iwasawa main conjecture for modular forms formulated by Kato implies the Tamagawa number formula for modular forms of analytic rank 0.
In this talk I'll first briefly review the above theory. Then we will focus on a different Iwasawa theory approach for this problem. The starting point is a recent joint work with Jetchev and Skinner proving the BSD formula for elliptic curves of analytic rank 1. We will discuss how such results are generalized to modular forms. If time allowed we may also explain the possibility to use it to deduce Bloch-Kato conjectures in both analytic rank 0 and 1 cases. In certain aspects such approach should be more powerful than classical Iwasawa theory, and has some potential to attack cases with bad ramification at p.
2017/11/07
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Shin Hayashi (AIST-TohokuU MathAM-OIL)
On an explicit example of topologically protected corner states (JAPANESE)
Shin Hayashi (AIST-TohokuU MathAM-OIL)
On an explicit example of topologically protected corner states (JAPANESE)
[ Abstract ]
In condensed matter physics, topologically protected (codimension-one) edge states are known to appear on the surface of some insulators reflecting some topology of its bulk. Such phenomena can be understood from the point of view of an index theory associated to the Toeplitz extension and are called the bulk-edge correspondence. In this talk, we consider instead the quarter-plane Toeplitz extension and index theory associated with it. As a result, we show that topologically protected (codimension-two) corner states appear reflecting some topology of the gapped bulk and two edges. Such new topological phases can be obtained by taking a ``product’’ of two classically known topological phases (2d type A and 1d type AIII topological phases). By using this construction, we obtain an example of a continuous family of bounded self-adjoint Fredholm quarter-plane Toeplitz operators whose spectral flow is nontrivial, which gives an explicit example of topologically protected corner states.
In condensed matter physics, topologically protected (codimension-one) edge states are known to appear on the surface of some insulators reflecting some topology of its bulk. Such phenomena can be understood from the point of view of an index theory associated to the Toeplitz extension and are called the bulk-edge correspondence. In this talk, we consider instead the quarter-plane Toeplitz extension and index theory associated with it. As a result, we show that topologically protected (codimension-two) corner states appear reflecting some topology of the gapped bulk and two edges. Such new topological phases can be obtained by taking a ``product’’ of two classically known topological phases (2d type A and 1d type AIII topological phases). By using this construction, we obtain an example of a continuous family of bounded self-adjoint Fredholm quarter-plane Toeplitz operators whose spectral flow is nontrivial, which gives an explicit example of topologically protected corner states.
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Takumi Murayama (University of Michigan)
Characterizations of projective space and Seshadri constants in arbitrary characteristic
Takumi Murayama (University of Michigan)
Characterizations of projective space and Seshadri constants in arbitrary characteristic
[ Abstract ]
Mori and Mukai conjectured that projective space should be the only n-dimensional Fano variety whose anti-canonical bundle has degree at least n + 1 along every curve. While this conjecture has been proved in characteristic zero, it remains open in positive characteristic. We will present some progress in this direction by giving another characterization of projective space using Seshadri constants and the Frobenius morphism. The key ingredient is a positive-characteristic analogue of Demailly’s criterion for separation of higher-order jets by adjoint bundles, whose proof gives new results for adjoint bundles even in characteristic zero.
Mori and Mukai conjectured that projective space should be the only n-dimensional Fano variety whose anti-canonical bundle has degree at least n + 1 along every curve. While this conjecture has been proved in characteristic zero, it remains open in positive characteristic. We will present some progress in this direction by giving another characterization of projective space using Seshadri constants and the Frobenius morphism. The key ingredient is a positive-characteristic analogue of Demailly’s criterion for separation of higher-order jets by adjoint bundles, whose proof gives new results for adjoint bundles even in characteristic zero.
2017/11/06
FMSP Lectures
17:00-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)
V. G. Romanov (Sobolev Institute of Mathematics)
Phaseless inverse problems for Maxwell equations (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Romanov2.pdf
V. G. Romanov (Sobolev Institute of Mathematics)
Phaseless inverse problems for Maxwell equations (ENGLISH)
[ Abstract ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Romanov2.pdf
[ Reference URL ]http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Romanov2.pdf
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Romanov2.pdf
2017/11/02
Seminar on Probability and Statistics
14:00-15:10 Room #052 (Graduate School of Math. Sci. Bldg.)
Tudor Ciprian (Université Lille 1)
Hermite processes and sheets
Tudor Ciprian (Université Lille 1)
Hermite processes and sheets
[ Abstract ]
The Hermite process of order $\geq 1$ is a self-similar stochastic process with stationary increments living in the $q$th Wiener chaos. The class of Hermite processes includes the fractional Brownian motion (for $q=1$) and the Rosenblatt process (for $q=2$). We present the basic properties of these processes and we introduce their multiparameter version. We also discuss the behavior with respect to the self-similarity index and the possibility so solve stochastic equations with Hermite noise.
The Hermite process of order $\geq 1$ is a self-similar stochastic process with stationary increments living in the $q$th Wiener chaos. The class of Hermite processes includes the fractional Brownian motion (for $q=1$) and the Rosenblatt process (for $q=2$). We present the basic properties of these processes and we introduce their multiparameter version. We also discuss the behavior with respect to the self-similarity index and the possibility so solve stochastic equations with Hermite noise.
2017/11/01
Discrete mathematical modelling seminar
17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Basile Grammaticos (Université de Paris VII・XI)
Discrete Painlevé equations associated with the E8 group (ENGLISH)
Basile Grammaticos (Université de Paris VII・XI)
Discrete Painlevé equations associated with the E8 group (ENGLISH)
[ Abstract ]
I'll present a summary of the results of the Paris-Tokyo-Pondicherry group on equations associated with the affine Weyl group E8. I shall review the various parametrisations of the E8-related equations, introducing the trihomographic representation and the ancillary variable. Several examples of E8-associated equations will be given including what we believe is the simplest form for the generic elliptic discrete Painlevé equation.
I'll present a summary of the results of the Paris-Tokyo-Pondicherry group on equations associated with the affine Weyl group E8. I shall review the various parametrisations of the E8-related equations, introducing the trihomographic representation and the ancillary variable. Several examples of E8-associated equations will be given including what we believe is the simplest form for the generic elliptic discrete Painlevé equation.
2017/10/31
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Yash Lodha (École Polytechnique Fédérale de Lausanne)
Nonamenable groups of piecewise projective homeomorphisms (ENGLISH)
Yash Lodha (École Polytechnique Fédérale de Lausanne)
Nonamenable groups of piecewise projective homeomorphisms (ENGLISH)
[ Abstract ]
Groups of piecewise projective homeomorphisms provide elegant examples of groups that are non amenable, yet do not contain non abelian free subgroups. In this talk I will present a survey of these groups and discuss their striking properties. I will discuss properties such as (non)amenability, finiteness properties, normal subgroup structure, actions by various degrees of regularity and Tarski numbers.
Groups of piecewise projective homeomorphisms provide elegant examples of groups that are non amenable, yet do not contain non abelian free subgroups. In this talk I will present a survey of these groups and discuss their striking properties. I will discuss properties such as (non)amenability, finiteness properties, normal subgroup structure, actions by various degrees of regularity and Tarski numbers.
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Zhan Li (Beijing)
ACC for log canonical threshold polytopes (English)
Zhan Li (Beijing)
ACC for log canonical threshold polytopes (English)
[ Abstract ]
We show that the log canonical threshold polytopes of varieties with log canonical singularities satisfy the ascending chain condition. This is a joint work with Jingjun Han and Lu Qi.
We show that the log canonical threshold polytopes of varieties with log canonical singularities satisfy the ascending chain condition. This is a joint work with Jingjun Han and Lu Qi.
Discrete mathematical modelling seminar
16:30-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Basile Grammaticos (Université de Paris VII・XI)
The end of the World (ENGLISH)
Basile Grammaticos (Université de Paris VII・XI)
The end of the World (ENGLISH)
[ Abstract ]
This is not a seminar on astrophysics or cosmology. I am not going to talk about something that will happen in billions of years. I will rather explain the menace to our civilisation and to the human species. Inspired from the works of several authors I will explain the existing risks. I will also present mathematical models which show that a general collapse is possible in the decades that follow.
This is not a seminar on astrophysics or cosmology. I am not going to talk about something that will happen in billions of years. I will rather explain the menace to our civilisation and to the human species. Inspired from the works of several authors I will explain the existing risks. I will also present mathematical models which show that a general collapse is possible in the decades that follow.
Discrete mathematical modelling seminar
15:30-16:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Fon-Che Liu (National Taiwan University)
A hierarchy of approximate regularity of functions (ENGLISH)
Fon-Che Liu (National Taiwan University)
A hierarchy of approximate regularity of functions (ENGLISH)
[ Abstract ]
A hierarchy of a certain weakly sensed regularity of functions defined on subsets of Euclidean n-space which originated from the well-known Lusin theorem that characterizes measurable functions in terms of approximate continuity will be introduced. Its intimate relations with the ordinary hierarchy of regularity in terms of order of continuous differentiability will be exposed and explained.
A hierarchy of a certain weakly sensed regularity of functions defined on subsets of Euclidean n-space which originated from the well-known Lusin theorem that characterizes measurable functions in terms of approximate continuity will be introduced. Its intimate relations with the ordinary hierarchy of regularity in terms of order of continuous differentiability will be exposed and explained.
FMSP Lectures
16:00-17:00 Room #118 (Graduate School of Math. Sci. Bldg.)
V. G. Romanov (Sobolev Institute of Mathematics)
Some Geometric Aspects in Inverse Problems (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Romanov.pdf
V. G. Romanov (Sobolev Institute of Mathematics)
Some Geometric Aspects in Inverse Problems (ENGLISH)
[ Abstract ]
We consider inverse problems related to recovering coefficients in partial differential equations of the second order. It is supposed that some measurements of solutions to direct problems are produced on convenient sets. A study of some inverse problems for hyperbolic equations leads to geometric problems: recovering a function from its integrals along geodesic lines of the Riemannian metric or recovering the Riemannian metric inside a domain from given distances between arbitrary points of the domain boundary. Our main goal here is to demonstrate how such geometric problems arise for equations of parabolic and elliptic types.
[ Reference URL ]We consider inverse problems related to recovering coefficients in partial differential equations of the second order. It is supposed that some measurements of solutions to direct problems are produced on convenient sets. A study of some inverse problems for hyperbolic equations leads to geometric problems: recovering a function from its integrals along geodesic lines of the Riemannian metric or recovering the Riemannian metric inside a domain from given distances between arbitrary points of the domain boundary. Our main goal here is to demonstrate how such geometric problems arise for equations of parabolic and elliptic types.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Romanov.pdf
2017/10/30
Tokyo Probability Seminar
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Yu Ito (Department of Mathematics, Faculty of Science, Kyoto Sangyo University)
Integration of controlled rough paths via fractional calculus (JAPANESE)
Yu Ito (Department of Mathematics, Faculty of Science, Kyoto Sangyo University)
Integration of controlled rough paths via fractional calculus (JAPANESE)
Operator Algebra Seminars
16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
Yusuke Sawada (Nagoya Univ.)
The bicategory of $W^*$-bimodules
Yusuke Sawada (Nagoya Univ.)
The bicategory of $W^*$-bimodules
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Masahide Kato (Sophia University)
Odd dimensional complex analytic Kleinian groups
Masahide Kato (Sophia University)
Odd dimensional complex analytic Kleinian groups
[ Abstract ]
In this talk, I would explain an idea to construct a higher dimensional analogue of the classical Kleinian group theory. For a group $G$ of a certain class of discrete subgroups of $\mathrm{PGL}(2n+2,\mathbf{C})$ which act on $\mathbf{P}^{2n+1}$, there is a canonical way to define the region of discontinuity, on which $G$ acts properly discontinuously. General principle in the discussion is to regard $\mathbf{P}^{n}$ in $\mathbf{P}^{2n+1}$ as a single point. We can consider the quotient space of the discontinuity region by the action of $G$. Though the Ahlfors finiteness theorem is hopeless because of a counter example, the Klein combination theorem and the handle attachment can be defined similarly. Any compact quotients which appear here are non-Kaehler. In the case $n=1$, we explain a new example of compact quotients which is related to a classical Kleinian group.
In this talk, I would explain an idea to construct a higher dimensional analogue of the classical Kleinian group theory. For a group $G$ of a certain class of discrete subgroups of $\mathrm{PGL}(2n+2,\mathbf{C})$ which act on $\mathbf{P}^{2n+1}$, there is a canonical way to define the region of discontinuity, on which $G$ acts properly discontinuously. General principle in the discussion is to regard $\mathbf{P}^{n}$ in $\mathbf{P}^{2n+1}$ as a single point. We can consider the quotient space of the discontinuity region by the action of $G$. Though the Ahlfors finiteness theorem is hopeless because of a counter example, the Klein combination theorem and the handle attachment can be defined similarly. Any compact quotients which appear here are non-Kaehler. In the case $n=1$, we explain a new example of compact quotients which is related to a classical Kleinian group.
Algebraic Geometry Seminar
10:30-12:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Robeto Svaldi (Cambridge)
Towards birational boundedness of elliptic Calabi-Yau varieties (English)
Robeto Svaldi (Cambridge)
Towards birational boundedness of elliptic Calabi-Yau varieties (English)
[ Abstract ]
I will discuss new results towards the birational boundedness of
low-dimensional elliptic Calabi-Yau varieties, joint work with Gabriele
Di Certo.
Recent work in the minimal model program suggests that pairs with trivial log canonical
class should satisfy some boundedness properties.
I will show that 4-dimensional Calabi-Yau pairs which are not birational to a product are
indeed log birationally bounded. This implies birational boundedness of elliptically fibered
Calabi-Yau manifolds with a section, in dimension up to 5.
If time allows, I will also try to discuss a first approach towards boundedness of rationally
connected CY varieties in low dimension.
I will discuss new results towards the birational boundedness of
low-dimensional elliptic Calabi-Yau varieties, joint work with Gabriele
Di Certo.
Recent work in the minimal model program suggests that pairs with trivial log canonical
class should satisfy some boundedness properties.
I will show that 4-dimensional Calabi-Yau pairs which are not birational to a product are
indeed log birationally bounded. This implies birational boundedness of elliptically fibered
Calabi-Yau manifolds with a section, in dimension up to 5.
If time allows, I will also try to discuss a first approach towards boundedness of rationally
connected CY varieties in low dimension.
2017/10/25
Lectures
11:00-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Ahmed Abbes (CNRS/IHES)
On Faltings' main comparison theorem in p-adic Hodge theory : the relative case (ENGLISH)
Ahmed Abbes (CNRS/IHES)
On Faltings' main comparison theorem in p-adic Hodge theory : the relative case (ENGLISH)
[ Abstract ]
In the appendix of his 2002 Asterisque article, Faltings roughly sketched a proof of a relative version of his main comparison theorem in p-adic Hodge theory. I will briefly review the absolute case and then explain some of the key new inputs for the proof of the relative case (joint work with Michel Gros).
In the appendix of his 2002 Asterisque article, Faltings roughly sketched a proof of a relative version of his main comparison theorem in p-adic Hodge theory. I will briefly review the absolute case and then explain some of the key new inputs for the proof of the relative case (joint work with Michel Gros).
2017/10/24
Seminar on Mathematics for various disciplines
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Christian Klingenberg (Würzburg University)
The initial value problem for the multidimensional system of gas dynamics may have infinitely many weak solutions (English)
Christian Klingenberg (Würzburg University)
The initial value problem for the multidimensional system of gas dynamics may have infinitely many weak solutions (English)
[ Abstract ]
We consider the isentropic compressible Euler equations in two space dimensions together with particular initial data. This data consists of two constant states only, where one state lies on the lower and the other state on the upper half plane. The aim is to investigate if there exists a unique entropy solution or if the convex integration method produces infinitely many entropy solutions. In this lecture we will show that the solution of this Riemann problem for the 2-d isentropic Euler equations is non-unique (except if the solution is smooth). Next we are able to show that there exist Lipschitz data that may lead to infinitely many solutions even for the full system of Euler equations. This is joint work with Simon Markfelder.
We consider the isentropic compressible Euler equations in two space dimensions together with particular initial data. This data consists of two constant states only, where one state lies on the lower and the other state on the upper half plane. The aim is to investigate if there exists a unique entropy solution or if the convex integration method produces infinitely many entropy solutions. In this lecture we will show that the solution of this Riemann problem for the 2-d isentropic Euler equations is non-unique (except if the solution is smooth). Next we are able to show that there exist Lipschitz data that may lead to infinitely many solutions even for the full system of Euler equations. This is joint work with Simon Markfelder.
Tuesday Seminar on Topology
17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Reiko Miyaoka (Tohoku University)
Approach from the submanifold theory to the Floer homology of Lagrangian intersections (JAPANESE)
Reiko Miyaoka (Tohoku University)
Approach from the submanifold theory to the Floer homology of Lagrangian intersections (JAPANESE)
[ Abstract ]
The Gauss map images of isoparametric hypersurfaces in the spheres supply a rich family of minimal Lagrangian submanifolds of the complex hyperquadric Q_n(C). In simple cases, these are real forms of Q_n(C), and their Floer homology is known. In this talk, we consider the case when the number of distinct principal curvatures is 3,4,6, and report our results. This is a joint work with Hiroshi Iriyeh (Ibaraki U.), Hui Ma (Tsinghua U.) and Yoshihiro Ohnita (Osaka City U.).
The Gauss map images of isoparametric hypersurfaces in the spheres supply a rich family of minimal Lagrangian submanifolds of the complex hyperquadric Q_n(C). In simple cases, these are real forms of Q_n(C), and their Floer homology is known. In this talk, we consider the case when the number of distinct principal curvatures is 3,4,6, and report our results. This is a joint work with Hiroshi Iriyeh (Ibaraki U.), Hui Ma (Tsinghua U.) and Yoshihiro Ohnita (Osaka City U.).
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