## Seminar information archive

Seminar information archive ～02/20｜Today's seminar 02/21 | Future seminars 02/22～

#### Seminar on Probability and Statistics

13:00-16:40 Room #052 (Graduate School of Math. Sci. Bldg.)

### 2015/10/16

#### FMSP Lectures

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

Introduction to BV quantization IV (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Reshetikhin.pdf

**Nicolai Reshetikhin**(University of California, Berkeley)Introduction to BV quantization IV (ENGLISH)

[ Abstract ]

The lectures will focus on Batalin-Vilkovisky (BV) framework for gauge field theories. We will start with examples of gauge theories such Yang-Mills, BF-theory, Chern-Simons and others. The Hamiltonian structure for field theories will be explained on these examples. Then the classical BV-BFV (Batalin-Fradkin-Vilkovisky) setting will be introduced as a Z-graded extension of the Hamiltonian structure of field theories. The AKSZ (Aleksandrov-Kontsevich-Swartz-Zaboronskij) construction of topological field theories will be introduced. We will construct corresponding BV-BFV theory and its extension to strata of all codimensions. We will also see that Chern-Simons theory, BF theory are of the AKSZ type. The geometry of BV theories is also known as derived geometry. The classical part will be followed by an outline of what is a quantum gauge theory and what is a path integral quantization of a classical gauge theory in the BV-BFV setting. Then we will discuss BV-integrals, fibered BV integrals and perturbative quantization.

[ Reference URL ]The lectures will focus on Batalin-Vilkovisky (BV) framework for gauge field theories. We will start with examples of gauge theories such Yang-Mills, BF-theory, Chern-Simons and others. The Hamiltonian structure for field theories will be explained on these examples. Then the classical BV-BFV (Batalin-Fradkin-Vilkovisky) setting will be introduced as a Z-graded extension of the Hamiltonian structure of field theories. The AKSZ (Aleksandrov-Kontsevich-Swartz-Zaboronskij) construction of topological field theories will be introduced. We will construct corresponding BV-BFV theory and its extension to strata of all codimensions. We will also see that Chern-Simons theory, BF theory are of the AKSZ type. The geometry of BV theories is also known as derived geometry. The classical part will be followed by an outline of what is a quantum gauge theory and what is a path integral quantization of a classical gauge theory in the BV-BFV setting. Then we will discuss BV-integrals, fibered BV integrals and perturbative quantization.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Reshetikhin.pdf

#### Geometry Colloquium

10:00-11:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Meromorphic connections on the Riemann sphere and quiver varieties (Japanese)

**Daisuke Yamakawa**(Tokyo Institute of Technology)Meromorphic connections on the Riemann sphere and quiver varieties (Japanese)

[ Abstract ]

I will show that some moduli spaces of meromorphic connections on the Riemann sphere are isomorphic to Nakajima's quiver varieties as complex symplectic manifolds (joint work with Kazuki Hiroe). This was conjectured by Boalch and generalizes Crawley-Boevey's result for logarithmic connections. Also I will mention Weyl group symmetries of isomonodromic deformations of meromorphic connections.

I will show that some moduli spaces of meromorphic connections on the Riemann sphere are isomorphic to Nakajima's quiver varieties as complex symplectic manifolds (joint work with Kazuki Hiroe). This was conjectured by Boalch and generalizes Crawley-Boevey's result for logarithmic connections. Also I will mention Weyl group symmetries of isomonodromic deformations of meromorphic connections.

### 2015/10/15

#### FMSP Lectures

15:00-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Introduction to 1-summability and resurgence (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Sauzin.pdf

**David Sauzin**(CNRS - Centro di Ricerca Matematica Ennio De Giorgi Scuola Normale Superiore di Pisa)Introduction to 1-summability and resurgence (ENGLISH)

[ Abstract ]

The theories of summability and resurgence deal with the mathematical use of certain divergent power series. The first part of the lecure is an introduction to 1-summability. The definitions rely on the formal Borel transform and the Laplace transform along an arbitrary direction of the complex plane. Given an arc of directions, if a power series is 1-summable in that arc, then one can attach to it a Borel-Laplace sum, i.e. a holomorphic function defined in a large enough sector and asymptotic to that power series in Gevrey sense. The second part is an introduction to Ecalle's resurgence theory. A power series is said to be resurgent when its Borel transform is convergent and has good analytic continuation properties: there may be singularities but they must be isolated. The analysis of these singularities, through the so-called alien calculus, allows one to compare the various Borel-Laplace sums attached to the same resurgent 1-summable series. In the context of analytic difference-or-differential equations, this sheds light on the Stokes phenomenon. A few elementary or classical examples will be considered (the Euler series, the Stirling series, a less known example by Poincaré). Special attention must be devoted to non-linear operations: 1-summable series as well as resurgent series form algebras which are stable by composition. An example of a class of non-linear differential equations giving rise to resurgent solutions will be analyzed. The exposition requires only some familiarity with holomorphic functions of one complex variable.

[ Reference URL ]The theories of summability and resurgence deal with the mathematical use of certain divergent power series. The first part of the lecure is an introduction to 1-summability. The definitions rely on the formal Borel transform and the Laplace transform along an arbitrary direction of the complex plane. Given an arc of directions, if a power series is 1-summable in that arc, then one can attach to it a Borel-Laplace sum, i.e. a holomorphic function defined in a large enough sector and asymptotic to that power series in Gevrey sense. The second part is an introduction to Ecalle's resurgence theory. A power series is said to be resurgent when its Borel transform is convergent and has good analytic continuation properties: there may be singularities but they must be isolated. The analysis of these singularities, through the so-called alien calculus, allows one to compare the various Borel-Laplace sums attached to the same resurgent 1-summable series. In the context of analytic difference-or-differential equations, this sheds light on the Stokes phenomenon. A few elementary or classical examples will be considered (the Euler series, the Stirling series, a less known example by Poincaré). Special attention must be devoted to non-linear operations: 1-summable series as well as resurgent series form algebras which are stable by composition. An example of a class of non-linear differential equations giving rise to resurgent solutions will be analyzed. The exposition requires only some familiarity with holomorphic functions of one complex variable.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Sauzin.pdf

#### FMSP Lectures

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

Introduction to BV quantization III (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Reshetikhin.pdf

**Nicolai Reshetikhin**(University of California, Berkeley)Introduction to BV quantization III (ENGLISH)

[ Abstract ]

The lectures will focus on Batalin-Vilkovisky (BV) framework for gauge field theories. We will start with examples of gauge theories such Yang-Mills, BF-theory, Chern-Simons and others. The Hamiltonian structure for field theories will be explained on these examples. Then the classical BV-BFV (Batalin-Fradkin-Vilkovisky) setting will be introduced as a Z-graded extension of the Hamiltonian structure of field theories. The AKSZ (Aleksandrov-Kontsevich-Swartz-Zaboronskij) construction of topological field theories will be introduced. We will construct corresponding BV-BFV theory and its extension to strata of all codimensions. We will also see that Chern-Simons theory, BF theory are of the AKSZ type. The geometry of BV theories is also known as derived geometry. The classical part will be followed by an outline of what is a quantum gauge theory and what is a path integral quantization of a classical gauge theory in the BV-BFV setting. Then we will discuss BV-integrals, fibered BV integrals and perturbative quantization.

[ Reference URL ]The lectures will focus on Batalin-Vilkovisky (BV) framework for gauge field theories. We will start with examples of gauge theories such Yang-Mills, BF-theory, Chern-Simons and others. The Hamiltonian structure for field theories will be explained on these examples. Then the classical BV-BFV (Batalin-Fradkin-Vilkovisky) setting will be introduced as a Z-graded extension of the Hamiltonian structure of field theories. The AKSZ (Aleksandrov-Kontsevich-Swartz-Zaboronskij) construction of topological field theories will be introduced. We will construct corresponding BV-BFV theory and its extension to strata of all codimensions. We will also see that Chern-Simons theory, BF theory are of the AKSZ type. The geometry of BV theories is also known as derived geometry. The classical part will be followed by an outline of what is a quantum gauge theory and what is a path integral quantization of a classical gauge theory in the BV-BFV setting. Then we will discuss BV-integrals, fibered BV integrals and perturbative quantization.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Reshetikhin.pdf

### 2015/10/14

#### FMSP Lectures

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

Introduction to BV quantization II (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Reshetikhin.pdf

**Nicolai Reshetikhin**(University of California, Berkeley)Introduction to BV quantization II (ENGLISH)

[ Abstract ]

The lectures will focus on Batalin-Vilkovisky (BV) framework for gauge field theories. We will start with examples of gauge theories such Yang-Mills, BF-theory, Chern-Simons and others. The Hamiltonian structure for field theories will be explained on these examples. Then the classical BV-BFV (Batalin-Fradkin-Vilkovisky) setting will be introduced as a Z-graded extension of the Hamiltonian structure of field theories. The AKSZ (Aleksandrov-Kontsevich-Swartz-Zaboronskij) construction of topological field theories will be introduced. We will construct corresponding BV-BFV theory and its extension to strata of all codimensions. We will also see that Chern-Simons theory, BF theory are of the AKSZ type. The geometry of BV theories is also known as derived geometry. The classical part will be followed by an outline of what is a quantum gauge theory and what is a path integral quantization of a classical gauge theory in the BV-BFV setting. Then we will discuss BV-integrals, fibered BV integrals and perturbative quantization.

[ Reference URL ]The lectures will focus on Batalin-Vilkovisky (BV) framework for gauge field theories. We will start with examples of gauge theories such Yang-Mills, BF-theory, Chern-Simons and others. The Hamiltonian structure for field theories will be explained on these examples. Then the classical BV-BFV (Batalin-Fradkin-Vilkovisky) setting will be introduced as a Z-graded extension of the Hamiltonian structure of field theories. The AKSZ (Aleksandrov-Kontsevich-Swartz-Zaboronskij) construction of topological field theories will be introduced. We will construct corresponding BV-BFV theory and its extension to strata of all codimensions. We will also see that Chern-Simons theory, BF theory are of the AKSZ type. The geometry of BV theories is also known as derived geometry. The classical part will be followed by an outline of what is a quantum gauge theory and what is a path integral quantization of a classical gauge theory in the BV-BFV setting. Then we will discuss BV-integrals, fibered BV integrals and perturbative quantization.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Reshetikhin.pdf

#### Operator Algebra Seminars

16:45-18:15 Room #118 (Graduate School of Math. Sci. Bldg.)

Fraisse Theory for Metric Structures (English)

**Shuhei Masumoto**(Univ. Tokyo)Fraisse Theory for Metric Structures (English)

### 2015/10/13

#### FMSP Lectures

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

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 ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Reshetikhin.pdf

**Nicolai Reshetikhin**(University of California, Berkeley)Introduction to BV quantization I (ENGLISH)

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)

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