"Spatial propagation for nonlocal non-autonomous Fisher-KPP equation"
Arnaud Ducrot (Université Le Havre Normandie, France)
In this lecture we discuss existence results of travelling wave solutions and spreading speed fora non-autonomous Fisher-KPP equation with nonlocal diffusion. We prove that under suitable time
averaging properties for the coefficients, the equation exhibits a definite spreading speed. We also
study non-autonomous Fisher-KPP equation on a lattice and deduce from our analysis
spreading phenomenon for some predator-prey systems on lattice.

some"Ecocultural range-expansion model of modern humans in Paleolithic"
Joe Yuichiro Wakano (Meiji University, Japan)
Modern human range expansion and the resulting extinction or assimilation of archaic humans
such as Neanderthals took place roughly 50,000 years ago. This phenomenon is recently very
actively studied by using genetic methods such as ancient DNA analysis. In this talk, a reaction
diffusion model is proposed with emphasis on archaeological and ecological aspects. Range
expansion dynamics are studied as the traveling wave solutions in the system.

"Traveling wave solutions for a three-species diffusive competition system"
Jong-Shenq Guo (Tamkang University, Taiwan)
We shall discuss the existence and stability of traveling waves for a three-species diffusivecompetition system.
This talk is based on some recent joint works with Karen Guo and Masahiko Shimojo.

"Stability of single transition layer solutions in mass-conserving
reaction-diffusion systems with bistable nonlinearity "Hideo Ikeda（University of Toyama, Japan）
Mass-conserving reaction-diffusion systems with bistable nonlinearity are considered undergeneral assumptions, which are useful models for studying cell polarity formation, whose process iskey in cell division and differentiation. The existence of stationary solutions with a single internaltransition layer is shown by using the analytical singular perturbation theory. Moreover, a stability
criterion for the stationary solutions is provided by calculating the Evans function. This is a joint
work with Masataka Kuwamura of Kobe University.

"Traveling wave solutions of combustion in a narrow channel"
Hirofumi Izuhara (Miyazaki University, Japan)
It is reported that combustion in a narrow channel shows a variety of char patterns depending on
the airflow rate. In this talk, we consider a mathematical model which describes the combustion
experiment, and numerically study the existence of traveling wave solution in one space dimension.
In addition, we investigate the instability of its planar combustion wave which is the onset of thevariety of char patterns.

"Two phase Stefan problems as the singular limit ofcompetition-diffusion systems arising in population dynamics"
Danielle Hilhorst (Université Paris-Saclay, France)
Competition-diffusion systems are coupled systems of nonlinear parabolic equations, where theunknown functions represent the densities of interacting biological populations. We will first study
the singular limit of of a two-component competition-diffusion system in population dynamics when
the interspecific competition rate tends to infinity [7], [8]. Using energy estimates, we will prove thatthe solution converges to the weak solution of a problem with a free boundary, which Mayan Mimuraused to call a Stefan problem with zero latent heat [1], [2], [3]. In biological terms, this amounts toproving that the habitats of two interacting populations become completely disjoint in the fastreaction limit. We will then consider a three component competition-diffusion system and prove thatits solution converges to a Stefan problem with positive latent heat [4], [6].
Another question involves the limit of the Stefan problem as the latent heat coefficient tends to zero;
we will show that it converges to the Stefan problem with zero latent heat [5]. A question which wehave started to study is then the following : can we prove a similar result in the case that the partial
differential equations in the Stefan problems are perturbed by a white noise in time [9]References[1] Dancer, E. N.; Hilhorst, D.; Mimura, M.; Peletier, L. A. Spatial segregation limit of a competitiondiffusion system. European J. Appl. Math. 10 (1999), no. 2, 97-115.
[2] Crooks, E. C. M.; Dancer, E. N.; Hilhorst, D.; Mimura, M.; Ninomiya, H. Spatial segregation
limit of a competition-diffusion system with Dirichlet boundary conditions. Nonlinear Anal. RealWorld Appl. 5 (2004), no. 4, 645-665.
[3] Hilhorst, Danielle; Martin, Sébastien; Mimura, Masayasu Singular limit of a competitiondiffusion system with large interspecific interaction. J. Math. Anal. Appl. 390 (2012), no. 2, 488513.
[4] Hilhorst, Danielle; Iida, Masato; Mimura, Masayasu; Ninomiya, Hirokazu A competitiondiffusion system approximation to the classical two-phase Stefan problem. Recent topics inmathematics moving toward science and engineering. Japan J. Indust. Appl. Math. 18 (2001), no.
2, 161-180.
[5] Hilhorst, Danielle; Mimura, Masayasu; Schätzle, Reiner, Vanishing latent heat limit in a Stefanlike problem arising in biology, Nonlinear Anal. Real World Appl. 4 (2003), no. 2, 261–285.
[6] Hilhorst, Danielle; Iida, Masato; Mimura, Masayasu; Ninomiya, Hirokazu Relative compactness
in Lp of solutions of some 2m components competitiondiffusion systems. Discrete Contin. Dyn.
Syst. 21 (2008), no. 1, 233-244.
[7] Hilhorst, Danielle; Mimura, Masayasu; Ninomiya, Hirokazu Fast reaction limit of competitiondiffusion systems. Handbook of differential equations: evolutionary equations. Vol. V, 105-168,Handb. Differ. Equ., Elsevier/North-Holland, Amsterdam, 2009.
[8] Hilhorst, Danielle; Salin, Florian; Schneider, Victor; Gao, Yueyuan, Lecture notes on the singular
limit of reaction-diffusion systems dedicated to the Memory of Masayasu Mimura, Interdiscip.
Inform. Sci. 29 (2023), no. 1, 1–53.
[9] Ciotir, Ioana; El Kettani, Perla; Goreac, Dan; Hilhorst, Danielle, The vanishing latent heat limitof stochastic Stefan problems in population dynamics, in preparation.

"The floodgates to pattern formation problems"
Yasumasa Nishiura (Hokkaido University, Japan)
W. T. Gowers, a Fields medalist from Cambridge in 1998, eloquently expounded on the pivotal
role of Paul Erdős in his essay titled "The Two Cultures of Mathematics." He (Erdős) is famous not
because it has large numbers of applications, nor because it is difficult, nor because it solved a longstanding open problem. Its fame rests on the fact that it opened the floodgates to probabilistic
arguments in combinatorics.
In a similar vein, Mayan Mimura opened a parallel set of floodgates, ones that lead to themodeling and analysis of reaction-diffusion equations. I am eager to trace the initial footsteps of
Mayan and delve into the lasting impact of his contributions on present-day research.

"Keller-Segel type approximation for nonlocal Fokker-Planck equations in
one-dimensional bounded domain"
Yoshitaro Tanaka (Future University Hakodate, Japan)
To describe biological phenomena such as cell migration and cell adhesion many evolutional
equations are proposed in which an advective convolution term with a suitable integral kernel isimposed. It is well known that such nonlocal equations can reproduce various behaviors dependingon the shape of the integral kernel. These nonlocal evolutional equations are often difficult to analyze,
and the analytical method is developing. In the light of these background we approximate thenonlocal Fokker-Planck equations by the combination of a Keller-Segel system which is a typicaland locally dynamical system. We will show that the solution of the nonlocal Fokker-Planck equation
with any even continuous integral kernel can be approximated as a singular limit of the Keller-Segelsystem with specified parameters.

"Spreading fronts arising from the singular limit of reaction-diffusion systems"
Chang-Hong Wu (National Yang Ming Chiao Tung University, Taiwan)
To gain insight into the formation of spreading fronts of invasive species, in this presentation we will
focus on the singular limit of reaction-diffusion systems.
We investigate the dynamics of the limiting systems and give some interpretations for spreading
fronts from the modeling viewpoint. The talk is based on joint works with Hirofumi Izuhara andHarunori Monobe.

"Segregation pattern in a reaction-diffusion model of asymmetric cell division"
Yoshihisa Morita (Ryukoku University, Japan)
We deal with a mathematical model describing polarity in the asymmetric cell division of C.
elegans embryo. In the maintenance phase of asymmet- ric cell division anterior PAR protein (aPAR)
and posterior PAR protein (pPAR) are exclusively formed and a segregation pattern is created for thepolarizations of aPAR and pPAR. Seirin-Lee and Shibata (2015) proposed a 4-component reactiondiffusion system with mass conservation as a model to describe the segregation pattern. Later, somegradient-like dynamics and variational structure in a slightly modied model system were revealed byMorita and Serin-Lee (2021). In this talk we review their work and report a recent progress.

"Speed-up of traveling waves by negative chemotaxis"
Quentin Griette (Université Le Havre Normandie, France)
We consider the traveling wave speed for Fisher-KPP (FKPP) fronts under the influence ofchemotaxis and provide an almost complete picture of its asymptotic dependence on parameters
representing the strength and length-scale of chemotaxis.
Our study is based on the convergence to the porous medium FKPP traveling wave and a
hyperbolic FKPP-Keller-Segel traveling wave in certain asymptotic regimes.

In this way, itclarifies the relationship between three equations that have each garnered intense interest on theirown.

Our proofs involve a variety of techniques ranging from entropy methods and decay ofoscillations estimates to a general description of the qualitative behavior to the hyperbolic FKPPKeller-Segel equation. For this latter equation, we, as a part of our limiting arguments, establish anexplicit lower bound on the minimal traveling wave speed and provide a new construction oftraveling waves that extends the known existence range to all parameter values.
This is a joint work with Chris Henderson and Olga Turanova.

"A Billiard Problem in Nonlinear Dissipative Systems"
Shin-Ichiro Ei (Hokkaido University, Japan)
The motion of camphor discs in a square domain is considered. Different motions from a usual
Billiard problem are observed such as the existence of a stable limit cycle. This talk is mainly done
according to the content of the monograph by Miyaji, E. and Mimura. The interaction of elliptic
camphor discs is also mentioned.

"Convergence, concentration and critical mass phenomena fora model of cell migration with signal production on the boundary"Philippe Souplet (Université Sorbonne Paris Nord, France)(joint work with Nicolas MEUNIER (Université d'Evry-Val d'Essonne))

"Front propagation in the presence of obstacles"
Hiroshi Matano (Meiji University, Japan)
In this talk I will discuss the effect of geometric obstacles on the propagation of fronts. Two typesof fronts are considered. One is a transition layer in a bistable reaction diffusion equation. The otheris a curvature-dependent motion of plane curves. Both types of fronts are closely related. In the firstpart, I will present my joint work with Henri Berestycki and François Hamel. I will then discuss thecurvature-dependent motion of plane curves through an infinite channel with saw-toothedboundaries. For this second topic, I will first recall my joint work with Ken-Ichi Nakamura andBendong Lou (2006, 2013), which deal with domains with mildly undulating boundaries. I will thendiscuss my ongoing joint work with Ryunosuke Mori, which deals with domains whose boundaries
have steeper bumps. In such domains, a new type of phenomenon, which we call “obstacle-inducedpropagation”, can be observed.