**講演会**

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.

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).

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).

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.

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.

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.

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).

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.

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 Sakhnovich****，****Universität 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.

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.

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 Akhmediev****，****Australian 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.

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 Yeh****，****Oregon 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.

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。**

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 Ma****，****University 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.**

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.**

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.**

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).**

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. **

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.**

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：****Periodic waves and
stability in deep water**

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

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：****Asymptotic theories for
nonlinear water waves**

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

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**

日時：２０１４年7月２5日金曜日** **午後**４**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**

日時：２０１４年7月２5日金曜日** **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**

日時：２０１４年５月２２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６２**W**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**

世話人: 高橋大輔 (daisuket atmark waseda.jp), 丸野健一 (kmaruno atmark waseda.jp). “atmark”は @に置き換えてください..