## FMSP Lectures

Seminar information archive ～04/13｜Next seminar｜Future seminars 04/14～

**Seminar information archive**

### 2015/10/30

15:00-16:15 Room #128 (Graduate School of Math. Sci. Bldg.)

Asymptotic behaviour of a nonlocal logistic equation (ENGLISH)

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

**Arnaud Ducrot**(University of Bordeaux)Asymptotic behaviour of a nonlocal logistic equation (ENGLISH)

[ Abstract ]

In this talk we consider a nonlocal logistic equation endowed with periodic boundary conditions modelling the motion of cells. This equation takes into account birth and death process using a simple logistic effect while the motion of particles follows a nonlocal Darcy law with a smooth kernel.

We first investigate the well-posedness of the problem before investigating the long time behaviour of the solutions. The lack of asymptotic compactness of the semiflow is overcome by using a Young measure framework. Using a suitable energy functional, we

establish the convergence of the solutions with respect to the Young measure topology.

[ Reference URL ]In this talk we consider a nonlocal logistic equation endowed with periodic boundary conditions modelling the motion of cells. This equation takes into account birth and death process using a simple logistic effect while the motion of particles follows a nonlocal Darcy law with a smooth kernel.

We first investigate the well-posedness of the problem before investigating the long time behaviour of the solutions. The lack of asymptotic compactness of the semiflow is overcome by using a Young measure framework. Using a suitable energy functional, we

establish the convergence of the solutions with respect to the Young measure topology.

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

### 2015/10/30

16:30-17:45 Room #128 (Graduate School of Math. Sci. Bldg.)

How should a drop of liquid on a smooth curved surface move in zero gravity? (ENGLISH)

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

**Peter Bates**(Michigan State University)How should a drop of liquid on a smooth curved surface move in zero gravity? (ENGLISH)

[ Abstract ]

Questions such as this may be formulated as questions regarding solutions to nonlinear evolutionary partial differential equations having a small coefficient on the leading order derivative term. Evolutionary partial differential equations may be regarded as (semi-) dynamical systems in an infinite-dimensional space. An abstract theorem is proved giving the existence of an invariant manifold for a semi-dynamical system when an approximately invariant manifold exists with a certain topological nondegeneracy condition in a neighborhood. This is then used to prove the existence of eternal solutions to the nonlinear PDE and answer the question about the motion of a droplet on a curved manifold. The abstract theorem extends fundamental work of Hirsch-Pugh-Shub and Fenichel on the perturbation of invariant manifolds from the 1970's to infinite-dimensional semi-dynamical systems.

This represents joint work with Kening Lu and Chongchun Zeng.

[ Reference URL ]Questions such as this may be formulated as questions regarding solutions to nonlinear evolutionary partial differential equations having a small coefficient on the leading order derivative term. Evolutionary partial differential equations may be regarded as (semi-) dynamical systems in an infinite-dimensional space. An abstract theorem is proved giving the existence of an invariant manifold for a semi-dynamical system when an approximately invariant manifold exists with a certain topological nondegeneracy condition in a neighborhood. This is then used to prove the existence of eternal solutions to the nonlinear PDE and answer the question about the motion of a droplet on a curved manifold. The abstract theorem extends fundamental work of Hirsch-Pugh-Shub and Fenichel on the perturbation of invariant manifolds from the 1970's to infinite-dimensional semi-dynamical systems.

This represents joint work with Kening Lu and Chongchun Zeng.

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

### 2015/10/22

16:00-16:50 Room #002 (Graduate School of Math. Sci. Bldg.)

The semiflow of a delay differential equation on its solution manifold (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/Walther-abstract-1.pdf

**Hans-Otto Walther**(University of Giessen)The semiflow of a delay differential equation on its solution manifold (ENGLISH)

[ Abstract ]

The lecture surveys work after the turn of the millenium on well-posedness of initial value problems for di_erential equations with variable delay. The focus is on results which provide continuously di_erentiable solution operators, so that in case studies ingredients of dynamical systems theory, such as local invariant manifolds or Poincar_e return maps, become available. We explain why the familar theory of retarded functional di_erential equations [1,2,4] fails for equations with variable delay, discuss what has been achieved for the latter, for autonomous and for nonautonomous equations, with delays bounded or unbounded, and address open problems.

[ Reference URL ]The lecture surveys work after the turn of the millenium on well-posedness of initial value problems for di_erential equations with variable delay. The focus is on results which provide continuously di_erentiable solution operators, so that in case studies ingredients of dynamical systems theory, such as local invariant manifolds or Poincar_e return maps, become available. We explain why the familar theory of retarded functional di_erential equations [1,2,4] fails for equations with variable delay, discuss what has been achieved for the latter, for autonomous and for nonautonomous equations, with delays bounded or unbounded, and address open problems.

http://fmsp.ms.u-tokyo.ac.jp/Walther-abstract-1.pdf

### 2015/10/22

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)

http://fmsp.ms.u-tokyo.ac.jp/Walther-abstract-2.pdf

**Hans-Otto Walther**(University of Giessen)Shilnikov chaos due to state-dependent delay, by means of the fixed point index (ENGLISH)

[ Abstract ]

What can variability of a delay in a delay differential equation do to the dynamics? We find a bounded delay functional d(¥phi), with d(¥phi)=1 on a neighborhood of ¥phi=0, such that the equation x'(t)=-a x(t-d(x_t)) has a solution which is homoclinic to 0, with shift dynamics in its vicinity, whereas the linear equation x'(t)=-a x(t-1) with constant time lag, for small solutions, is hyperbolic with 2-dimensional unstable space.

The proof involves regularity properties of the semiflow close to the homoclinic loop in the solution manifold and a generalization of a method due to Piotr Zgliczynsky which uses the fixed point index and a closing argument in order to establish shift dynamics when certain covering relations hold. (Joint work with Bernhard Lani-Wayda)

[ Reference URL ]What can variability of a delay in a delay differential equation do to the dynamics? We find a bounded delay functional d(¥phi), with d(¥phi)=1 on a neighborhood of ¥phi=0, such that the equation x'(t)=-a x(t-d(x_t)) has a solution which is homoclinic to 0, with shift dynamics in its vicinity, whereas the linear equation x'(t)=-a x(t-1) with constant time lag, for small solutions, is hyperbolic with 2-dimensional unstable space.

The proof involves regularity properties of the semiflow close to the homoclinic loop in the solution manifold and a generalization of a method due to Piotr Zgliczynsky which uses the fixed point index and a closing argument in order to establish shift dynamics when certain covering relations hold. (Joint work with Bernhard Lani-Wayda)

http://fmsp.ms.u-tokyo.ac.jp/Walther-abstract-2.pdf

### 2015/10/20

16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)

Existence of an entropy solution in the sense of Young measures for a first order conservation law with a stochastic source term (ENGLISH)

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Hilhorst151020.pdf

**Danielle Hilhorst**(CNRS / University of Paris-Sud)Existence of an entropy solution in the sense of Young measures for a first order conservation law with a stochastic source term (ENGLISH)

[ Abstract ]

We consider a finite volume scheme for a first order conservation law with a monotone flux function and a multiplicative source term involving a Q-Wiener process. We define a stochastic entropy solution in the sense of Young measures. We present some a priori estimates for the discrete solution including a weak BV estimate. After performing a time interpolation, we prove two entropy inequalities and show that the discrete solution converges along a subsequence to an entropy solution in the sense of Young measures.

This is joint work with T. Funaki, Y. Gao and H. Weber.

[ Reference URL ]We consider a finite volume scheme for a first order conservation law with a monotone flux function and a multiplicative source term involving a Q-Wiener process. We define a stochastic entropy solution in the sense of Young measures. We present some a priori estimates for the discrete solution including a weak BV estimate. After performing a time interpolation, we prove two entropy inequalities and show that the discrete solution converges along a subsequence to an entropy solution in the sense of Young measures.

This is joint work with T. Funaki, Y. Gao and H. Weber.

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Hilhorst151020.pdf

### 2015/10/16

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

### 2015/10/15

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

### 2015/10/15

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

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

### 2015/10/13

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

### 2015/10/13

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

### 2015/10/13

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)

### 2015/09/11

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

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

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

### 2015/09/02

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

### 2015/07/24

16:00-19:00 Room #268 (Graduate School of Math. Sci. Bldg.)

Solvability and approximate solution of a coefficient inverse problem for the kinetic equation (ENGLISH)

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

**Fikret Golgeleyen**(Bulent Ecevit University)Solvability and approximate solution of a coefficient inverse problem for the kinetic equation (ENGLISH)

[ Abstract ]

The existence, uniqueness and stability of the solution of a coefficient inverse problem for the kinetic equation are proven.

The approximate solution of the problem in one-dimensional case is investigated by using two different techniques: finite difference approximation (FDA) and symbolic computation approach (SCA).

A comparison among the exact solution of the problem, the numerical solution obtained from FDA and the approximate analytical solution obtained from SCA is presented.

[ Reference URL ]The existence, uniqueness and stability of the solution of a coefficient inverse problem for the kinetic equation are proven.

The approximate solution of the problem in one-dimensional case is investigated by using two different techniques: finite difference approximation (FDA) and symbolic computation approach (SCA).

A comparison among the exact solution of the problem, the numerical solution obtained from FDA and the approximate analytical solution obtained from SCA is presented.

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

### 2015/07/22

16:45-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)

Recent progress in the classification of amenable C*-algebras (ENGLISH)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

**George Elliott**(Univ. Toronto)Recent progress in the classification of amenable C*-algebras (ENGLISH)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

### 2015/07/08

16:45-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)

Conformal field theory, subfactors and planar algebras (ENGLISH)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

**Marcel Bischoff**(Vanderbilt Univ.)Conformal field theory, subfactors and planar algebras (ENGLISH)

[ Reference URL ]

https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

### 2015/03/19

9:00-11:00 Room #大講義室 (Graduate School of Math. Sci. Bldg.)

Critical metrics for quadratic Riemannian functionals in dimension four (ENGLISH)

https://sites.google.com/site/princetontokyo/mini-courses

Hessian type equations on compact Kähler manifolds (ENGLISH)

https://sites.google.com/site/princetontokyo/mini-courses

**Matthew Gursky**(Univ. Nortre Dame) 9:00-9:50Critical metrics for quadratic Riemannian functionals in dimension four (ENGLISH)

[ Abstract ]

In these lectures I will give an overview of a proof of existence, via gluing methods, of metrics which are critical points of quadratic Riemannian functionals. This is a joint project with J. Viaclovsky.

These are functionals on the space of metrics which are given by integrals of quadratic polynomials in the curvature tensor. Our approach is to construct these metrics on connected sums of Einstein four-manifolds, specifically the Fubini-Study metric on CP2 and the product metric on S2 X S2. Using these metrics in various gluing configurations, toric-invariant critical metrics are found on connected sums for a specific quadratic functional, which depends on the global geometry of the factors.

I will also explain some recent work which attempts to understand the moduli space of critical metrics.

[ Reference URL ]In these lectures I will give an overview of a proof of existence, via gluing methods, of metrics which are critical points of quadratic Riemannian functionals. This is a joint project with J. Viaclovsky.

These are functionals on the space of metrics which are given by integrals of quadratic polynomials in the curvature tensor. Our approach is to construct these metrics on connected sums of Einstein four-manifolds, specifically the Fubini-Study metric on CP2 and the product metric on S2 X S2. Using these metrics in various gluing configurations, toric-invariant critical metrics are found on connected sums for a specific quadratic functional, which depends on the global geometry of the factors.

I will also explain some recent work which attempts to understand the moduli space of critical metrics.

https://sites.google.com/site/princetontokyo/mini-courses

**Gábor Székelyhidi**(Univ. Nortre Dame) 10:10-11:00Hessian type equations on compact Kähler manifolds (ENGLISH)

[ Abstract ]

I will discuss a priori estimates for a general class of nonlinear equations on compact Kähler manifolds. This unifies and generalizes several previous works on specific equations, such as the complex Monge-Ampère, Hessian, and inverse Hessian equations.

[ Reference URL ]I will discuss a priori estimates for a general class of nonlinear equations on compact Kähler manifolds. This unifies and generalizes several previous works on specific equations, such as the complex Monge-Ampère, Hessian, and inverse Hessian equations.

https://sites.google.com/site/princetontokyo/mini-courses

### 2015/03/18

9:00-11:00 Room #大講義室 (Graduate School of Math. Sci. Bldg.)

Critical metrics for quadratic Riemannian functionals in dimension four (ENGLISH)

https://sites.google.com/site/princetontokyo/mini-courses

Hessian type equations on compact Kähler manifolds (ENGLISH)

https://sites.google.com/site/princetontokyo/mini-courses

**Matthew Gursky**(Univ. Nortre Dame) 9:00-9:50Critical metrics for quadratic Riemannian functionals in dimension four (ENGLISH)

[ Abstract ]

In these lectures I will give an overview of a proof of existence, via gluing methods, of metrics which are critical points of quadratic Riemannian functionals. This is a joint project with J. Viaclovsky.

These are functionals on the space of metrics which are given by integrals of quadratic polynomials in the curvature tensor. Our approach is to construct these metrics on connected sums of Einstein four-manifolds, specifically the Fubini-Study metric on CP2 and the product metric on S2 X S2. Using these metrics in various gluing configurations, toric-invariant critical metrics are found on connected sums for a specific quadratic functional, which depends on the global geometry of the factors.

I will also explain some recent work which attempts to understand the moduli space of critical metrics.

[ Reference URL ]In these lectures I will give an overview of a proof of existence, via gluing methods, of metrics which are critical points of quadratic Riemannian functionals. This is a joint project with J. Viaclovsky.

These are functionals on the space of metrics which are given by integrals of quadratic polynomials in the curvature tensor. Our approach is to construct these metrics on connected sums of Einstein four-manifolds, specifically the Fubini-Study metric on CP2 and the product metric on S2 X S2. Using these metrics in various gluing configurations, toric-invariant critical metrics are found on connected sums for a specific quadratic functional, which depends on the global geometry of the factors.

I will also explain some recent work which attempts to understand the moduli space of critical metrics.

https://sites.google.com/site/princetontokyo/mini-courses

**Gábor Székelyhidi**(Univ. Nortre Dame) 10:10-11:00Hessian type equations on compact Kähler manifolds (ENGLISH)

[ Abstract ]

I will discuss a priori estimates for a general class of nonlinear equations on compact Kähler manifolds. This unifies and generalizes several previous works on specific equations, such as the complex Monge-Ampère, Hessian, and inverse Hessian equations.

[ Reference URL ]I will discuss a priori estimates for a general class of nonlinear equations on compact Kähler manifolds. This unifies and generalizes several previous works on specific equations, such as the complex Monge-Ampère, Hessian, and inverse Hessian equations.

https://sites.google.com/site/princetontokyo/mini-courses

### 2015/03/17

13:30-15:00, 15:30-17:30 Room #Balcony A, Kavli IPMU (Graduate School of Math. Sci. Bldg.)

Toric mirror symmetry via shift operators (ENGLISH)

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

**Hiroshi Iritani**(Kyoto University)Toric mirror symmetry via shift operators (ENGLISH)

[ Abstract ]

Recently, shift operator for equivariant quantum cohomology

has been introduced in the work of Braverman, Maulik, Okounkov and

Pandharipande. This can be viewed as an equivariant lift of the

Seidel representation, and intertwines quantum connections with

different equivariant parameters.

In this series of talks, I will explain that shift operators essentially

"reconstruct" mirrors of toric varieties. More precisely we obtain the

following from basic properties of shift operators:

1. Givental's mirror theorem.

2. Landau-Ginzburg potential and primitive form.

3. Extended I-functions.

We will also see that the Gamma integral structure arises as

a solution to the difference equation defined by shift operators.

[ Reference URL ]Recently, shift operator for equivariant quantum cohomology

has been introduced in the work of Braverman, Maulik, Okounkov and

Pandharipande. This can be viewed as an equivariant lift of the

Seidel representation, and intertwines quantum connections with

different equivariant parameters.

In this series of talks, I will explain that shift operators essentially

"reconstruct" mirrors of toric varieties. More precisely we obtain the

following from basic properties of shift operators:

1. Givental's mirror theorem.

2. Landau-Ginzburg potential and primitive form.

3. Extended I-functions.

We will also see that the Gamma integral structure arises as

a solution to the difference equation defined by shift operators.

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

### 2015/03/17

9:00-11:00 Room #大講義室 (Graduate School of Math. Sci. Bldg.)

Critical metrics for quadratic Riemannian functionals in dimension four (ENGLISH)

https://sites.google.com/site/princetontokyo/mini-courses

Hessian type equations on compact Kähler manifolds (ENGLISH)

https://sites.google.com/site/princetontokyo/mini-courses

**Matthew Gursky**(Univ. Nortre Dame) 9:00-9:50Critical metrics for quadratic Riemannian functionals in dimension four (ENGLISH)

[ Abstract ]

In these lectures I will give an overview of a proof of existence, via gluing methods, of metrics which are critical points of quadratic Riemannian functionals. This is a joint project with J. Viaclovsky.

These are functionals on the space of metrics which are given by integrals of quadratic polynomials in the curvature tensor. Our approach is to construct these metrics on connected sums of Einstein four-manifolds, specifically the Fubini-Study metric on CP2 and the product metric on S2 X S2. Using these metrics in various gluing configurations, toric-invariant critical metrics are found on connected sums for a specific quadratic functional, which depends on the global geometry of the factors.

I will also explain some recent work which attempts to understand the moduli space of critical metrics.

[ Reference URL ]In these lectures I will give an overview of a proof of existence, via gluing methods, of metrics which are critical points of quadratic Riemannian functionals. This is a joint project with J. Viaclovsky.

These are functionals on the space of metrics which are given by integrals of quadratic polynomials in the curvature tensor. Our approach is to construct these metrics on connected sums of Einstein four-manifolds, specifically the Fubini-Study metric on CP2 and the product metric on S2 X S2. Using these metrics in various gluing configurations, toric-invariant critical metrics are found on connected sums for a specific quadratic functional, which depends on the global geometry of the factors.

I will also explain some recent work which attempts to understand the moduli space of critical metrics.

https://sites.google.com/site/princetontokyo/mini-courses

**Gábor Székelyhidi**(Univ. Nortre Dame) 10:10-11:00Hessian type equations on compact Kähler manifolds (ENGLISH)

[ Abstract ]

I will discuss a priori estimates for a general class of nonlinear equations on compact Kähler manifolds. This unifies and generalizes several previous works on specific equations, such as the complex Monge-Ampère, Hessian, and inverse Hessian equations.

[ Reference URL ]I will discuss a priori estimates for a general class of nonlinear equations on compact Kähler manifolds. This unifies and generalizes several previous works on specific equations, such as the complex Monge-Ampère, Hessian, and inverse Hessian equations.

https://sites.google.com/site/princetontokyo/mini-courses

### 2015/03/16

13:30-15:00, 15:30-17:30 Room #Balcony A, Kavli IPMU (Graduate School of Math. Sci. Bldg.)

Toric mirror symmetry via shift operators (ENGLISH)

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

**Hiroshi Iritani**(Kyoto University)Toric mirror symmetry via shift operators (ENGLISH)

[ Abstract ]

Recently, shift operator for equivariant quantum cohomology

has been introduced in the work of Braverman, Maulik, Okounkov and

Pandharipande. This can be viewed as an equivariant lift of the

Seidel representation, and intertwines quantum connections with

different equivariant parameters.

In this series of talks, I will explain that shift operators essentially

"reconstruct" mirrors of toric varieties. More precisely we obtain the

following from basic properties of shift operators:

1. Givental's mirror theorem.

2. Landau-Ginzburg potential and primitive form.

3. Extended I-functions.

We will also see that the Gamma integral structure arises as

a solution to the difference equation defined by shift operators.

[ Reference URL ]Recently, shift operator for equivariant quantum cohomology

has been introduced in the work of Braverman, Maulik, Okounkov and

Pandharipande. This can be viewed as an equivariant lift of the

Seidel representation, and intertwines quantum connections with

different equivariant parameters.

In this series of talks, I will explain that shift operators essentially

"reconstruct" mirrors of toric varieties. More precisely we obtain the

following from basic properties of shift operators:

1. Givental's mirror theorem.

2. Landau-Ginzburg potential and primitive form.

3. Extended I-functions.

We will also see that the Gamma integral structure arises as

a solution to the difference equation defined by shift operators.

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

### 2015/01/28

12:00-16:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Limit order books III

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

**Frédéric Abergel**(École Centrale Paris)Limit order books III

[ Abstract ]

In this series of lectures, I will present results pertaining to the empirical properties, mathematical modeling and analysis of limit order books, an object that is now central in modern financial markets. Part of the lectures will be devoted to a survey of the quantitative finance and financial mathematics literature on the subject. I will also present some rather recent results related to the long time behaviour and stationarity of the limit order book.

[ Reference URL ]In this series of lectures, I will present results pertaining to the empirical properties, mathematical modeling and analysis of limit order books, an object that is now central in modern financial markets. Part of the lectures will be devoted to a survey of the quantitative finance and financial mathematics literature on the subject. I will also present some rather recent results related to the long time behaviour and stationarity of the limit order book.

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