講演会

 

English Version

 

25

日時:2020年1月17日(金)午後4時30分 − 午後6時

場所:早稲田大学西早稲田キャンパス63号館04−08号室

 

題目:On Geometric Curve Flows and Solitons

講演者:Dr.  Hsiao-Fan Liu (Tamkang University)

概要: Geometric curves flows are curve evolutions whose invariants flow according to some soliton equations. Such correspondences provide a systematic tool to study geometric curve flows via soliton theory,  and vice versa.  In this talk, we discuss certain geometric curve flows and explain how we build relations between curves and soliton equations, how we use the soliton theory to derive B\"acklund transformations for these curve flows, and to study the existence of solutions to the (periodic) Cauchy problems of curve flows. This also provides geometric algorithms to solve periodic Cauchy problems numerically.

 

24

日時:2019年12月13日(金)午後4時 − 午後6時

場所:早稲田大学西早稲田キャンパス63号館04−08号室

 

題目:Discrete Painlevé Equations and Orthogonal Polynomials

 

講演者:Prof.  Anton Dzhamay (University of Northern Colorado)

概要: Over the last decade it became clear that the role of discrete Painlevé equations in applications has been steadily growing. Thus, the question of recognizing a certain non-autonomous recurrence as a discrete Painlevé equation and understanding its position in Sakai’s classification scheme, recognizing whether it is equivalent to some known (model) example, and especially finding an explicit change of coordinates transforming it to such example, becomes one of the central ones. Fortunately, Sakai’s geometric theory provides an almost algorithmic procedure of answering this question. In this work we illustrate this procedure by studying an example coming from the theory of discrete orthogonal polynomials. There are many connections between orthogonal polynomials and Painlevé equations, both differential and discrete. In particular, often the coefficients of three-term recurrence relations for orthogonal polynomials can be expressed in terms of solutions of some discrete Painlevé equation. In this work we study orthogonal polynomials with
general hypergeometric weight and show that their recurrence coefficients satisfy, after some change of variables, the standard discrete Painlevé-V equation. We also provide an explicit change of variables transforming this equation to the standard form. This is joint work with Galina Filipuk (University of Warsaw, Poland) and Alexander Stokes (University College, London, UK).

 

 

23

日時:2019年12月11日(水)午後2時45分 − 午後6時

場所:早稲田大学西早稲田キャンパス51号館17−06号室

 

題目: Geometry of Discrete Painlevé Equations

 

講演者:Prof.  Anton Dzhamay (University of Northern Colorado)

概要: In this talk we give an introduction to some geometric ideas and tools used to study discrete integrable systems. Our main goal is to give an introduction to Sakai’s geometric theory of discrete Painlevé equations. However, we first consider an autonomous example of a dynamical system known as the QRT map. For this example we explain the geometry behind indeterminate (or base)points of birational maps, as well as how to fix such indeterminacies by changing the geometry of the configuration space using the so-called blowup procedure. In the process we also introduce the notions of the Picard lattice of the algebraic surface that is the configuration space of the dynamics, the anti-canonical divisor class, and the linearization of the mapping on the level of the Picard lattice. After that we consider an idea of geometric deautonomzation. Using this approach we introduce discrete Painlevé equations as deautonomizations of QRT maps. We show how such deautonomization results in the decomposition of the Picard lattice into complementary pairs of the surface and symmetry sub-lattices and explain the construction of a binational representation of affine Weyl symmetry groups that gives a complete algebraic description of our non-linear dynamic. We show how to represent a discrete Painlevé equation as a composition of elementary birational transformations (Cremona isometries). We conclude the tutorial by a brief introduction into Sakai’s classification scheme for discrete Painlevé equations.This talk is based on joint work with Stefan Carstea (Bucharest) and Tomoyuki Takenawa (Tokyo).

 

 

 

22

日時:2019年6月4日(火) 午後4時30分− 午後6時

場所:早稲田大学西早稲田キャンパス51号館17−04号室

 

題目: Rational space curves and solitons for the Gelfand-Dickey reductions of the KP hierarchy.

 

講演者:Prof.  Yuji Kodama (Ohio State University)

概要:  It is well known that the algebro-geometric solutions of the KdV hierarchy are

constructed from the Riemann theta functions associated with the hyperelliptic curves,

and that the soliton solutions can be obtained by rational (singular) limits of the hyperelliptic curves.

 

In this talk, I will discuss certain class of KP solitons in the connections with space curves,

which are labeled by certain types of numerical semigroups. In particular, I will show that

the (singular and complex) KP solitons of the Gelfand-Dickey reduction ($l$-reduction)

are associated with the rational space curves of $<l,lm+1,\ldots, lm+k>$ where $m\ge 1$ and

$1\le k\le l-1$. This is a part of the PhD project of my student, Yuancheng Xie.

 

21

日時:2019年3月7日(木) 午後4時 − 午後5時30分

場所:早稲田大学西早稲田キャンパス52号館103号室

 

題目: On the inverse spectral transform for the conservative Camassa-Holm flow

 

講演者:Prof.  Jonathan Eckhardt (Loughborough University)

概要:  The Camassa-Holm equation is a nonlinear partial differential equation that models unidirectional wave propagation on shallow water. I will show how this equation can be integrated by means of the inverse spectral transform method. The global conservative solutions obtained in this way form into a train of solitons (peakons) in the long-time limit.

 

20

日時:2018年11月19日(月) 午後4時30分 − 午後6時

場所:早稲田大学西早稲田キャンパス63号館04―22

 

題目: Detecting and determining preserved measures and integrals of rational maps

 

講演者:Prof.  Reinout Quispel (La Trobe University)

概要:  The search for preserved measures and integrals of ordinary differential equations has been at the forefront of mathematical physics since the time of Galileo and Newton. In this talk our aim will be to develop an analogous theory for the (arguably more general) discrete-time case. This will lead to linear algorithms for detecting and determining preserved measures and integrals of rational maps.

19

日時:2018年11月9日(金) 午後4時00分 − 午後5時30分

場所:早稲田大学西早稲田キャンパス63号館2階05会議室

 

題目:Symmetry through Geometry

講演者:Prof.  Nalini Joshi (University of Sydney)

概要:  Discrete integrable equations can be considered in two, three or N-dimensions, as equations fitted together in a self-consistent way on a square, a cube or an N-dimensional cube. We show to find their symmetry reductions (and other properties) through a geometric perspective.

 

• N. Joshi and N. Nakazono: Elliptic Painlevé equations from next-nearest-neighbor translations on the E8(1) lattice, Journal of Physics A: Mathematical and Theoretical, 50 (2017), Art. 305205 (17 pp)

• J. Atkinson, P. Howes, N. Joshi and N. Nakazono: Geometry of an elliptic difference equation related to Q4, Journal of the London Mathematical Society, 93 (2016), no. 93, 763–784

• N. Joshi, N. Nakazono, Y. Shi: Reflection groups and discrete integrable systems, Journal of Integrable Systems, (2016), (37 pp).

• N. Joshi and N. Nakazono: Lax pairs of discrete Painlevé equations: (A2+A1)(1) case, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 472 (2016), no. 2196 (13 pp).

• N. Joshi, N. Nakazono and Y. Shi (2014). "Geometric reductions of ABS equations on an n-cube to discrete Painlevé systems." Journal of Physics A-Mathematical and Theoretical 47: 505201 (16pp).

 

18

日時:2018年7月24日(火) 午後3時30分 − 午後4時30分

場所:早稲田大学西早稲田キャンパス62W号館一階大会議室

 

題目:Semilinear Klein-Gordon Equation in the Friedmann-Lamaitre-Robertson-Walker spacetime

講演者:Prof. Anahit Galtsyan (University of Texas Rio Grande Valley)

概要:  We present some results on the semilinear massless waves propagating in the Einstein-de Sitter spacetime and semilinear Klein-Gordon Equation in the de Sitter spacetime. We examine the solutions of the semilinear wave equation, and, in particular, of the $\varphi^p$ model of quantum field theory in the curved space-time. More precisely, for $1 < p < 4$ we prove that solution of the massless self-interacting scalar field equation in the Einstein-de Sitter universe has finite lifespan. Furthermore, we present a condition on the self-interaction term that guaranties the existence of the global in time solution of the Cauchy problem for the semilinear Klein-Gordon equation in the FLRW (Friedmann- Lamaitre-Robertson-Walker) model of the contracting universe. For the equation with the Higgs potential we give an estimate for the lifespan of solution.

日時:2018年7月24日(火) 午後4時45分 − 午後5時45分

場所:早稲田大学西早稲田キャンパス62W号館一階大会議室

 

題目:A new integral transform approach to solving equations of the quantum field theory in the curved space-times

講演者:Prof. Karen Yagdjian (University of Texas Rio Grande Valley)

概要: In this talk we will present the integral transform that allows us to construct solutions of the hyperbolic partial differential equation with variable coefficients via solutions of a simpler equation. This transform was suggested by the author in the case when the last equation is a wave equation. Then it was used to investigate several well-known equations such as generalized Tricomi equation, the Klein–Gordon equation of the quantum field theory in the de Sitter and Einstein-de Sitter space-times of the expanding universe. In particular it was shown that a field with the mass √2 is huygensian. Moreover, the numbers √2, 0 are the only values of the mass such that equation obeys an incomplete Huygens Principle. Then, it was shown that in the de Sitter space-time the existence of two different scalar fields (with mass 0 and √2), which obey incomplete Huygens' principle, is equivalent to the condition that the spatial dimension of the physical world is 3. In this talk a special attention will be also given to the global in time existence of self-interacting scalar field in the de Sitter universe and to the Higuchi bound of the quantum field theory and equations with the Higgs potential.

 

17

日時:2018年7月14日(土) 午後3時30分 − 午後4時30分

場所:早稲田大学西早稲田キャンパス62W号館一階大会議室

 

題目:GBDT version of Backlund-Darboux transformation and evolution of Weyl functions

講演者:Prof. Alexander SakhnovichUniversität Wien

概要:  We consider applications of GBDT to dynamical systems and integrable nonlinear equations including nonlocal NLS equation and second harmonic generation equation. The initial-boundary problem for  second harmonic generation equation will be discussed as well.

 

16

日時:2018年6月23日(土) 午後2時 − 午後3時30分

場所:早稲田大学西早稲田キャンパス52号館102号室

 

題目:On the rational solutions and the solitons of the KP hierarchy

講演者:Prof. Yuji Kodama  (児玉裕治),Ohio State University

概要: It is well known that the Schur polynomials satisfy the Hirota bilinear equations of the KP hierarchy, and that each Schur polynomial can be parametrized by a unique Young diagram. We also know that the KP solitons (exponential solutions) can be parametrized by certain decomposition of the Grassmannians. In the talk, I will explain the connection between the rational solutions and the KP solitons in terms of the Young diagrams. More explicitly,  I will show how one gets a rational solution from a KP soliton. I will also discuss a connection between quasi-periodic solutions (theta or sigma functions) and the KP solitons.

 

15

日時:2018年5月28日月曜日 午後4時30分 − 午後6時

場所:早稲田大学西早稲田キャンパス62W号館1階大会議室

 

題目:The nonlinear Schroedinger equation and variety of it's nontrivial extensions

講演者:Prof. Nail AkhmedievAustralian National University

概要: The NLSE represents a dynamical system with an infinite number of degrees of freedom and as such it has an infinite number of solutions that includes solitons, breathers, rogue waves, radiation waves and their combinations. Every extension of the NLSE expands dramatically variety of it's solutions. Both conservative and dissipative extensions will be considered in this talk. 

 

14

日時:2018年5月21日月曜日 午後4時30分 − 午後6時

場所:早稲田大学西早稲田キャンパス62W号館1階大会議室

 

題目: Mach Reflection of a Solitary Wave: Experiments 

講演者:Prof. Harry YehOregon State University

概要: Laboratory and numerical experiments are presented for Mach reflection of an obliquely incident solitary wave at a vertical wall. The numerical model is based on the pseudo-spectral method for the full Euler formulation. With the aid of a laser sheet in the laboratory, the wave profiles are measured optically in sub-millimeter precision. Discrepancies reported in previous works are now substantially improved, partly because of the higher-order KP theory and in part because of the advancement in computational power and laboratory instrumentation. While the theory predicts the maximum of four-fold (4.0) amplification of the Mach stem, the maximum observed in the laboratory was 2.922 (the previous laboratory study had achieved the amplification of 2.4), while our numerical simulation reached the maximum of 3.91 (previously reported amplification was 2.897). Also presented are other laboratory realizations of soliton-soliton interaction predicted by the KP theory.

 

13

日時:2017年11月16日木曜日 午後5時 − 午後6時30分

場所:早稲田大学西早稲田キャンパス63号館2階05会議室

 

題目:ネットワーク上の蔵本モデルの同期現象

講演者:千葉逸人 氏,九州大学マス・フォア・インダストリ研究所

概要: 蔵本モデルは同期現象を記述する代表的な数理モデルである。ここでは一般のグラフの上で定義された蔵本モデルを考え、グラフの連続極限や一般化スペクトル理論を用いて、そのダイナミクスを調べる。特に、グラフの離散構造がダイナミクスにどのように影響するのかを明らかにする。

 

 

12

日時:2017年11月6日月曜日 午後2時45分 − 午後4時15分

場所:早稲田大学西早稲田キャンパス62W号館1階大会議室

 

題目:  Interaction solutions between lumps and solitons via symbolic computations 

講演者:Prof. Wen-Xiu MaUniversity of South Florida

概要: We will talk about interaction solutions between lump solutions and soliton solutions to integrable equations. A computational algorithm will be discussed, based on the bilinear formulation; and illustrative examples in the cases of the (2+1)-dimensional KP and Ito equations will be presented through Maple symbolic computations.

 

 

11

日時:2017年7月11日火曜日 午後5時15分 − 午後6時45分

場所:早稲田大学西早稲田キャンパス62W号館大会議室

 

題目:On nonlocal nonlinear Schrodinger equation and its discrete version

講演者:Prof. Zuo-Nong Zhu,   Shanghai Jiao Tong University,  P. R. China

概要: Very recently, Ablowitz and Musslimani introduced reverse space, reverse time, and reverse space-time nonlocal nonlinear integrable equations including the reverse space nonlocal NLS equation, the real and complex reverse space-time nonlocal mKdV, sine-Gordon, Davey-Stewartson equations, et.al. In this talk, we will show that, under the gauge transformations, the nonlocal focusing NLS (and it discrete version) and the nonlocal defocusing NLS (and it discrete version) are, respectively, gauge equivalent to the coupled Heisenberg equation (and it discrete version) and the coupled modified Heisenberg equation (and it discrete version). We will discuss the construction of discrete soliton solutions for the discrete nonlocal focusing NLS. We will demonstrate that the discrete soliton yields soliton of nonlocal focusing NLS under the continuous limit. The relations of these solutions between nonlocal NLS and classical NLS will be given. This is a joint work with Dr. Li-yuan Ma.

 

10

日時:2017年6月10日土曜日 午後1時 − 午後4時

場所:早稲田大学西早稲田キャンパス54号館101

 

題目:Hypergeometric functions and integrable hydrodynamic systems

 

講演者:Prof. Yuji Kodama (児玉裕治),  Ohio State University, USA

概要:I will show an interesting connection of (generalized) hypergeometric 
functions with integrable hydrodynamic-type systems. The lecture contains the following subjects.
(a) Integrable hydrodynamic systems generated by Lauricella functions.
(b) Confluence of the Lauricella functions and non-diagonalizable hydrodynamic-type systems.

 

9

日時:2017年6月6日火曜日 午後3時 − 午後6時

場所:早稲田大学西早稲田キャンパス51号館17-08

 

題目:KP solitons

 

講演者:Prof. Yuji Kodama (児玉裕治),  Ohio State University, USA

概要: I will discuss some combinatorial aspects of the KP solitons. This lecture is to explain the following subjects.
(a) Mathematical background of the regular soliton solutions (the totally non-negative Grassmannians and their parametrization).
(b) Applications of the KP solitons to shallow water waves (Mach reflection and rogue waves).

 

8

日時:2017年5月17日水曜日 午後3時 − 午後6時

場所:早稲田大学西早稲田キャンパス62W号館1階大会議室

 

題目:Riemann-Hilbert Methods in Integrable Systems II

Lecture  3: Asymptotic Analysis of Riemann-Hilbert Problems, Part I

Lecture  4: Asymptotic Analysis of Riemann-Hilbert Problems, Part II

 

講演者:Prof. Peter Miller, University of Michigan, USA

 

Lecture 3, Asymptotic Analysis of Riemann-Hilbert Problems, Part I: 

The Deift-Zhou steepest descent method is a powerful set of techniques applicable to Riemann-Hilbert problems that are generalizations of the classical steepest descent method for the asymptotic expansion of certain contour integrals.  This lecture will focus on the Fokas-Its'-Kitaev Riemann-Hilbert problem characterizing orthogonal polynomials with exponentially varying weights and the asymptotic limit of large degree as an example of the steepest descent method.  The goal of this lecture is to deform the Riemann-Hilbert problem to the point where it appears at a formal level to be asymptotically simple.  

Lecture 4, Asymptotic Analysis of Riemann-Hilbert Problems, Part II: 

This lecture picks up where Lecture 3 left off.  The deformed Riemann-Hilbert problem suggests an approximate solution, known as a parametrix.  The parametrix will be constructed explicitly with the help of elementary and special functions.  Then by comparing the parametrix to the exact solution we will arrive at a Riemann-Hilbert problem of small-norm type (cf., Lecture 2). Estimates on the solution of the latter problem yield explicit leading-order asymptotic formulae for the orthogonal polynomials and related quantities of interest in applications such as random matrix theory.  

 

 

7

日時:2017年5月16日火曜日 午後3時 − 午後6時

場所:早稲田大学西早稲田キャンパス62W号館1階大会議室

 

題目:Riemann-Hilbert Methods in Integrable Systems I

Lecture  1: Riemann-Hilbert Problems and Lax Pairs

Lecture  2: Some Theory of Riemann-Hilbert Problems

 

講演者:Prof. Peter Miller, University of Michigan, USA

 

Lecture 1, Riemann-Hilbert Problems and Lax Pairs: 

The inverse-scattering transform can be used to study the initial-value problem for certain nonlinear wave equations, and the most important part of this analysis frequently leads to a Riemann-Hilbert problem of complex function theory.  This lecture will explain how Riemann-Hilbert problems arise in this setting, and will then reveal why Riemann-Hilbert problems are fundamentally related to integrability by means of Lax pairs arising from the dressing construction. 

 

Lecture 2, Some Theory of Riemann-Hilbert Problems: 

A Riemann-Hilbert problem is fundamentally a problem of complex analysis, a kind of boundary-value problem for the Cauchy-Riemann equations.  However, as with many problems of elliptic partial differential equations, a Riemann-Hilbert problem can be recast as a singular integral equation.  This lecture will highlight some of the key ideas of the connection between Riemann-Hilbert problems and integral equations, with emphasis on the small-norm setting and how to achieve it by deformation techniques.

 

 

6

日時:2016年5月17日火曜日 午後1時00分 − 午後2時30分

場所:早稲田大学西早稲田キャンパス62W号館1階大会議室

 

題目:Unidirectional wave propagation and integrable models in shallow water

 

講演者:Prof. Roberto Camassa, University of North Carolina, USA

 

日時:2016年5月17日火曜日 午後245分 − 午後415

場所:早稲田大学西早稲田キャンパス62W号館1階大会議室

 

題目:Periodic waves and stability in deep water

 

講演者;Prof. Wooyoung Choi,  New Jersey Institute of Technology, USA

 

 

5

日時:2016年5月16日月曜日 午後1時00分 − 午後2時30分

場所:早稲田大学西早稲田キャンパス62W号館1階大会議室

 

題目:Fundamentals of fluid mechanics and free surface flows

 

講演者;Prof. Roberto Camassa, University of North Carolina, USA

 

日時:2016年5月16日月曜日 午後245分 − 午後415

場所:早稲田大学西早稲田キャンパス62W号館1階大会議室

 

題目:Asymptotic theories for nonlinear water waves

 

講演者:Prof. Wooyoung Choi,  New Jersey Institute of Technology, USA

 

4

日時:2015年3月16日月曜日 午後3時00分 − 午後5時00分

場所:早稲田大学西早稲田キャンパス62W号館1階大会議室

 

題目:From Schlesinger Transformations to Difference Painlevé Equations

 

講演者;Prof. Anton Dzhamay, School of Mathematical Sciences, University of Northern Colorado, USA

 

 

3

日時:2014年7月25日金曜日 午後時30分 − 午後6時00分

場所:早稲田大学西早稲田キャンパス63号館1階数学応数会議室

 

題目:Triangulations of convex polygon and solitons in 2-dimension

講演者;Prof. Yuji Kodama, Department of Mathematics, Ohio State University, USA

 

2

日時:2014年7月25日金曜日 午後時45分 − 午後4時15分

場所:早稲田大学西早稲田キャンパス63号館1階数学応数会議室

 

題目:Beach waves and line-solitons of the KP equation

講演者:Prof. Sarbarish Chakravarty, Department of Mathematics, The University of Colorado at Colorado Springs, USA

 

1

日時:2014年5月22日木曜日 午後時 − 午後6時30分

場所:早稲田大学西早稲田キャンパス62W号館1階大会議室

 

題目:The complex and coupled complex short pulse equations, their integrable discretizations and novel numerical simulations

講演者:Prof. Baofeng Feng, Department of Mathematics, The University of Texas Pan American, USA

 

 

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