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Seminar information archive
Seminar information archive ～04/18｜Today's seminar 04/19 | Future seminars 04/20～
2013/04/09
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Hiroyuki Fuji (The University of Tokyo)
Colored HOMFLY Homology and Super-A-polynomial (JAPANESE)
Hiroyuki Fuji (The University of Tokyo)
Colored HOMFLY Homology and Super-A-polynomial (JAPANESE)
[ Abstract ]
This talk is based on works in collaboration with S. Gukov, M. Stosic,
and P. Sulkowski. We study the colored HOMFLY homology for knots and
its asymptotic behavior. In recent years, the categorification of the
colored HOMFLY polynomial is proposed in term of homological
discussions via spectral sequence and physical discussions via refined
topological string, and these proposals give the same answer
miraculously. In this talk, we consider the asymptotic behavior of the
colored HOMFLY homology \\`a la the generalized volume conjecture, and
discuss the quantum structure of the colored HOMFLY homology for the
complete symmetric representations via the generalized A-polynomial
which we call “super-A-polynomial”.
This talk is based on works in collaboration with S. Gukov, M. Stosic,
and P. Sulkowski. We study the colored HOMFLY homology for knots and
its asymptotic behavior. In recent years, the categorification of the
colored HOMFLY polynomial is proposed in term of homological
discussions via spectral sequence and physical discussions via refined
topological string, and these proposals give the same answer
miraculously. In this talk, we consider the asymptotic behavior of the
colored HOMFLY homology \\`a la the generalized volume conjecture, and
discuss the quantum structure of the colored HOMFLY homology for the
complete symmetric representations via the generalized A-polynomial
which we call “super-A-polynomial”.
Lie Groups and Representation Theory
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Atsumu Sasaki (Tokai University)
A characterization of non-tube type Hermitian symmetric spaces by visible actions
(JAPANESE)
Atsumu Sasaki (Tokai University)
A characterization of non-tube type Hermitian symmetric spaces by visible actions
(JAPANESE)
[ Abstract ]
We consider a non-symmetric complex Stein manifold D
which is realized as a line bundle over the complexification of a non-compact irreducible Hermitian symmetric space G/K.
In this talk, we will explain that the compact group action on D is strongly visible in the sense of Toshiyuki Kobayashi if and only if G/K is of non-tube type.
In particular, we focus on our construction of slice which meets every orbit in D from the viewpoint of group theory, namely,
we find an A-part of a generalized Cartan decomposition for homogeneous space D.
We note that our choice of A-part is an abelian.
We consider a non-symmetric complex Stein manifold D
which is realized as a line bundle over the complexification of a non-compact irreducible Hermitian symmetric space G/K.
In this talk, we will explain that the compact group action on D is strongly visible in the sense of Toshiyuki Kobayashi if and only if G/K is of non-tube type.
In particular, we focus on our construction of slice which meets every orbit in D from the viewpoint of group theory, namely,
we find an A-part of a generalized Cartan decomposition for homogeneous space D.
We note that our choice of A-part is an abelian.
2013/04/08
Seminar on Geometric Complex Analysis
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Akito Futaki (University of Tokyo)
K\\"ahler-Einstein metrics and K stability (JAPANESE)
Akito Futaki (University of Tokyo)
K\\"ahler-Einstein metrics and K stability (JAPANESE)
[ Abstract ]
I will describe an outline of the proof of the equivalence between the existence of K\\"ahler-Einstein metrics and K-stablity after Chen-Donaldson-Sun and Tian.
I will describe an outline of the proof of the equivalence between the existence of K\\"ahler-Einstein metrics and K-stablity after Chen-Donaldson-Sun and Tian.
2013/04/02
Lie Groups and Representation Theory
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Yoshiki Oshima (Kavli IPMU, the University of Tokyo)
Discrete branching laws of Zuckerman's derived functor modules (JAPANESE)
Yoshiki Oshima (Kavli IPMU, the University of Tokyo)
Discrete branching laws of Zuckerman's derived functor modules (JAPANESE)
[ Abstract ]
We consider the restriction of Zuckerman's derived functor modules with respect to symmetric pairs of real reductive groups. When they are discretely decomposable, explicit formulas for the branching laws are obtained by using a realization as D-module on the flag variety and the generalized BGG resolution. In this talk we would like to illustrate how to derive the formulas with a few examples.
We consider the restriction of Zuckerman's derived functor modules with respect to symmetric pairs of real reductive groups. When they are discretely decomposable, explicit formulas for the branching laws are obtained by using a realization as D-module on the flag variety and the generalized BGG resolution. In this talk we would like to illustrate how to derive the formulas with a few examples.
2013/03/30
Infinite Analysis Seminar Tokyo
13:30-15:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Simon Wood (Kavli IPMU)
On the extended algebra of type sl_2 at positive rational level (ENGLISH)
Simon Wood (Kavli IPMU)
On the extended algebra of type sl_2 at positive rational level (ENGLISH)
[ Abstract ]
I will be presenting my recent work with Akihiro Tsuchiya
(arXiv:1302.6435).
I will explain how to construct a certain VOA called the "extended
algebra of type sl_2 at positive rational level"
as a subVOA of a lattice VOA, by means of screening operators. I will
then show that this VOA carries a kind of exterior sl_2 action and then
show how one can compute the structure Zhu's algebra and the Poisson
algebra as well as classify all simple modules by using the screening
operators and the sl_2 action. Important concepts such as screening
operators or Zhu's algebra and the Poisson algebra of a VOA will be
reviewed in the talk.
I will be presenting my recent work with Akihiro Tsuchiya
(arXiv:1302.6435).
I will explain how to construct a certain VOA called the "extended
algebra of type sl_2 at positive rational level"
as a subVOA of a lattice VOA, by means of screening operators. I will
then show that this VOA carries a kind of exterior sl_2 action and then
show how one can compute the structure Zhu's algebra and the Poisson
algebra as well as classify all simple modules by using the screening
operators and the sl_2 action. Important concepts such as screening
operators or Zhu's algebra and the Poisson algebra of a VOA will be
reviewed in the talk.
2013/03/19
Tuesday Seminar on Topology
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Keiko Kawamuro (University of Iowa)
Open book foliation and application to contact topology (ENGLISH)
Keiko Kawamuro (University of Iowa)
Open book foliation and application to contact topology (ENGLISH)
[ Abstract ]
Open book foliation is a generalization of Birman and Menasco's braid foliation. Any 3-manifold admits open book decompositions. Open book foliation is a singular foliation on an embedded surface, and is define by the intersection of a surface and the pages of the open book decomposition. By Giroux's identification of open books and contact structures one can use open book foliation method to study contact structures. In this talk I define the open book foliation and show some applications to contact topology. This is joint work with Tetsuya Ito (University of British Columbia).
Open book foliation is a generalization of Birman and Menasco's braid foliation. Any 3-manifold admits open book decompositions. Open book foliation is a singular foliation on an embedded surface, and is define by the intersection of a surface and the pages of the open book decomposition. By Giroux's identification of open books and contact structures one can use open book foliation method to study contact structures. In this talk I define the open book foliation and show some applications to contact topology. This is joint work with Tetsuya Ito (University of British Columbia).
2013/03/18
Operator Algebra Seminars
16:00-17:30 Room #118 (Graduate School of Math. Sci. Bldg.)
Hiroshi Ando (IHES)
Ultraproducts of von Neumann algebras (JAPANESE)
Hiroshi Ando (IHES)
Ultraproducts of von Neumann algebras (JAPANESE)
Colloquium
15:00-17:30 Room #050 (Graduate School of Math. Sci. Bldg.)
NOGUCHI, Junjiro (University of Tokyo) 15:00-16:00
Value distribution theory and analytic function theory in several variables (JAPANESE)
OSHIMA, Toshio (University of Tokyo) 16:30-17:30
My fifty years of differential equations (JAPANESE)
NOGUCHI, Junjiro (University of Tokyo) 15:00-16:00
Value distribution theory and analytic function theory in several variables (JAPANESE)
OSHIMA, Toshio (University of Tokyo) 16:30-17:30
My fifty years of differential equations (JAPANESE)
2013/03/15
Operator Algebra Seminars
15:45-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Lucio Cirio (Univ. M\"unster) 15:45-16:45
Infinitesimal 2-Yang-Baxter operators from a categorification
of the Knizhnik-Zamolodchikov connection (ENGLISH)
Sutanu Roy (Univ. G\"ottingen) 17:00-18:00
Twisted tensor product of $C^*$-algebras (ENGLISH)
Lucio Cirio (Univ. M\"unster) 15:45-16:45
Infinitesimal 2-Yang-Baxter operators from a categorification
of the Knizhnik-Zamolodchikov connection (ENGLISH)
Sutanu Roy (Univ. G\"ottingen) 17:00-18:00
Twisted tensor product of $C^*$-algebras (ENGLISH)
Numerical Analysis Seminar
10:00-12:15 Room #056 (Graduate School of Math. Sci. Bldg.)
Irene Vignon-Clementel (INRIA Paris Rocquencourt )
Complex flow at the boundaries of branched models: numerical aspects (ENGLISH)
[ Reference URL ]
http://www.infsup.jp/utnas/
Irene Vignon-Clementel (INRIA Paris Rocquencourt )
Complex flow at the boundaries of branched models: numerical aspects (ENGLISH)
[ Reference URL ]
http://www.infsup.jp/utnas/
Operator Algebra Seminars
14:30-15:30 Room #118 (Graduate School of Math. Sci. Bldg.)
Stefano Rossi (Univ. Roma II)
The connected component of a compact quantum group (ENGLISH)
Stefano Rossi (Univ. Roma II)
The connected component of a compact quantum group (ENGLISH)
Operator Algebra Seminars
13:15-14:15 Room #118 (Graduate School of Math. Sci. Bldg.)
Jean Roydor (Univ. Bordeaux)
Two Amir-Cambern type theorems for $C^*$-algebras (ENGLISH)
Jean Roydor (Univ. Bordeaux)
Two Amir-Cambern type theorems for $C^*$-algebras (ENGLISH)
PDE Real Analysis Seminar
10:30-11:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Caterina Zeppieri (Universität Münster)
Geometric rigidity for incompatible fields and an application to strain-gradient plasticity (ENGLISH)
Caterina Zeppieri (Universität Münster)
Geometric rigidity for incompatible fields and an application to strain-gradient plasticity (ENGLISH)
[ Abstract ]
Motivated by the study of nonlinear plane elasticity in presence of edge dislocations, in this talk we show that in dimension two the Friesecke, James, and Müller Rigidity Estimate holds true also for matrix-fields with nonzero curl, modulo an error depending on the total mass of the curl.
The above generalised rigidity is then used to derive a strain-gradient model for plasticity from semi-discrete nonlinear dislocation energies by Gamma-convergence.
The above results are obtained in collaboration with S. Müller (University of Bonn, Germany) and L. Scardia (University of Glasgow, UK).
Motivated by the study of nonlinear plane elasticity in presence of edge dislocations, in this talk we show that in dimension two the Friesecke, James, and Müller Rigidity Estimate holds true also for matrix-fields with nonzero curl, modulo an error depending on the total mass of the curl.
The above generalised rigidity is then used to derive a strain-gradient model for plasticity from semi-discrete nonlinear dislocation energies by Gamma-convergence.
The above results are obtained in collaboration with S. Müller (University of Bonn, Germany) and L. Scardia (University of Glasgow, UK).
2013/03/11
Operator Algebra Seminars
09:45-12:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Tristan Bice (York Univ.) 09:45-10:45
Traces and Ultrapowers (ENGLISH)
David Penneys (Univ. Toronto) 11:00-12:00
Constructing subfactors with jellyfish (ENGLISH)
Tristan Bice (York Univ.) 09:45-10:45
Traces and Ultrapowers (ENGLISH)
David Penneys (Univ. Toronto) 11:00-12:00
Constructing subfactors with jellyfish (ENGLISH)
Operator Algebra Seminars
13:30-18:15 Room #123 (Graduate School of Math. Sci. Bldg.)
Danny Hey (Univ. Toronto) 13:30-14:30
Classification and the Toms-Winter Conjecture (ENGLISH)
Stephen Curran (UCLA) 14:45-15:45
Free probability and planar algebras (ENGLISH)
Rasmus Bentmann (Univ. Copenhagen) 16:00-17:00
Kirchberg $X$-algebras with real rank zero and intermediate cancellation (ENGLISH)
Luis Santiago-Moreno (Univ. Oregon) 17:15-18:15
Classifying $C^*$-algebras up to W-stability (ENGLISH)
Danny Hey (Univ. Toronto) 13:30-14:30
Classification and the Toms-Winter Conjecture (ENGLISH)
Stephen Curran (UCLA) 14:45-15:45
Free probability and planar algebras (ENGLISH)
Rasmus Bentmann (Univ. Copenhagen) 16:00-17:00
Kirchberg $X$-algebras with real rank zero and intermediate cancellation (ENGLISH)
Luis Santiago-Moreno (Univ. Oregon) 17:15-18:15
Classifying $C^*$-algebras up to W-stability (ENGLISH)
GCOE Seminars
14:45-15:45 Room #123 (Graduate School of Math. Sci. Bldg.)
Stephen Curran (UCLA)
Free probability and planar algebras (ENGLISH)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/mini2013-4.htm
Stephen Curran (UCLA)
Free probability and planar algebras (ENGLISH)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/mini2013-4.htm
2013/03/08
FMSP Lectures
10:30-12:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Benjamin Burton (The University of Queensland, Australia)
Knots, algorithms and linear programming: the quest to solve unknot recognition in polynomial time (ENGLISH)
Benjamin Burton (The University of Queensland, Australia)
Knots, algorithms and linear programming: the quest to solve unknot recognition in polynomial time (ENGLISH)
[ Abstract ]
In this talk we explore new approaches to the old and difficult computational problem of unknot recognition. Although the best known algorithms for this problem run in exponential time, there is increasing evidence that a polynomial time solution might be possible. We outline several promising approaches, in which computational geometry, linear programming and greedy algorithms all play starring roles. We finish with a new algorithm that combines techniques from topology and combinatorial optimisation, which is the first to exhibit "real world" polynomial time behaviour: although it is still exponential time in theory, exhaustive experimentation shows that this algorithm can solve unknot recognition for "practical" inputs by running just a linear number of linear programs.
This is joint work with Melih Ozlen.
In this talk we explore new approaches to the old and difficult computational problem of unknot recognition. Although the best known algorithms for this problem run in exponential time, there is increasing evidence that a polynomial time solution might be possible. We outline several promising approaches, in which computational geometry, linear programming and greedy algorithms all play starring roles. We finish with a new algorithm that combines techniques from topology and combinatorial optimisation, which is the first to exhibit "real world" polynomial time behaviour: although it is still exponential time in theory, exhaustive experimentation shows that this algorithm can solve unknot recognition for "practical" inputs by running just a linear number of linear programs.
This is joint work with Melih Ozlen.
2013/03/07
Seminar on Probability and Statistics
14:50-16:00 Room #006 (Graduate School of Math. Sci. Bldg.)
MAESONO, Yoshihiko (Kyushu University)
Smoothing of sign test and approximation of its p-value (JAPANESE)
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/16.html
MAESONO, Yoshihiko (Kyushu University)
Smoothing of sign test and approximation of its p-value (JAPANESE)
[ Abstract ]
In this talk we discuss theoretical properties of smoothed sign test, which based on a kernel estimator of the underlying distribution function of data. We show the smoothed sign test is equivalent to the usual sign test in the sense of Pitman efficiency, and its main term of the variance does not depend on the distribution of the population, under the null hypothesis. Though smoothed sign test is not distribution-free, we can obtain Edgeworth expansion which does not depend on the distribution. This is a joint work with Ms. Mengxin Lu of Kyushu University.
[ Reference URL ]In this talk we discuss theoretical properties of smoothed sign test, which based on a kernel estimator of the underlying distribution function of data. We show the smoothed sign test is equivalent to the usual sign test in the sense of Pitman efficiency, and its main term of the variance does not depend on the distribution of the population, under the null hypothesis. Though smoothed sign test is not distribution-free, we can obtain Edgeworth expansion which does not depend on the distribution. This is a joint work with Ms. Mengxin Lu of Kyushu University.
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/16.html
2013/03/06
Lectures
16:00-17:30 Room #117 (Graduate School of Math. Sci. Bldg.)
Frederic Le Roux (Institut de Mathematiques de Jussieu, Universite Pierre et Marie Curie)
The rotation set around a fixed point for surface homeomorphisms. (ENGLISH)
Frederic Le Roux (Institut de Mathematiques de Jussieu, Universite Pierre et Marie Curie)
The rotation set around a fixed point for surface homeomorphisms. (ENGLISH)
[ Abstract ]
We propose two definitions of a local rotation set. As applications, one
gets some criteria for the existence of periodic orbits, and a clear
explanation of Gambaudo-Le Calvez-Pecou's version of the Naishul theorem:
for surface diffeomorphisms, the rotation number of the derivative at a
fixed point which is not a sink nor a source is a topological invariant.
Tha local rotation set also provide an unexpected topological
characterization for the parabolic fixed points of holomorphic maps.
We propose two definitions of a local rotation set. As applications, one
gets some criteria for the existence of periodic orbits, and a clear
explanation of Gambaudo-Le Calvez-Pecou's version of the Naishul theorem:
for surface diffeomorphisms, the rotation number of the derivative at a
fixed point which is not a sink nor a source is a topological invariant.
Tha local rotation set also provide an unexpected topological
characterization for the parabolic fixed points of holomorphic maps.
2013/03/05
Seminar on Probability and Statistics
14:50-16:00 Room #006 (Graduate School of Math. Sci. Bldg.)
TANAKA, Fuyuhiko (University of Tokyo)
ベイズ予測に基いた波動関数の推定と純粋状態モデルの無情報事前分布 (JAPANESE)
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/15.html
TANAKA, Fuyuhiko (University of Tokyo)
ベイズ予測に基いた波動関数の推定と純粋状態モデルの無情報事前分布 (JAPANESE)
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/15.html
GCOE Seminars
17:00-18:00 Room #270 (Graduate School of Math. Sci. Bldg.)
Oleg Emanouilov (Colorado State University)
Uniqueness for inverse boundary value problems by Dirichlet-to
-Neumann map on subboundaries (ENGLISH)
Oleg Emanouilov (Colorado State University)
Uniqueness for inverse boundary value problems by Dirichlet-to
-Neumann map on subboundaries (ENGLISH)
[ Abstract ]
We consider inverse boundary value problems for elliptic equations of second order and survey recent results on the uniqueness mainly by partial boundary data. In particular, in two dimensions, we show uniqueness results by means of Dirichlet data supported on an arbitrary subboundary $\\widetilde\\Gamma$ and Neumann data measured on $\\widetilde\\Gamma$. We describe the key idea for the proof: complex geometric optics solutions which are constructed by a Carleman estimate. Also we show the uniqueness by Dirichlet-to-Neumann map on subboundaries in three dimensions.
We consider inverse boundary value problems for elliptic equations of second order and survey recent results on the uniqueness mainly by partial boundary data. In particular, in two dimensions, we show uniqueness results by means of Dirichlet data supported on an arbitrary subboundary $\\widetilde\\Gamma$ and Neumann data measured on $\\widetilde\\Gamma$. We describe the key idea for the proof: complex geometric optics solutions which are constructed by a Carleman estimate. Also we show the uniqueness by Dirichlet-to-Neumann map on subboundaries in three dimensions.
2013/03/04
GCOE Seminars
17:00-18:00 Room #270 (Graduate School of Math. Sci. Bldg.)
M.I. Tribelsky (Landau Institute)
Resonant Light Scattering by Small Particles (ENGLISH)
M.I. Tribelsky (Landau Institute)
Resonant Light Scattering by Small Particles (ENGLISH)
[ Abstract ]
The problem of light scattering by a small spherical particle is studied within the framework of the exact solution of the Maxwell equations. It is shown that if imaginary part of the dielectric permittivity of the particle is small enough, the problem exhibits sharp giant resonances with very unusual properties. Specifically, the characteristic values of the electric and magnetic fields inside the particle and in its immediate vicinity are singular in the particle size. In non-dissipative case these quantities do not have definite limits when the radius of the particle tends to zero. The field of the Poynting vector in the immediate vicinity of the particle includes singular points, whose number, types and positions are very sensitive to the changes in the incident light frequency. As an example a bifurcation diagram, describing the behavior of the singular points in the vicinity of the dipole resonance for a particle with a certain fixed size is discussed.
The problem of light scattering by a small spherical particle is studied within the framework of the exact solution of the Maxwell equations. It is shown that if imaginary part of the dielectric permittivity of the particle is small enough, the problem exhibits sharp giant resonances with very unusual properties. Specifically, the characteristic values of the electric and magnetic fields inside the particle and in its immediate vicinity are singular in the particle size. In non-dissipative case these quantities do not have definite limits when the radius of the particle tends to zero. The field of the Poynting vector in the immediate vicinity of the particle includes singular points, whose number, types and positions are very sensitive to the changes in the incident light frequency. As an example a bifurcation diagram, describing the behavior of the singular points in the vicinity of the dipole resonance for a particle with a certain fixed size is discussed.
2013/02/28
GCOE Seminars
16:00-17:00 Room #270 (Graduate School of Math. Sci. Bldg.)
Mourad Choulli (Univ. Lorraine)
Stability of the determination of the surface impedance of an
obstacle from the scattering amplitude (ENGLISH)
Mourad Choulli (Univ. Lorraine)
Stability of the determination of the surface impedance of an
obstacle from the scattering amplitude (ENGLISH)
[ Abstract ]
In this joint work with Mourad Bellassoued and Aymen Jbalia, we prove a stability estimate of logarithmic type for the inverse problem consisting in the determination of the surface impedance of an obstacle from the scattering amplitude. We present a simple and direct proof which is essentially based on an elliptic Carleman inequality.
In this joint work with Mourad Bellassoued and Aymen Jbalia, we prove a stability estimate of logarithmic type for the inverse problem consisting in the determination of the surface impedance of an obstacle from the scattering amplitude. We present a simple and direct proof which is essentially based on an elliptic Carleman inequality.
GCOE Seminars
17:00-18:00 Room #270 (Graduate School of Math. Sci. Bldg.)
Kazufumi Ito (North Carolina State Univ.)
$L_0$ optimization and Lagrange multiplier (ENGLISH)
Kazufumi Ito (North Carolina State Univ.)
$L_0$ optimization and Lagrange multiplier (ENGLISH)
[ Abstract ]
$L_p$ optimization with $p ¥in[0,1)$ is investigated. The difficulty of natural lack of weak lower-semicontinuity is addressed and the Lagrange multiplier theory is developed. Existence results and necessary optimality conditions are obtained, and the semismooth Newton method using the primal-dual active set is developed. The theory and algorithm are demonstrated for the case of optimal control problems. A maximum principle is derived and existence of controls, in some cases relaxed controls, is proved.
$L_p$ optimization with $p ¥in[0,1)$ is investigated. The difficulty of natural lack of weak lower-semicontinuity is addressed and the Lagrange multiplier theory is developed. Existence results and necessary optimality conditions are obtained, and the semismooth Newton method using the primal-dual active set is developed. The theory and algorithm are demonstrated for the case of optimal control problems. A maximum principle is derived and existence of controls, in some cases relaxed controls, is proved.
2013/02/27
GCOE Seminars
10:00-11:00 Room #270 (Graduate School of Math. Sci. Bldg.)
Dietmar Hoemberg (Weierstrass Institute)
Sufficient optimality conditions for a semi-linear parabolic system related to multiphase steel production (ENGLISH)
Dietmar Hoemberg (Weierstrass Institute)
Sufficient optimality conditions for a semi-linear parabolic system related to multiphase steel production (ENGLISH)
[ Abstract ]
Multiphase steels combine good formability properties with high strength and have therefore become important construction materials, especially in automotive industry. The standard process route is hot rolling with subsequent controlled cooling to adjust the desired phase mixture. In the first part of the talk a phenomenological model for the austenite ferrite phase transition is developed in terms of a nucleation and growth process, where the growth rate depends on the carbon concentration in austenite. The approach allows for further extensions, e.g., to account for a speed up of nucleation due to deformation of austenite grains. The model is coupled with an energy balance to describe the phase transitions on a run-out table after hot rolling. Here, the most important control parameters are the amount of water flowing per time and the feed velocity of the strip. The spatial flux profile of the water nozzles has been identified from experiments.
Since the process window for the adjustment of the phase composition is very tight the computation of optimal process parameters is an important task also in practice. This is discussed in the second part of the talk using a classical optimal control approach, where a coefficient in the Robin boundary condition acts as the control. I will discuss necessary and sufficient optimality conditions, describe a SQP-approach for its numerical solution and conclude with some numerical results.
(joint work with K. Krumbiegel and N. Togobytska, WIAS)
Multiphase steels combine good formability properties with high strength and have therefore become important construction materials, especially in automotive industry. The standard process route is hot rolling with subsequent controlled cooling to adjust the desired phase mixture. In the first part of the talk a phenomenological model for the austenite ferrite phase transition is developed in terms of a nucleation and growth process, where the growth rate depends on the carbon concentration in austenite. The approach allows for further extensions, e.g., to account for a speed up of nucleation due to deformation of austenite grains. The model is coupled with an energy balance to describe the phase transitions on a run-out table after hot rolling. Here, the most important control parameters are the amount of water flowing per time and the feed velocity of the strip. The spatial flux profile of the water nozzles has been identified from experiments.
Since the process window for the adjustment of the phase composition is very tight the computation of optimal process parameters is an important task also in practice. This is discussed in the second part of the talk using a classical optimal control approach, where a coefficient in the Robin boundary condition acts as the control. I will discuss necessary and sufficient optimality conditions, describe a SQP-approach for its numerical solution and conclude with some numerical results.
(joint work with K. Krumbiegel and N. Togobytska, WIAS)
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