## Seminar information archive

Seminar information archive ～05/23｜Today's seminar 05/24 | Future seminars 05/25～

### 2015/10/13

#### FMSP Lectures

15:00-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)

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.)

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.)

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.)

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.)

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.)

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.)

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.)

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.)

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.)

Embedding relations between $L^p$--Sobolev and $\alpha$--modulation spaces

(日本語)

On multilinear Fourier multipliers with minimal Sobolev regularity

(日本語)

**Tomoya Kato**(Nagoya University) 13:30-15:00Embedding relations between $L^p$--Sobolev and $\alpha$--modulation spaces

(日本語)

**Naohito Tomita**(Osaka University) 15:30-17:00On 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.)

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.)

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.)

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.)

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.)

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)### 2015/09/25

#### Colloquium

16:50-17:50 Room #大講義室 (Graduate School of Math. Sci. Bldg.)

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.)

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.)

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.)

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.)

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.)

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.)

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.)

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.)

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 differentiability 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 differentiability 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.

< Previous 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135 Next >