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Seminar information archive
Seminar information archive ～12/05｜Today's seminar 12/06 | Future seminars 12/07～
2015/10/23
Geometry Colloquium
10:00-11:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Nobuhiko Otoba (Keio University)
Metrics of constant scalar curvature on sphere bundles (Japanese)
Nobuhiko Otoba (Keio University)
Metrics of constant scalar curvature on sphere bundles (Japanese)
[ Abstract ]
This talk is based on joint work with Jimmy Petean (CIMAT).
I'd like to talk about our attempt to study the Yamabe PDE on Riemannian twisted product manifolds, more precisely, the total spaces of Riemannian submersions with totally geodesic fibers. To demonstrate how the argument works,
I construct metrics of constant scalar curvature on unit sphere bundles for real vector bundles of the type $E \oplus L$,
the Whitney sum of a vector bundle $E$ and a line bundle $L$ with respective inner products, and then estimate the number of solutions to the corresponding Yamabe PDE.
This talk is based on joint work with Jimmy Petean (CIMAT).
I'd like to talk about our attempt to study the Yamabe PDE on Riemannian twisted product manifolds, more precisely, the total spaces of Riemannian submersions with totally geodesic fibers. To demonstrate how the argument works,
I construct metrics of constant scalar curvature on unit sphere bundles for real vector bundles of the type $E \oplus L$,
the Whitney sum of a vector bundle $E$ and a line bundle $L$ with respective inner products, and then estimate the number of solutions to the corresponding Yamabe PDE.
2015/10/22
FMSP Lectures
16:00-16:50 Room #002 (Graduate School of Math. Sci. Bldg.)
Hans-Otto Walther (University of Giessen)
The semiflow of a delay differential equation on its solution manifold (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/Walther-abstract-1.pdf
Hans-Otto Walther (University of Giessen)
The semiflow of a delay differential equation on its solution manifold (ENGLISH)
[ Abstract ]
The lecture surveys work after the turn of the millenium on well-posedness of initial value problems for di_erential equations with variable delay. The focus is on results which provide continuously di_erentiable solution operators, so that in case studies ingredients of dynamical systems theory, such as local invariant manifolds or Poincar_e return maps, become available. We explain why the familar theory of retarded functional di_erential equations [1,2,4] fails for equations with variable delay, discuss what has been achieved for the latter, for autonomous and for nonautonomous equations, with delays bounded or unbounded, and address open problems.
[ Reference URL ]The lecture surveys work after the turn of the millenium on well-posedness of initial value problems for di_erential equations with variable delay. The focus is on results which provide continuously di_erentiable solution operators, so that in case studies ingredients of dynamical systems theory, such as local invariant manifolds or Poincar_e return maps, become available. We explain why the familar theory of retarded functional di_erential equations [1,2,4] fails for equations with variable delay, discuss what has been achieved for the latter, for autonomous and for nonautonomous equations, with delays bounded or unbounded, and address open problems.
http://fmsp.ms.u-tokyo.ac.jp/Walther-abstract-1.pdf
FMSP Lectures
17:00-17:50 Room #002 (Graduate School of Math. Sci. Bldg.)
Hans-Otto Walther (University of Giessen)
Shilnikov chaos due to state-dependent delay, by means of the fixed point index (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/Walther-abstract-2.pdf
Hans-Otto Walther (University of Giessen)
Shilnikov chaos due to state-dependent delay, by means of the fixed point index (ENGLISH)
[ Abstract ]
What can variability of a delay in a delay differential equation do to the dynamics? We find a bounded delay functional d(¥phi), with d(¥phi)=1 on a neighborhood of ¥phi=0, such that the equation x'(t)=-a x(t-d(x_t)) has a solution which is homoclinic to 0, with shift dynamics in its vicinity, whereas the linear equation x'(t)=-a x(t-1) with constant time lag, for small solutions, is hyperbolic with 2-dimensional unstable space.
The proof involves regularity properties of the semiflow close to the homoclinic loop in the solution manifold and a generalization of a method due to Piotr Zgliczynsky which uses the fixed point index and a closing argument in order to establish shift dynamics when certain covering relations hold. (Joint work with Bernhard Lani-Wayda)
[ Reference URL ]What can variability of a delay in a delay differential equation do to the dynamics? We find a bounded delay functional d(¥phi), with d(¥phi)=1 on a neighborhood of ¥phi=0, such that the equation x'(t)=-a x(t-d(x_t)) has a solution which is homoclinic to 0, with shift dynamics in its vicinity, whereas the linear equation x'(t)=-a x(t-1) with constant time lag, for small solutions, is hyperbolic with 2-dimensional unstable space.
The proof involves regularity properties of the semiflow close to the homoclinic loop in the solution manifold and a generalization of a method due to Piotr Zgliczynsky which uses the fixed point index and a closing argument in order to establish shift dynamics when certain covering relations hold. (Joint work with Bernhard Lani-Wayda)
http://fmsp.ms.u-tokyo.ac.jp/Walther-abstract-2.pdf
Applied Analysis
16:00-17:50 Room #002 (Graduate School of Math. Sci. Bldg.)
Hans-Otto Walther (University of Giessen)
(Part I) The semiflow of a delay differential equation on its solution manifold
(Part II) Shilnikov chaos due to state-dependent delay, by means of the fixed point index
(ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/Walther-abstract-1.pdf
Hans-Otto Walther (University of Giessen)
(Part I) The semiflow of a delay differential equation on its solution manifold
(Part II) Shilnikov chaos due to state-dependent delay, by means of the fixed point index
(ENGLISH)
[ Abstract ]
(Part I) 16:00 - 16:50
The semiflow of a delay differential equation on its solution manifold
(Part II) 17:00 - 17:50
Shilnikov chaos due to state-dependent delay, by means of the fixed point index
(Part I)
The lecture surveys recent work on initial value problems for differential equations with variable delay. The focus is on differentiable solution operators.
The lecture explains why the theory for retarded functional differential equations which is familiar from monographs before the turn of the millenium fails in case of variable delay, discusses what has been achieved in this case, for autonomous and non-autonomous equations, with delays bounded and unbounded, and addresses open problems.
[detailed abstract]
http://fmsp.ms.u-tokyo.ac.jp/Walther-abstract-1.pdf
(Part II)
What can variability of a delay in a delay differential equation do to the dynamics? We find a bounded delay functional $d(\phi)$, with $d(\phi)=1$ on a neighborhood of $\phi=0$, such that the equation $x'(t)=-a x(t-d(x_t))$ has a solution which is homoclinic to $0$, with shift dynamics in its vicinity, whereas the linear equation $x'(t)=-a x(t-1)$ with constant time lag, for small solutions, is hyperbolic with 2-dimensional unstable space.
The proof involves regularity properties of the semiflow close to the homoclinic loop in the solution manifold and a generalization of a method due to Piotr Zgliczynsky which uses the fixed point index and a closing argument in order to establish shift dynamics when certain covering relations hold. (Joint work with Bernhard Lani-Wayda)
[detailed abstract]
http://fmsp.ms.u-tokyo.ac.jp/Walther-abstract-2.pdf
[ Reference URL ](Part I) 16:00 - 16:50
The semiflow of a delay differential equation on its solution manifold
(Part II) 17:00 - 17:50
Shilnikov chaos due to state-dependent delay, by means of the fixed point index
(Part I)
The lecture surveys recent work on initial value problems for differential equations with variable delay. The focus is on differentiable solution operators.
The lecture explains why the theory for retarded functional differential equations which is familiar from monographs before the turn of the millenium fails in case of variable delay, discusses what has been achieved in this case, for autonomous and non-autonomous equations, with delays bounded and unbounded, and addresses open problems.
[detailed abstract]
http://fmsp.ms.u-tokyo.ac.jp/Walther-abstract-1.pdf
(Part II)
What can variability of a delay in a delay differential equation do to the dynamics? We find a bounded delay functional $d(\phi)$, with $d(\phi)=1$ on a neighborhood of $\phi=0$, such that the equation $x'(t)=-a x(t-d(x_t))$ has a solution which is homoclinic to $0$, with shift dynamics in its vicinity, whereas the linear equation $x'(t)=-a x(t-1)$ with constant time lag, for small solutions, is hyperbolic with 2-dimensional unstable space.
The proof involves regularity properties of the semiflow close to the homoclinic loop in the solution manifold and a generalization of a method due to Piotr Zgliczynsky which uses the fixed point index and a closing argument in order to establish shift dynamics when certain covering relations hold. (Joint work with Bernhard Lani-Wayda)
[detailed abstract]
http://fmsp.ms.u-tokyo.ac.jp/Walther-abstract-2.pdf
http://fmsp.ms.u-tokyo.ac.jp/Walther-abstract-1.pdf
2015/10/21
Mathematical Biology Seminar
14:55-16:40 Room #128演習室 (Graduate School of Math. Sci. Bldg.)
Ryosuke Omori (Research Center for Zoonosis Control, Hokkaido University, Japan)
The distribution of the duration of immunity determines the periodicity of Mycoplasma pneumoniae incidence. (JAPANESE)
http://researchers.general.hokudai.ac.jp/profile/ja.e3OkdvtshzEabOVZ2w5OYw==.html
Ryosuke Omori (Research Center for Zoonosis Control, Hokkaido University, Japan)
The distribution of the duration of immunity determines the periodicity of Mycoplasma pneumoniae incidence. (JAPANESE)
[ Abstract ]
Estimating the periodicity of outbreaks is sometimes equivalent to the
prediction of future outbreaks. However, the periodicity may change
over time so understanding the mechanism of outbreak periodicity is
important. So far, mathematical modeling studies suggest several
drivers for outbreak periodicity including, 1) environmental factors
(e.g. temperature) and 2) host behavior (contact patterns between host
individuals). Among many diseases, multiple determinants can be
considered to cause the outbreak periodicity and it is difficult to
understand the periodicity quantitatively. Here we introduce our case
study of Mycoplasma pneumoniae (MP) which shows three to five year
periodic outbreaks, with multiple candidates for determinants for the
outbreak periodicity being narrowed down to the last one, the variance
of the length of the immunity duration. To our knowledge this is the
first study showing that the variance in the length of the immunity
duration is essential for the periodicity of the outbreaks.
[ Reference URL ]Estimating the periodicity of outbreaks is sometimes equivalent to the
prediction of future outbreaks. However, the periodicity may change
over time so understanding the mechanism of outbreak periodicity is
important. So far, mathematical modeling studies suggest several
drivers for outbreak periodicity including, 1) environmental factors
(e.g. temperature) and 2) host behavior (contact patterns between host
individuals). Among many diseases, multiple determinants can be
considered to cause the outbreak periodicity and it is difficult to
understand the periodicity quantitatively. Here we introduce our case
study of Mycoplasma pneumoniae (MP) which shows three to five year
periodic outbreaks, with multiple candidates for determinants for the
outbreak periodicity being narrowed down to the last one, the variance
of the length of the immunity duration. To our knowledge this is the
first study showing that the variance in the length of the immunity
duration is essential for the periodicity of the outbreaks.
http://researchers.general.hokudai.ac.jp/profile/ja.e3OkdvtshzEabOVZ2w5OYw==.html
2015/10/20
FMSP Lectures
16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)
Danielle Hilhorst (CNRS / University of Paris-Sud)
Existence of an entropy solution in the sense of Young measures for a first order conservation law with a stochastic source term (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Hilhorst151020.pdf
Danielle Hilhorst (CNRS / University of Paris-Sud)
Existence of an entropy solution in the sense of Young measures for a first order conservation law with a stochastic source term (ENGLISH)
[ Abstract ]
We consider a finite volume scheme for a first order conservation law with a monotone flux function and a multiplicative source term involving a Q-Wiener process. We define a stochastic entropy solution in the sense of Young measures. We present some a priori estimates for the discrete solution including a weak BV estimate. After performing a time interpolation, we prove two entropy inequalities and show that the discrete solution converges along a subsequence to an entropy solution in the sense of Young measures.
This is joint work with T. Funaki, Y. Gao and H. Weber.
[ Reference URL ]We consider a finite volume scheme for a first order conservation law with a monotone flux function and a multiplicative source term involving a Q-Wiener process. We define a stochastic entropy solution in the sense of Young measures. We present some a priori estimates for the discrete solution including a weak BV estimate. After performing a time interpolation, we prove two entropy inequalities and show that the discrete solution converges along a subsequence to an entropy solution in the sense of Young measures.
This is joint work with T. Funaki, Y. Gao and H. Weber.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Hilhorst151020.pdf
Tuesday Seminar of Analysis
16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)
Danielle Hilhorst (CNRS / University of Paris-Sud)
Existence of an entropy solution in the sense of Young measures for a first order conservation law with a stochastic source term (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Hilhorst151020.pdf
Danielle Hilhorst (CNRS / University of Paris-Sud)
Existence of an entropy solution in the sense of Young measures for a first order conservation law with a stochastic source term (ENGLISH)
[ Abstract ]
We consider a finite volume scheme for a first order conservation law with a monotone flux function and a multiplicative source term involving a Q-Wiener process. We define a stochastic entropy solution in the sense of Young measures. We present some a priori estimates for the discrete solution including a weak BV estimate. After performing a time interpolation, we prove two entropy inequalities and show that the discrete solution converges along a subsequence to an entropy solution in the sense of Young measures.
This is joint work with T. Funaki, Y. Gao and H. Weber.
[ Reference URL ]We consider a finite volume scheme for a first order conservation law with a monotone flux function and a multiplicative source term involving a Q-Wiener process. We define a stochastic entropy solution in the sense of Young measures. We present some a priori estimates for the discrete solution including a weak BV estimate. After performing a time interpolation, we prove two entropy inequalities and show that the discrete solution converges along a subsequence to an entropy solution in the sense of Young measures.
This is joint work with T. Funaki, Y. Gao and H. Weber.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Hilhorst151020.pdf
Tuesday Seminar on Topology
17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Bruno Scardua (Universidade Federal do Rio de Janeiro)
On the existence of stable compact leaves for
transversely holomorphic foliations (ENGLISH)
Bruno Scardua (Universidade Federal do Rio de Janeiro)
On the existence of stable compact leaves for
transversely holomorphic foliations (ENGLISH)
[ Abstract ]
One of the most important results in the theory of foliations is
the celebrated Local stability theorem of Reeb :
A compact leaf of a foliation having finite holonomy group is
stable, indeed, it admits a fundamental system of invariant
neighborhoods where each leaf is compact with finite holonomy
group. This result, together with the Global stability theorem of Reeb
(for codimension one real foliations), has many important consequences
and motivates several questions in the theory of foliations. In this talk
we show how to prove:
A transversely holomorphic foliation on a compact complex manifold, exhibits a compact stable
leaf if and only if the set of compact leaves is not a zero measure subset of the manifold.
This is a joint work with Cesar Camacho.
One of the most important results in the theory of foliations is
the celebrated Local stability theorem of Reeb :
A compact leaf of a foliation having finite holonomy group is
stable, indeed, it admits a fundamental system of invariant
neighborhoods where each leaf is compact with finite holonomy
group. This result, together with the Global stability theorem of Reeb
(for codimension one real foliations), has many important consequences
and motivates several questions in the theory of foliations. In this talk
we show how to prove:
A transversely holomorphic foliation on a compact complex manifold, exhibits a compact stable
leaf if and only if the set of compact leaves is not a zero measure subset of the manifold.
This is a joint work with Cesar Camacho.
2015/10/19
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Atsushi Moriwaki (Kyoto University)
Semiample invertible sheaves with semipositive continuous hermitian metrics (Japanese)
Atsushi Moriwaki (Kyoto University)
Semiample invertible sheaves with semipositive continuous hermitian metrics (Japanese)
[ Abstract ]
Let $(L,h)$ be a pair of a semi ample invertible sheaf and a semipositive continuous hermitian metric on a proper algebraic variety over $C$. In this talk, we would like to present the result that $(L, h)$ has the extension property, answering a generalization of a question of S. Zhang. Moreover, we consider its non-archimedean analogue.
Let $(L,h)$ be a pair of a semi ample invertible sheaf and a semipositive continuous hermitian metric on a proper algebraic variety over $C$. In this talk, we would like to present the result that $(L, h)$ has the extension property, answering a generalization of a question of S. Zhang. Moreover, we consider its non-archimedean analogue.
Tokyo Probability Seminar
16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)
Stefano Olla (University of Paris-Dauphine)
Entropy and hypo-coercive methods in hydrodynamic limits
Stefano Olla (University of Paris-Dauphine)
Entropy and hypo-coercive methods in hydrodynamic limits
[ Abstract ]
Relative Entropy and entropy production have been main tools
in obtaining hydrodynamic limits Entropic hypo-coercivity can be used to
extend this method to dynamics with highly degenerate noise. I will
apply it to a chain of anharmonic oscillators immersed in a temperature
gradient. Stationary states of these dynamics are of ’non equilibrium’,
and their entropy production does not allow the application of previous
techniques. These dynamics model microscopically an isothermal
thermodynamic transformation between non-equilibrium stationary states.
Ref: http://arxiv.org/abs/1505.05002
Relative Entropy and entropy production have been main tools
in obtaining hydrodynamic limits Entropic hypo-coercivity can be used to
extend this method to dynamics with highly degenerate noise. I will
apply it to a chain of anharmonic oscillators immersed in a temperature
gradient. Stationary states of these dynamics are of ’non equilibrium’,
and their entropy production does not allow the application of previous
techniques. These dynamics model microscopically an isothermal
thermodynamic transformation between non-equilibrium stationary states.
Ref: http://arxiv.org/abs/1505.05002
Seminar on Probability and Statistics
13:00-16:40 Room #052 (Graduate School of Math. Sci. Bldg.)
2015/10/16
FMSP Lectures
15:00-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Nicolai Reshetikhin (University of California, Berkeley)
Introduction to BV quantization IV (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Reshetikhin.pdf
Nicolai Reshetikhin (University of California, Berkeley)
Introduction to BV quantization IV (ENGLISH)
[ Abstract ]
The lectures will focus on Batalin-Vilkovisky (BV) framework for gauge field theories. We will start with examples of gauge theories such Yang-Mills, BF-theory, Chern-Simons and others. The Hamiltonian structure for field theories will be explained on these examples. Then the classical BV-BFV (Batalin-Fradkin-Vilkovisky) setting will be introduced as a Z-graded extension of the Hamiltonian structure of field theories. The AKSZ (Aleksandrov-Kontsevich-Swartz-Zaboronskij) construction of topological field theories will be introduced. We will construct corresponding BV-BFV theory and its extension to strata of all codimensions. We will also see that Chern-Simons theory, BF theory are of the AKSZ type. The geometry of BV theories is also known as derived geometry. The classical part will be followed by an outline of what is a quantum gauge theory and what is a path integral quantization of a classical gauge theory in the BV-BFV setting. Then we will discuss BV-integrals, fibered BV integrals and perturbative quantization.
[ Reference URL ]The lectures will focus on Batalin-Vilkovisky (BV) framework for gauge field theories. We will start with examples of gauge theories such Yang-Mills, BF-theory, Chern-Simons and others. The Hamiltonian structure for field theories will be explained on these examples. Then the classical BV-BFV (Batalin-Fradkin-Vilkovisky) setting will be introduced as a Z-graded extension of the Hamiltonian structure of field theories. The AKSZ (Aleksandrov-Kontsevich-Swartz-Zaboronskij) construction of topological field theories will be introduced. We will construct corresponding BV-BFV theory and its extension to strata of all codimensions. We will also see that Chern-Simons theory, BF theory are of the AKSZ type. The geometry of BV theories is also known as derived geometry. The classical part will be followed by an outline of what is a quantum gauge theory and what is a path integral quantization of a classical gauge theory in the BV-BFV setting. Then we will discuss BV-integrals, fibered BV integrals and perturbative quantization.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Reshetikhin.pdf
Geometry Colloquium
10:00-11:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Daisuke Yamakawa (Tokyo Institute of Technology)
Meromorphic connections on the Riemann sphere and quiver varieties (Japanese)
Daisuke Yamakawa (Tokyo Institute of Technology)
Meromorphic connections on the Riemann sphere and quiver varieties (Japanese)
[ Abstract ]
I will show that some moduli spaces of meromorphic connections on the Riemann sphere are isomorphic to Nakajima's quiver varieties as complex symplectic manifolds (joint work with Kazuki Hiroe). This was conjectured by Boalch and generalizes Crawley-Boevey's result for logarithmic connections. Also I will mention Weyl group symmetries of isomonodromic deformations of meromorphic connections.
I will show that some moduli spaces of meromorphic connections on the Riemann sphere are isomorphic to Nakajima's quiver varieties as complex symplectic manifolds (joint work with Kazuki Hiroe). This was conjectured by Boalch and generalizes Crawley-Boevey's result for logarithmic connections. Also I will mention Weyl group symmetries of isomonodromic deformations of meromorphic connections.
2015/10/15
FMSP Lectures
15:00-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
David Sauzin (CNRS - Centro di Ricerca Matematica Ennio De Giorgi Scuola Normale Superiore di Pisa)
Introduction to 1-summability and resurgence (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Sauzin.pdf
David Sauzin (CNRS - Centro di Ricerca Matematica Ennio De Giorgi Scuola Normale Superiore di Pisa)
Introduction to 1-summability and resurgence (ENGLISH)
[ Abstract ]
The theories of summability and resurgence deal with the mathematical use of certain divergent power series. The first part of the lecure is an introduction to 1-summability. The definitions rely on the formal Borel transform and the Laplace transform along an arbitrary direction of the complex plane. Given an arc of directions, if a power series is 1-summable in that arc, then one can attach to it a Borel-Laplace sum, i.e. a holomorphic function defined in a large enough sector and asymptotic to that power series in Gevrey sense. The second part is an introduction to Ecalle's resurgence theory. A power series is said to be resurgent when its Borel transform is convergent and has good analytic continuation properties: there may be singularities but they must be isolated. The analysis of these singularities, through the so-called alien calculus, allows one to compare the various Borel-Laplace sums attached to the same resurgent 1-summable series. In the context of analytic difference-or-differential equations, this sheds light on the Stokes phenomenon. A few elementary or classical examples will be considered (the Euler series, the Stirling series, a less known example by Poincaré). Special attention must be devoted to non-linear operations: 1-summable series as well as resurgent series form algebras which are stable by composition. An example of a class of non-linear differential equations giving rise to resurgent solutions will be analyzed. The exposition requires only some familiarity with holomorphic functions of one complex variable.
[ Reference URL ]The theories of summability and resurgence deal with the mathematical use of certain divergent power series. The first part of the lecure is an introduction to 1-summability. The definitions rely on the formal Borel transform and the Laplace transform along an arbitrary direction of the complex plane. Given an arc of directions, if a power series is 1-summable in that arc, then one can attach to it a Borel-Laplace sum, i.e. a holomorphic function defined in a large enough sector and asymptotic to that power series in Gevrey sense. The second part is an introduction to Ecalle's resurgence theory. A power series is said to be resurgent when its Borel transform is convergent and has good analytic continuation properties: there may be singularities but they must be isolated. The analysis of these singularities, through the so-called alien calculus, allows one to compare the various Borel-Laplace sums attached to the same resurgent 1-summable series. In the context of analytic difference-or-differential equations, this sheds light on the Stokes phenomenon. A few elementary or classical examples will be considered (the Euler series, the Stirling series, a less known example by Poincaré). Special attention must be devoted to non-linear operations: 1-summable series as well as resurgent series form algebras which are stable by composition. An example of a class of non-linear differential equations giving rise to resurgent solutions will be analyzed. The exposition requires only some familiarity with holomorphic functions of one complex variable.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Sauzin.pdf
FMSP Lectures
15:00-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Nicolai Reshetikhin (University of California, Berkeley)
Introduction to BV quantization III (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Reshetikhin.pdf
Nicolai Reshetikhin (University of California, Berkeley)
Introduction to BV quantization III (ENGLISH)
[ Abstract ]
The lectures will focus on Batalin-Vilkovisky (BV) framework for gauge field theories. We will start with examples of gauge theories such Yang-Mills, BF-theory, Chern-Simons and others. The Hamiltonian structure for field theories will be explained on these examples. Then the classical BV-BFV (Batalin-Fradkin-Vilkovisky) setting will be introduced as a Z-graded extension of the Hamiltonian structure of field theories. The AKSZ (Aleksandrov-Kontsevich-Swartz-Zaboronskij) construction of topological field theories will be introduced. We will construct corresponding BV-BFV theory and its extension to strata of all codimensions. We will also see that Chern-Simons theory, BF theory are of the AKSZ type. The geometry of BV theories is also known as derived geometry. The classical part will be followed by an outline of what is a quantum gauge theory and what is a path integral quantization of a classical gauge theory in the BV-BFV setting. Then we will discuss BV-integrals, fibered BV integrals and perturbative quantization.
[ Reference URL ]The lectures will focus on Batalin-Vilkovisky (BV) framework for gauge field theories. We will start with examples of gauge theories such Yang-Mills, BF-theory, Chern-Simons and others. The Hamiltonian structure for field theories will be explained on these examples. Then the classical BV-BFV (Batalin-Fradkin-Vilkovisky) setting will be introduced as a Z-graded extension of the Hamiltonian structure of field theories. The AKSZ (Aleksandrov-Kontsevich-Swartz-Zaboronskij) construction of topological field theories will be introduced. We will construct corresponding BV-BFV theory and its extension to strata of all codimensions. We will also see that Chern-Simons theory, BF theory are of the AKSZ type. The geometry of BV theories is also known as derived geometry. The classical part will be followed by an outline of what is a quantum gauge theory and what is a path integral quantization of a classical gauge theory in the BV-BFV setting. Then we will discuss BV-integrals, fibered BV integrals and perturbative quantization.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Reshetikhin.pdf
2015/10/14
FMSP Lectures
15:00-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Nicolai Reshetikhin (University of California, Berkeley)
Introduction to BV quantization II (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Reshetikhin.pdf
Nicolai Reshetikhin (University of California, Berkeley)
Introduction to BV quantization II (ENGLISH)
[ Abstract ]
The lectures will focus on Batalin-Vilkovisky (BV) framework for gauge field theories. We will start with examples of gauge theories such Yang-Mills, BF-theory, Chern-Simons and others. The Hamiltonian structure for field theories will be explained on these examples. Then the classical BV-BFV (Batalin-Fradkin-Vilkovisky) setting will be introduced as a Z-graded extension of the Hamiltonian structure of field theories. The AKSZ (Aleksandrov-Kontsevich-Swartz-Zaboronskij) construction of topological field theories will be introduced. We will construct corresponding BV-BFV theory and its extension to strata of all codimensions. We will also see that Chern-Simons theory, BF theory are of the AKSZ type. The geometry of BV theories is also known as derived geometry. The classical part will be followed by an outline of what is a quantum gauge theory and what is a path integral quantization of a classical gauge theory in the BV-BFV setting. Then we will discuss BV-integrals, fibered BV integrals and perturbative quantization.
[ Reference URL ]The lectures will focus on Batalin-Vilkovisky (BV) framework for gauge field theories. We will start with examples of gauge theories such Yang-Mills, BF-theory, Chern-Simons and others. The Hamiltonian structure for field theories will be explained on these examples. Then the classical BV-BFV (Batalin-Fradkin-Vilkovisky) setting will be introduced as a Z-graded extension of the Hamiltonian structure of field theories. The AKSZ (Aleksandrov-Kontsevich-Swartz-Zaboronskij) construction of topological field theories will be introduced. We will construct corresponding BV-BFV theory and its extension to strata of all codimensions. We will also see that Chern-Simons theory, BF theory are of the AKSZ type. The geometry of BV theories is also known as derived geometry. The classical part will be followed by an outline of what is a quantum gauge theory and what is a path integral quantization of a classical gauge theory in the BV-BFV setting. Then we will discuss BV-integrals, fibered BV integrals and perturbative quantization.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Reshetikhin.pdf
Operator Algebra Seminars
16:45-18:15 Room #118 (Graduate School of Math. Sci. Bldg.)
Shuhei Masumoto (Univ. Tokyo)
Fraisse Theory for Metric Structures (English)
Shuhei Masumoto (Univ. Tokyo)
Fraisse Theory for Metric Structures (English)
2015/10/13
FMSP Lectures
15:00-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Nicolai Reshetikhin (University of California, Berkeley)
Introduction to BV quantization I (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Reshetikhin.pdf
Nicolai Reshetikhin (University of California, Berkeley)
Introduction to BV quantization I (ENGLISH)
[ Abstract ]
The lectures will focus on Batalin-Vilkovisky (BV) framework for gauge field theories. We will start with examples of gauge theories such Yang-Mills, BF-theory, Chern-Simons and others. The Hamiltonian structure for field theories will be explained on these examples. Then the classical BV-BFV (Batalin-Fradkin-Vilkovisky) setting will be introduced as a Z-graded extension of the Hamiltonian structure of field theories. The AKSZ (Aleksandrov-Kontsevich-Swartz-Zaboronskij) construction of topological field theories will be introduced. We will construct corresponding BV-BFV theory and its extension to strata of all codimensions. We will also see that Chern-Simons theory, BF theory are of the AKSZ type. The geometry of BV theories is also known as derived geometry. The classical part will be followed by an outline of what is a quantum gauge theory and what is a path integral quantization of a classical gauge theory in the BV-BFV setting. Then we will discuss BV-integrals, fibered BV integrals and perturbative quantization.
[ Reference URL ]The lectures will focus on Batalin-Vilkovisky (BV) framework for gauge field theories. We will start with examples of gauge theories such Yang-Mills, BF-theory, Chern-Simons and others. The Hamiltonian structure for field theories will be explained on these examples. Then the classical BV-BFV (Batalin-Fradkin-Vilkovisky) setting will be introduced as a Z-graded extension of the Hamiltonian structure of field theories. The AKSZ (Aleksandrov-Kontsevich-Swartz-Zaboronskij) construction of topological field theories will be introduced. We will construct corresponding BV-BFV theory and its extension to strata of all codimensions. We will also see that Chern-Simons theory, BF theory are of the AKSZ type. The geometry of BV theories is also known as derived geometry. The classical part will be followed by an outline of what is a quantum gauge theory and what is a path integral quantization of a classical gauge theory in the BV-BFV setting. Then we will discuss BV-integrals, fibered BV integrals and perturbative quantization.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Reshetikhin.pdf
FMSP Lectures
15:00-16:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Jens Starke (Queen Mary University of London)
Implicit multiscale analysis of the macroscopic behaviour in microscopic models (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Starke.pdf
Jens Starke (Queen Mary University of London)
Implicit multiscale analysis of the macroscopic behaviour in microscopic models (ENGLISH)
[ Abstract ]
A numerical multiscale approach (equation-free analysis) is further improved in the framework of slow-fast dynamical systems and demonstrated for the example of a particle model for traffic flow. The method allows to perform numerical investigations of the macroscopic behavior of microscopically defined systems including continuation and bifurcation analysis on the coarse or macroscopic level where no explicit equations are available. This approach fills a gap in the analysis of many complex real-world applications including particle models with intermediate number of particles where the microscopic system is too large for a direct numerical analysis of the full system and too small to justify large-particle limits.
An implicit equation-free method is presented which reduces numerical errors of the equation-free analysis considerably. It can be shown that the implicitly defined coarse-level time stepper converges to the true dynamics on the slow manifold. The method is applied to perform a coarse bifurcation analysis of microscopic particle models describing car traffic on single lane highways. The results include an equation-free continuation of traveling wave solutions, identification of bifurcations as well as two-parameter continuations of bifurcation points. This is joint work with Christian Marschler and Jan Sieber.
[ Reference URL ]A numerical multiscale approach (equation-free analysis) is further improved in the framework of slow-fast dynamical systems and demonstrated for the example of a particle model for traffic flow. The method allows to perform numerical investigations of the macroscopic behavior of microscopically defined systems including continuation and bifurcation analysis on the coarse or macroscopic level where no explicit equations are available. This approach fills a gap in the analysis of many complex real-world applications including particle models with intermediate number of particles where the microscopic system is too large for a direct numerical analysis of the full system and too small to justify large-particle limits.
An implicit equation-free method is presented which reduces numerical errors of the equation-free analysis considerably. It can be shown that the implicitly defined coarse-level time stepper converges to the true dynamics on the slow manifold. The method is applied to perform a coarse bifurcation analysis of microscopic particle models describing car traffic on single lane highways. The results include an equation-free continuation of traveling wave solutions, identification of bifurcations as well as two-parameter continuations of bifurcation points. This is joint work with Christian Marschler and Jan Sieber.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Starke.pdf
FMSP Lectures
17:00-17:50 Room #002 (Graduate School of Math. Sci. Bldg.)
Hans-Otto Walther (University of Giessen)
Shilnikov chaos due to state-dependent delay, by means of the fixed point index (ENGLISH)
Hans-Otto Walther (University of Giessen)
Shilnikov chaos due to state-dependent delay, by means of the fixed point index (ENGLISH)
Tuesday Seminar of Analysis
16:50-18:20 Room #126 (Graduate School of Math. Sci. Bldg.)
David Sauzin (CNRS, France)
Nonlinear analysis with endlessly continuable functions (joint work with Shingo Kamimoto) (English)
David Sauzin (CNRS, France)
Nonlinear analysis with endlessly continuable functions (joint work with Shingo Kamimoto) (English)
[ Abstract ]
We give estimates for the convolution products of an arbitrary number of endlessly continuable functions. This allows us to deal with nonlinear operations for the corresponding resurgent series, e.g. substitution into a convergent power series.
We give estimates for the convolution products of an arbitrary number of endlessly continuable functions. This allows us to deal with nonlinear operations for the corresponding resurgent series, e.g. substitution into a convergent power series.
2015/10/06
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Sho Saito (Kavli IPMU)
Delooping theorem in K-theory (JAPANESE)
Sho Saito (Kavli IPMU)
Delooping theorem in K-theory (JAPANESE)
[ Abstract ]
There is an important special class of infinite dimensional vector spaces, formed by those called Tate vector spaces. Since their first appearance in Tate’s work on residues of differentials on curves, they have been playing important roles in several different contexts including the study of formal loop spaces and semi-infinite Hodge theory. They have more sophisticated linear algebraic invariant than finite dimensional vector spaces, for instance the dimension of a Tate vector spaces is not a single integer, but a torsor acted upon by the all integers, and the determinant of an automorphism is not a single invertible scalar, but a torsor acted upon by the all invertible scalars. In this talk I will show how a delooping theorem in K-theory provides a clarified perspective on this phenomenon, using the recently developed higher categorical framework of infinity-topoi.
There is an important special class of infinite dimensional vector spaces, formed by those called Tate vector spaces. Since their first appearance in Tate’s work on residues of differentials on curves, they have been playing important roles in several different contexts including the study of formal loop spaces and semi-infinite Hodge theory. They have more sophisticated linear algebraic invariant than finite dimensional vector spaces, for instance the dimension of a Tate vector spaces is not a single integer, but a torsor acted upon by the all integers, and the determinant of an automorphism is not a single invertible scalar, but a torsor acted upon by the all invertible scalars. In this talk I will show how a delooping theorem in K-theory provides a clarified perspective on this phenomenon, using the recently developed higher categorical framework of infinity-topoi.
Seminar on Mathematics for various disciplines
13:30-14:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Mohammad Hassan Farshbaf Shaker (Weierstrass Institute, Berlin)
Multi-material phase field approach to structural topology optimization and its relation to sharp interface approach (English)
Mohammad Hassan Farshbaf Shaker (Weierstrass Institute, Berlin)
Multi-material phase field approach to structural topology optimization and its relation to sharp interface approach (English)
[ Abstract ]
A phase field approach for structural topology optimization which allows for topology changes and multiple materials is analyzed. First order optimality conditions are rigorously derived and it is shown via formally matched asymptotic expansions that these conditions converge to classical first order conditions obtained in the context of shape calculus. Finally, we present several numerical results for mean compliance problems and a cost involving the least square error to a target displacement. This is joint work with Luise Blank, Harald Garcke and Vanessa Styles.
A phase field approach for structural topology optimization which allows for topology changes and multiple materials is analyzed. First order optimality conditions are rigorously derived and it is shown via formally matched asymptotic expansions that these conditions converge to classical first order conditions obtained in the context of shape calculus. Finally, we present several numerical results for mean compliance problems and a cost involving the least square error to a target displacement. This is joint work with Luise Blank, Harald Garcke and Vanessa Styles.
2015/10/05
Tokyo Probability Seminar
16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)
Satoshi Ishiwata (Faculty of Science, Yamagata University)
Heat kernel on connected sums of parabolic manifolds (日本語)
Satoshi Ishiwata (Faculty of Science, Yamagata University)
Heat kernel on connected sums of parabolic manifolds (日本語)
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Taiji Marugame (The Univ. of Tokyo)
On the volume expansion of the Blaschke metric on strictly convex domains
Taiji Marugame (The Univ. of Tokyo)
On the volume expansion of the Blaschke metric on strictly convex domains
[ Abstract ]
The Blaschke metric is a projectively invariant metric on a strictly convex domain in a projective manifold, which is a real analogue of the complete Kahler-Einstein metric on strictly pseudoconvex domains. We consider the asymptotic expansion of the volume of subdomains and construct a global conformal invariant of the boundary. We also give some variational formulas under a deformation of the domain.
The Blaschke metric is a projectively invariant metric on a strictly convex domain in a projective manifold, which is a real analogue of the complete Kahler-Einstein metric on strictly pseudoconvex domains. We consider the asymptotic expansion of the volume of subdomains and construct a global conformal invariant of the boundary. We also give some variational formulas under a deformation of the domain.
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