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Seminar information archive
Seminar information archive ～04/17｜Today's seminar 04/18 | Future seminars 04/19～
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.
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Evangelos Routis (IPMU)
Weighted Compactifications of Configuration Spaces (English)
Evangelos Routis (IPMU)
Weighted Compactifications of Configuration Spaces (English)
[ Abstract ]
In the early 90's, Fulton and MacPherson provided a natural and beautiful way of compactifying the configuration space F(X,n) of n distinct labeled points on an arbitrary nonsingular variety. In this talk, I will present an alternate compactification of F(X,n), which generalizes the work of Fulton and MacPherson and is parallel to Hassett's weighted generalization of the moduli space of n-pointed stable curves. After discussing its main properties, I will give a presentation of its intersection ring and as an application, I will describe the intersection ring of Hassett's spaces in genus 0. Finally, as time permits, I will discuss some additional moduli problems associated with weighted compactifications.
In the early 90's, Fulton and MacPherson provided a natural and beautiful way of compactifying the configuration space F(X,n) of n distinct labeled points on an arbitrary nonsingular variety. In this talk, I will present an alternate compactification of F(X,n), which generalizes the work of Fulton and MacPherson and is parallel to Hassett's weighted generalization of the moduli space of n-pointed stable curves. After discussing its main properties, I will give a presentation of its intersection ring and as an application, I will describe the intersection ring of Hassett's spaces in genus 0. Finally, as time permits, I will discuss some additional moduli problems associated with weighted compactifications.
2015/10/03
Harmonic Analysis Komaba Seminar
13:00-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Tomoya Kato (Nagoya University) 13:30-15:00
Embedding relations between $L^p$--Sobolev and $\alpha$--modulation spaces
(日本語)
Naohito Tomita (Osaka University) 15:30-17:00
On multilinear Fourier multipliers with minimal Sobolev regularity
(日本語)
Tomoya Kato (Nagoya University) 13:30-15:00
Embedding relations between $L^p$--Sobolev and $\alpha$--modulation spaces
(日本語)
Naohito Tomita (Osaka University) 15:30-17:00
On multilinear Fourier multipliers with minimal Sobolev regularity
(日本語)
2015/10/02
Geometry Colloquium
10:00-11:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Takahashi Ryosuke (Nagoya University, Graduate School of Mathematics)
Asymptotic stability for K¥"ahler-Ricci solitons (Japanese)
Takahashi Ryosuke (Nagoya University, Graduate School of Mathematics)
Asymptotic stability for K¥"ahler-Ricci solitons (Japanese)
[ Abstract ]
K¥"ahler-Ricci solitons arise from the geometric analysis, such as Hamilton’s Ricci flow, and have been studied extensively in recent years. It is expected that the existence of a canonical metric is closely related to some GIT stability of manifolds. For instance, Donaldson showed that any cscK polarized manifold with discrete automorphisms admits a sequence of balanced metrics and this sequence converges to the cscK metric. In this talk, we explain that the same result holds for K¥ahler-Ricci solitons. This generalizes a previous work of Berman-Witt Nystr¥"om, and is an analogous result on asymptotic relative Chow stability for extremal metrics obtained by Mabuchi.
K¥"ahler-Ricci solitons arise from the geometric analysis, such as Hamilton’s Ricci flow, and have been studied extensively in recent years. It is expected that the existence of a canonical metric is closely related to some GIT stability of manifolds. For instance, Donaldson showed that any cscK polarized manifold with discrete automorphisms admits a sequence of balanced metrics and this sequence converges to the cscK metric. In this talk, we explain that the same result holds for K¥ahler-Ricci solitons. This generalizes a previous work of Berman-Witt Nystr¥"om, and is an analogous result on asymptotic relative Chow stability for extremal metrics obtained by Mabuchi.
2015/09/30
Number Theory Seminar
17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Alan Lauder (University of Oxford)
Stark points and p-adic iterated integrals attached to modular forms of weight one (English)
Alan Lauder (University of Oxford)
Stark points and p-adic iterated integrals attached to modular forms of weight one (English)
[ Abstract ]
Given an elliptic curve over Q the only well-understood construction of global points is that of "Heegner points", which are defined over ring class fields of imaginary quadratic fields and are non-torsion only in rank one settings. I will present some new constructions and explicit formulae, in situations of rank one and two, of global points over ring class fields of real or imaginary quadratic fields, cyclotomic fields, and extensions of Q with Galois group A_4, S_4 or A_5. Our constructions and formulae are proven in certain cases - when they can be related to Heegner points - and conjectural, but supported by experimental evidence, otherwise. This is joint work with Henri Darmon and Victor Rotger.
Given an elliptic curve over Q the only well-understood construction of global points is that of "Heegner points", which are defined over ring class fields of imaginary quadratic fields and are non-torsion only in rank one settings. I will present some new constructions and explicit formulae, in situations of rank one and two, of global points over ring class fields of real or imaginary quadratic fields, cyclotomic fields, and extensions of Q with Galois group A_4, S_4 or A_5. Our constructions and formulae are proven in certain cases - when they can be related to Heegner points - and conjectural, but supported by experimental evidence, otherwise. This is joint work with Henri Darmon and Victor Rotger.
2015/09/29
PDE Real Analysis Seminar
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Tuomo Kuusi (Aalto University)
Nonlocal self-improving properties (English)
Tuomo Kuusi (Aalto University)
Nonlocal self-improving properties (English)
[ Abstract ]
The classical Gehring lemma for elliptic equations with measurable coefficients states that an energy solution, which is initially assumed to be $W^{1,2}$-Sobolev regular, is actually in a better Sobolev space space $W^{1,q}$ for some $q>2$. This is a consequence of a self-improving property that so-called reverse Hölder inequality implies. In the case of nonlocal equations a self-improving effect appears: Energy solutions are also more differentiable. This is a new, purely nonlocal phenomenon, which is not present in the local case. The proof relies on a nonlocal version of the Gehring lemma involving new exit time and dyadic decomposition arguments. This is a joint work with G. Mingione and Y. Sire.
The classical Gehring lemma for elliptic equations with measurable coefficients states that an energy solution, which is initially assumed to be $W^{1,2}$-Sobolev regular, is actually in a better Sobolev space space $W^{1,q}$ for some $q>2$. This is a consequence of a self-improving property that so-called reverse Hölder inequality implies. In the case of nonlocal equations a self-improving effect appears: Energy solutions are also more differentiable. This is a new, purely nonlocal phenomenon, which is not present in the local case. The proof relies on a nonlocal version of the Gehring lemma involving new exit time and dyadic decomposition arguments. This is a joint work with G. Mingione and Y. Sire.
Tuesday Seminar of Analysis
16:50-18:20 Room #126 (Graduate School of Math. Sci. Bldg.)
Otto Liess (University of Bologna, Italy)
On the Phragmén-Lindelöf principle for holomorphic functions and factor classes of higher order complex forms in several complex variables
Otto Liess (University of Bologna, Italy)
On the Phragmén-Lindelöf principle for holomorphic functions and factor classes of higher order complex forms in several complex variables
[ Abstract ]
In this talk we will discuss maximum principles in unbounded domains in one or several complex variables. We will mainly be interested in these principles for plurisubharmonic (in the one-dimensional case, "subharmonic") or holomorphic functions, when the principles are of
Phragmen-Lindel{＼"o}f principle (henceforth called "PL") type. It will turn out that for 2 or more complex variables it will be useful to study our principles together with associated principles for factor classes of complex (0,q) forms with growth type conditions at infinity.
In this abstract we only say something concerning the case of functions. We consider then an open set U in C^n in one or several complex variables. We assume that we are given two real-valued continuous functions f and g on U. We say that PL holds for plurisubharmonic (respectively for holomorphic) functions, if the following implication is true for every plurisubharmonic function $ ＼rho $ (respectively for every $ ＼rho $ of form log |h| with h holomorphic) on U: if we know that $ ＼rho ＼leq f$ on the boundary of U and if $ (＼rho - f)$ is bounded on U, then it must follow that $ ＼rho ＼leq g$ on U. ($＼rho ＼leq f$ on the boundary has the following meaning: for ever z in the boundary of U and for every sequence of points y_j in U which tends to z, we have limsup (＼rho - f)(y_j) leq 0.) A trivial condition under which PL is true, is when there exists a plurisubharmonic function u on U such that
(*) -g(z) ＼leq u(z) ＼leq - f(z) for every z in U.
In fact, if such a function exists, then we can apply the classical maximal principle for unbounded domains to the function $ ＼rho'= ＼rho+u$ to obtain at first $ ＼rho' ＼leq 0$ and then $ ＼rho ＼leq - u ＼leq g$. It is one of the main goals of the talk to explain how far (*) is from being also a necessary condition for PL. Some examples are intended to justify our approach and applications will be given to problems in convex analysis.
In this talk we will discuss maximum principles in unbounded domains in one or several complex variables. We will mainly be interested in these principles for plurisubharmonic (in the one-dimensional case, "subharmonic") or holomorphic functions, when the principles are of
Phragmen-Lindel{＼"o}f principle (henceforth called "PL") type. It will turn out that for 2 or more complex variables it will be useful to study our principles together with associated principles for factor classes of complex (0,q) forms with growth type conditions at infinity.
In this abstract we only say something concerning the case of functions. We consider then an open set U in C^n in one or several complex variables. We assume that we are given two real-valued continuous functions f and g on U. We say that PL holds for plurisubharmonic (respectively for holomorphic) functions, if the following implication is true for every plurisubharmonic function $ ＼rho $ (respectively for every $ ＼rho $ of form log |h| with h holomorphic) on U: if we know that $ ＼rho ＼leq f$ on the boundary of U and if $ (＼rho - f)$ is bounded on U, then it must follow that $ ＼rho ＼leq g$ on U. ($＼rho ＼leq f$ on the boundary has the following meaning: for ever z in the boundary of U and for every sequence of points y_j in U which tends to z, we have limsup (＼rho - f)(y_j) leq 0.) A trivial condition under which PL is true, is when there exists a plurisubharmonic function u on U such that
(*) -g(z) ＼leq u(z) ＼leq - f(z) for every z in U.
In fact, if such a function exists, then we can apply the classical maximal principle for unbounded domains to the function $ ＼rho'= ＼rho+u$ to obtain at first $ ＼rho' ＼leq 0$ and then $ ＼rho ＼leq - u ＼leq g$. It is one of the main goals of the talk to explain how far (*) is from being also a necessary condition for PL. Some examples are intended to justify our approach and applications will be given to problems in convex analysis.
2015/09/28
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Ryushi Goto (Osaka University)
Flat structures on moduli spaces of generalized complex surfaces
Ryushi Goto (Osaka University)
Flat structures on moduli spaces of generalized complex surfaces
[ Abstract ]
The 2 dimensional complex projective space $P^2$ is rigid as a complex manifold, however $P^2$ admits 2 dimensional moduli spaces of generalized complex structures which has a torsion free flat connection on a open strata. We show that logarithmic generalized complex structure with smooth elliptic curve as type changing loci has unobstructed deformations which are parametrized by an open set of the second de Rham cohomology group of the complement of type changing loci. Then we will construct moduli spaces of generalized del Pezzo surfaces. We further investigate deformations of logarithmic generalized complex structures in the cases of type changing loci with singularities. By using types of singularities, we obtain a stratification of moduli spaces of generalized complex structures on complex surfaces and it turns out that each strata corresponding to nodes admits a flat torsion free connection.
The 2 dimensional complex projective space $P^2$ is rigid as a complex manifold, however $P^2$ admits 2 dimensional moduli spaces of generalized complex structures which has a torsion free flat connection on a open strata. We show that logarithmic generalized complex structure with smooth elliptic curve as type changing loci has unobstructed deformations which are parametrized by an open set of the second de Rham cohomology group of the complement of type changing loci. Then we will construct moduli spaces of generalized del Pezzo surfaces. We further investigate deformations of logarithmic generalized complex structures in the cases of type changing loci with singularities. By using types of singularities, we obtain a stratification of moduli spaces of generalized complex structures on complex surfaces and it turns out that each strata corresponding to nodes admits a flat torsion free connection.
Tokyo Probability Seminar
16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)
Keiji Saito (Faculty of Science and Technology, Keio University)
Keiji Saito (Faculty of Science and Technology, Keio University)
2015/09/25
Colloquium
16:50-17:50 Room #大講義室 (Graduate School of Math. Sci. Bldg.)
Gerhard Huisken (The Mathematisches Forschungsinstitut Oberwolfach )
Mean curvature flow with surgery
http://www.mfo.de/about-the-institute/staff/prof.-dr.-gerhard-huisken
Gerhard Huisken (The Mathematisches Forschungsinstitut Oberwolfach )
Mean curvature flow with surgery
[ Abstract ]
We study the motion of hypersurfaces in a Riemannian manifold
with normal velocity equal to the mean curvature of the
evolving hypersurface. In general this quasilinear, parabolic
evolution system may have complicated singularities in finite time.
However, under natural assumptions such as embeddedness of the surface
and positivity of the mean curvature (case of 2-dimensional surfaces)
all singularities can be classified and developing "necks" can be
removed by a surgery procedure similar to techniques employed
by Hamilton and Perelman in the Ricci-flow of Riemannian metrics.
The lecture describes results and techniques for mean curvature flow
with surgery developed in joint work with C. Sinestrari and S. Brendle.
[ Reference URL ]We study the motion of hypersurfaces in a Riemannian manifold
with normal velocity equal to the mean curvature of the
evolving hypersurface. In general this quasilinear, parabolic
evolution system may have complicated singularities in finite time.
However, under natural assumptions such as embeddedness of the surface
and positivity of the mean curvature (case of 2-dimensional surfaces)
all singularities can be classified and developing "necks" can be
removed by a surgery procedure similar to techniques employed
by Hamilton and Perelman in the Ricci-flow of Riemannian metrics.
The lecture describes results and techniques for mean curvature flow
with surgery developed in joint work with C. Sinestrari and S. Brendle.
http://www.mfo.de/about-the-institute/staff/prof.-dr.-gerhard-huisken
Classical Analysis
16:00-17:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Damiran Tseveennamjil (Mongolian University of Life Sciences)
Confluence of general Schlesinger systems from the viewpoint of Twistor theory (JAPANESE)
Damiran Tseveennamjil (Mongolian University of Life Sciences)
Confluence of general Schlesinger systems from the viewpoint of Twistor theory (JAPANESE)
2015/09/17
Seminar on Probability and Statistics
15:00-16:10 Room #052 (Graduate School of Math. Sci. Bldg.)
Stefano Iacus (University of Milan)
The use of S4 classes and methods in the Yuima R package
Stefano Iacus (University of Milan)
The use of S4 classes and methods in the Yuima R package
[ Abstract ]
In this talk we present the basic concept of S4 classes and methods approach for object oriented programming in R. As a working example, we introduce the structure of the Yuima package for simulation and inference of stochastic differential equations. We will describe the basic classes and objects as well as some recent extensions which allows for Carma and Co-Garch processes handling in Yuima.
In this talk we present the basic concept of S4 classes and methods approach for object oriented programming in R. As a working example, we introduce the structure of the Yuima package for simulation and inference of stochastic differential equations. We will describe the basic classes and objects as well as some recent extensions which allows for Carma and Co-Garch processes handling in Yuima.
Infinite Analysis Seminar Tokyo
14:00-15:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Simon Wood (The Australian National University)
Classifying simple modules at admissible levels through
symmetric polynomials (ENGLISH)
Simon Wood (The Australian National University)
Classifying simple modules at admissible levels through
symmetric polynomials (ENGLISH)
[ Abstract ]
From infinite dimensional Lie algebras such as the Virasoro
algebra or affine Lie (super)algebras one can construct universal
vertex operator algebras. These vertex operator algebras are simple at
generic central charges or levels and only contain proper ideals at so
called admissible levels. The simple quotient vertex operator algebras
at these admissible levels are called minimal model algebras. In this
talk I will present free field realisations of the universal vertex
operator algebras and show how they allow one to elegantly classify
the simple modules over the simple quotient vertex operator algebras
by using a deep connection to symmetric polynomials.
From infinite dimensional Lie algebras such as the Virasoro
algebra or affine Lie (super)algebras one can construct universal
vertex operator algebras. These vertex operator algebras are simple at
generic central charges or levels and only contain proper ideals at so
called admissible levels. The simple quotient vertex operator algebras
at these admissible levels are called minimal model algebras. In this
talk I will present free field realisations of the universal vertex
operator algebras and show how they allow one to elegantly classify
the simple modules over the simple quotient vertex operator algebras
by using a deep connection to symmetric polynomials.
2015/09/11
FMSP Lectures
17:00-18:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Alexander Voronov (Univ. of Minnesota)
Operads and their applications to Mathematical Physics (ENGLISH)
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Voronov.pdf
Alexander Voronov (Univ. of Minnesota)
Operads and their applications to Mathematical Physics (ENGLISH)
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Voronov.pdf
2015/09/10
FMSP Lectures
17:00-18:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Alexander Voronov (Univ. of Minnesota)
Operads and their applications to Mathematical Physics (ENGLISH)
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Voronov.pdf
Alexander Voronov (Univ. of Minnesota)
Operads and their applications to Mathematical Physics (ENGLISH)
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Voronov.pdf
FMSP Lectures
15:30-16:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Zhi Chen (Hefei University of Technology)
Lifting of maps between surfaces (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_ZhiChen.pdf
Zhi Chen (Hefei University of Technology)
Lifting of maps between surfaces (ENGLISH)
[ Abstract ]
The Thom conjecture says the algebraic curves have minimal genus among those surfaces Imbedded in CP^2 having fixed degree. This conjecture was solved by Kronheimer and Mrowka by using Seiberg-Witten invariants. In this talk we try to understand the content of this conjecture. We will construct these imbedded surface with minimal genus explicitly, and present some kind of generalization of this conjecture.
[ Reference URL ]The Thom conjecture says the algebraic curves have minimal genus among those surfaces Imbedded in CP^2 having fixed degree. This conjecture was solved by Kronheimer and Mrowka by using Seiberg-Witten invariants. In this talk we try to understand the content of this conjecture. We will construct these imbedded surface with minimal genus explicitly, and present some kind of generalization of this conjecture.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_ZhiChen.pdf
2015/09/09
Number Theory Seminar
17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Emmanuel Ullmo (IHES)
The hyperbolic Ax-Lindemann conjecture (English)
Emmanuel Ullmo (IHES)
The hyperbolic Ax-Lindemann conjecture (English)
[ Abstract ]
The hyperbolic Ax Lindemann conjecture is a functional transcendental statement which describes the Zariski closure of "algebraic flows" on Shimura varieties. We will describe the proof of this conjecture and its consequences for the André-Oort conjecture. This is a joint work with Bruno Klingler and Andrei Yafaev.
The hyperbolic Ax Lindemann conjecture is a functional transcendental statement which describes the Zariski closure of "algebraic flows" on Shimura varieties. We will describe the proof of this conjecture and its consequences for the André-Oort conjecture. This is a joint work with Bruno Klingler and Andrei Yafaev.
2015/09/08
Seminar on Mathematics for various disciplines
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Monika Muszkieta (Wroclaw University of Technology)
Duality based approaches to total variation-like flows with applications to image processing (English)
Monika Muszkieta (Wroclaw University of Technology)
Duality based approaches to total variation-like flows with applications to image processing (English)
[ Abstract ]
During the last years, total variation models have became very popular in image processing and analysis. They have been used to solve such problems as image restoration, image deblurring or image inpainting. Their interesting and successful applications became the motivation for many authors to rigorous analysis of properties of solutions to the corresponding total variation flows. The main difficulty in numerical approximation of solutions to these flows is caused by the lack of di fferentiability of the total variation term, and the commonly used approach to overcome this difficulty consists in considering of the dual formulation. In the talk, we consider two total variation flow models. The first one is the anisotropic total variation flow on $L^2$ with additional regularization, and the second one, is the total variation flow on $H^{-s}$. We introduce duality based numerical schemes for approximate solutions to corresponding equations and present some applications to image processing.
This talk is based on joint work with Y. Giga, P. Mucha and P. Rybka.
During the last years, total variation models have became very popular in image processing and analysis. They have been used to solve such problems as image restoration, image deblurring or image inpainting. Their interesting and successful applications became the motivation for many authors to rigorous analysis of properties of solutions to the corresponding total variation flows. The main difficulty in numerical approximation of solutions to these flows is caused by the lack of di fferentiability of the total variation term, and the commonly used approach to overcome this difficulty consists in considering of the dual formulation. In the talk, we consider two total variation flow models. The first one is the anisotropic total variation flow on $L^2$ with additional regularization, and the second one, is the total variation flow on $H^{-s}$. We introduce duality based numerical schemes for approximate solutions to corresponding equations and present some applications to image processing.
This talk is based on joint work with Y. Giga, P. Mucha and P. Rybka.
Tuesday Seminar of Analysis
16:50-18:20 Room #126 (Graduate School of Math. Sci. Bldg.)
Haruya Mizutani (School of Science, Osaka University)
Global-in-time Strichartz estimates for Schr\"odinger equations with long-range repulsive potentials (Japanese)
Haruya Mizutani (School of Science, Osaka University)
Global-in-time Strichartz estimates for Schr\"odinger equations with long-range repulsive potentials (Japanese)
[ Abstract ]
We will discuss a resent result on global-in-time Strichartz estimates for Schr\"odinger equations with slowly decreasing repulsive potentials. If the potential is of very short-range type, there is a simple method due to Rodnianski-Schlag or Burq et al, which seems to be difficult to apply for the present case. The proof instead follows a similar line as in speaker’s resent joint work with J.-M. Bouclet. In particular, we employ both Morawetz type estimates and the methods of micro local analysis such as the Isozaki-Kitada parametrix, even in the low frequency regime.
We will discuss a resent result on global-in-time Strichartz estimates for Schr\"odinger equations with slowly decreasing repulsive potentials. If the potential is of very short-range type, there is a simple method due to Rodnianski-Schlag or Burq et al, which seems to be difficult to apply for the present case. The proof instead follows a similar line as in speaker’s resent joint work with J.-M. Bouclet. In particular, we employ both Morawetz type estimates and the methods of micro local analysis such as the Isozaki-Kitada parametrix, even in the low frequency regime.
2015/09/02
FMSP Lectures
17:00-18:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Alexander Voronov (Univ. of Minnesota)
Operads and their applications to Mathematical Physics (ENGLISH)
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Voronov.pdf
Alexander Voronov (Univ. of Minnesota)
Operads and their applications to Mathematical Physics (ENGLISH)
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Voronov.pdf
2015/08/31
thesis presentations
16:30-17:45 Room #128 (Graduate School of Math. Sci. Bldg.)
藤城 謙一 (東京大学大学院数理科学研究科)
Approximate Controllability, Non-homogeneous Boundary Value Problems and Inverse Source Problems for Fractional Diffusion Equations（非整数階拡散方程式に対する近似可制御性、非斉次境界値問題およびソース項決定逆問題） (JAPANESE)
藤城 謙一 (東京大学大学院数理科学研究科)
Approximate Controllability, Non-homogeneous Boundary Value Problems and Inverse Source Problems for Fractional Diffusion Equations（非整数階拡散方程式に対する近似可制御性、非斉次境界値問題およびソース項決定逆問題） (JAPANESE)
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