Talks in 2021
 Goro Akagi, Traveling wave dynamics for a onedimensional constrained AllenCahn equation , Monday, 13 September 2021.
 Sandra Cerrai, Incompressible viscous fluids in the plane and SPDEs on graphs., Monday, 22 November 2021.
 Beomjun Choi, Liouville theorem for surfaces translating by subaffinecritical powers of Gauss curvature, Monday, 27 September 2021.
 ChiunChuan Chen, Traveling wave solutions for the diffusive LotkaVolterra system of 3 competing species, Monday,15 November 2021.
 Florica Cîrstea, Anisotropic elliptic equations with gradientdependent lower order terms and \(L^1\) data, Monday, 20 September 2021.
 Cristiana De Filippis, Perturbations beyond Schauder data, Monday, 8 November 2021.
 Serena Dipierro, Boundary behaviour of nonlocal minimal surfaces, Monday, 22 February 2021.
 Yihong Du, Spreading rate for the FisherKPP nonlocal diffusion equation with free boundary , Monday, 31 May 2021.
 Renjun Duan, Lowregularity solutions to the noncutoff Boltzmann equation: existence, regularity and grazing limit , Monday, 28 March 2021.
 Ilaria Fragala, Concavity properties of solutions to Robin problems , Monday, 5 July 2021.
 Rupert Frank, Blowup of solutions of critical elliptic equations in three dimensions , Monday, 10 May 2021.
 Nicola Garofalo, A heat equation approach to some problems in conformal geometry., Monday, 19 July 2021.
 François Hamel, Symmetry properties for the Euler equations and semilinear elliptic equations, Monday, 12 April 2021.
 InJee Jung, Illposedness for incompressible fluid models at critical Sobolev regularity, Monday, 26 April 2021.
 Yoshiyuki Kagei, Stability and bifurcation analysis of the compressible NavierStokes equations, Monday, 8 March 2021.
 Derek Kielty, Degeneration of the spectral gap with negative Robin parameter., Monday, 30 August 2021.
 Minhyun Kim, Nonlocal problems with nonstandard growth , Monday, 6 December 2021.
 WeiXi Li, Gevrey wellposedness of the 3D Prandtl equations without Structural Assumption , Monday, 26 July 2021.
 Yuan Lou, On principal eigenvalues for elliptic and parabolic operators , Monday, 1 November 2021.
 Tao Luo, Estimates and geometry for a free surface problem of fluids with heatconductivity , Monday, 17 May 2021.
 Yasunori Maekawa, Recent progress on the Prandtl boundary layer expansion for viscous incompressible flows , Monday, 7 June 2021.
 Shuang Miao, On the free boundary hard phase fluid in Minkowski spacetime, Monday, 15 February 2021.
 Tatsuya Miura, LiYau type inequality for curves and applications, Monday, 6 September 2021.
 Yoichi Miyazaki, A tour of Sobolev spaces by Muramatu's integral formula, Monday, 11 October 2021.
 Monica Musso, Vortex filaments for Euler equations , Monday, 25 October 2021.
 Toru Nogayama, Maximal regularity in BesovMorrey spaces and its application to KellerSegel System, Monday, 12 July 2021.
 Aaron Palmer, Hidden Convexity in problem of Nonlinear Elasticity, Monday, 22 March 2021.
 Adam Sikora, Square functions and Riesz transforms on a class of nondoubling manifolds , Monday, 21 June 2021.
 Mitsuru Sugimoto, A constructive approach to semilinear wave equations, Monday, 25 January 2021.
 Ryotaro Tanaka, Nonlinear Classification of Banach spaces based on BirkhoffJames orthogonality, Monday, 6 June 2021.
 Emmanuel Trélat, Spectral analysis of subRiemannian Laplacians and Weyl measure, 8, February 2021.
 Po Lam Yung, Sobolev spaces revisited, 29, November 2021.
 Rongchan Zhu, Large \(N\) Limit of the \(O(N)\) Linear Sigma Model via Stochastic Quantization, Monday, 25 January 2021.
See also the Talks in 2020 page.
Postdoctoral Fellow @ Bielefeld University, Germany.
Dr Kim received his PhD in 2020 from Seoul National University, Korea, where his supervisor was Prof. KiAhm Lee. Following this, he accepted his first postdoctoral position at ChungAng University, Korea and since 2021, he is a postdoctoral research fellow at Bielefeld University, Germany. Slides to the talk pending 
Nonlocal problems with nonstandard growth
In the calculus of variations, functionals with nonstandard growth have been studied extensively since the late 1980s. We introduce several nonlocal analogues of these classical models, attempting to develop parallel or unified theory. We study local regularity properties such as local boundedness, weak Harnack inequality, and local Hölder regularity. 
Senior Lecturer @ Australian National University in Canberra, Australia.
Professor Yung received his PhD in 2010 @Princton University, United States, under the supervision of Elias Stein. From 20102013, he held the Hill Assistant Professorship @ Rutgers, New Jersey. Following this, we became a Tichmarsh Fellow from 20132014 @ the University of Oxford and Assistant Professorship @ the Chinese University of Hong Kong from 20142020. In 2020, Yung was promoted to Associate Professor @ CUHK while he is on leave. Since 2019, he works as an ARC Future Fellow @ the Australian National University in Canberra. Recently, in 2021, we was awarded the prestigious Antonio Ambrosetti Medal for his new and surpising characterization of the Sobolev norm. Slides to the talk 
Sobolev spaces revisited
In this talk, we will describe some new ways of characterising Sobolev and BV functions, using sizes of superlevel sets of suitable difference quotients. They provide remedy in certain cases where some critical GagliardoNirenberg interpolation inequalities fail, and lead us to investigate real interpolations of certain fractional Besov spaces. Some connections will be drawn to earlier work by Bourgain, Brezis and Mironescu, and an image processing application will be given. Joint work with Haim Brezis, Jean Van Schaftingen, Qingsong Gu, Andreas Seeger, Brian Street and Oscar Dominguez. 
Professor @ University of Maryland, United States.
Sandra Cerrai received her Ph.D. in 1998 @ the Scuola Normale Superiore of Pisa, Italy, under the supervision of Giuseppe Da Prato. She started her academic career @ the University of Florence. In 2008, she moved to the University of Maryland. She has served and is still serving on the editorial board of several journals in probability and PDEs. She has held several visiting positions, among others @ the Newton Institute in Cambridge, @ the Institute MittagLeffler in Djursholm, @ the MSRI Berkeley, where she has been Eisenbud Professor, @ the Centre Bernoulli in Lausanne. Professor Cerrai is currently Simons Fellow in Mathematics. She is interested in the analysis of systems with multiple scales, that are described by stochastic partial differential equations. More specifically, she deals with the small noise asymptotics of those systems, their longtime behavior, averaging phenomena, diffusion approximation, and singular perturbation results. Slides to the talk 
Incompressible viscous fluids in the plane and SPDEs on graphs
I will present some results about the asymptotic behavior of a class of stochastic reactiondiffusionadvection equations in the plane. I will show that as the divergencefree advection term becomes larger and larger, the solutions of such equations converge to the solution of a suitable stochastic PDE defined on the graph associated with the Hamiltonian. I will deal with the case that the stochastic perturbation is given by a singular spatially homogeneous Wiener process taking values in the space of Schwartz distributions. As in previous works, I will assume that the derivative of the period of the motion on the level sets of the Hamiltonian does not vanish. Time permitting, without assuming this condition on the derivative of the period, I will study a weaker type of convergence for the solutions of a suitable class of linear SPDEs. 
Professor @ National Taiwan University (NTU), Taiwan.
Dr. ChiunChuan Chen is currently a professor @ National Taiwan University (NTU). He received
his Ph.D. in 1991 from NTU. He held a postdoctoral fellowship at Academia Sinica from 1991 to
1992. From 1992 to 1996, he was a faculty member at National ChungCheng University. In 1996,
he joined NTU and has been a professor there since 1998. He visited Harvard University for one
year during 20072008. He was awarded the National Chair Professorship in 2008. His research
interest mainly focuses on elliptic equations, variational problems, and reactiondiffusion
equations with applications to biology.
Slides to the talk 
Traveling wave solutions for the diffusive LotkaVolterra system of 3 competing species
This talk concerns with the 3species LotkaVolterra competition system. Especially we are interested in a type of traveling wave solutions with a nonmonotone profile. We will describe some approaches to prove the existence of the waves under suitable parameter ranges. Our results and related studies indicate that such waves are important in understanding the rich dynamics of 3 species and may provide a mechanism for species to coexist under strong competition. 
Assistant Professor @ University of Parma, Italy.
Professor De Filippis recieved her PhD @ University of Oxford (UK) in 2020. Before that, in 2019 she was awarded
the GResearch PhD prize from the UK and the Gioacchino Iapichino Prize from Accademia
Nazionale dei Lincei (Italian national academy). In July 2020, De Filippis accepted a postdoctoral position
@ the University of Turin, Italy. Since 1 November 2021, De Filippis holds a tenure track Assistant Professor
position @ the University of Parma. De Fillippis works in the regularity theory of elliptic
and parabolic partial differential equations and Calculus of Variations.
Slides to the talk 
Perturbations beyond Schauder
Socalled Schauder estimates are a standard tool in the analysis of linear elliptic and parabolic PDE. They had been originally obtained by Hopf (1929, interior case), and by Schauder and Caccioppoli (1934, global estimates). Since then, several proofs were given, (Campanato, Simon, Trudinger). The nonlinear case is a more recent achievement from the 80s (Giaquinta \& Giusti, Ivert, Lieberman, Manfredi). All these classical results hold in the uniformly elliptic framework. I will present recent advances in the nonuniformly elliptic one, discussing also delicate borderline cases and regularity criteria of interpolative nature. 
Professor in Mathematical Sciences @ Ohio State University, US.
Dr Yuan Lou received his bachelor's degree and master's degree from Peking University in 1988 and 1991, respectively. In 1995 he received his Ph.D. from the University of Minnesota. He was a postdoc fellow at MSRI (19951996) and Dickson Instructor at University of Chicago (19961998). Since 1998, he has been a faculty member at Ohio State University. Since 2021, he has been a visiting professor at Shanghai Jiaotong University. Dr. Lou's research interest is reactiondiffusion equations with applications to biology. He has authored 130+ papers on these topics. He served as Associate Director of Mathematical Biosciences Institute (20092013). Currently he is serving as Co EditorinChief of Discrete and Continuous Dynamical SystemsSeries B and in numerous editorial boards, including Journal of Differential Equations, Journal of Math Biology and SIAM Journal of Applied Mathematics.
Slides to the talk 
On principal eigenvalues for elliptic and parabolic operators
We will discuss some recent progress on the asymptotic behavior of principal eigenvalues for second order elliptic and timeperiodic parabolic operators. We will mainly focus on the dependencies of principal eigenvalues on diffusion rate and drift rate. Some applications to biology and infectious disease will be presented. 
Professor @ the University of Barth, UK.
Professor Since February 2018, Monica Musso is a Professor in the Department of Mathematical Sciences @ the University of Bath. Her previous positions were at the Department of Mathematics @ the Universidad Catolica de Chile (since 2004, as professor since 2012) and @ the Politecnico di Torino (since 1999, as Ricercatore in a permanent position). She obtained her PhD in 1997 from the Universita' di Pisa and she was a postdoctoral researcher in the Intenational School for Advanced Studies (SISSA) in Trieste during 1998.
She works in the area of Nonlinear Analysis and Partial Differential Equations (PDEs). Some of the topics she is interested in are Singularity formation in elliptic and parabolic equations, Concentration phenomena in critical problems, and Fractional Yamabe problem.
Slides to the talk 
Vortex filaments for Euler equations
We consider the Euler equations for incompressible fluids in 3dimension. A classical question that goes back to Helmholtz is to describe the evolution of vorticities with a high concentration around a cruve. The work of Da Rios in 1906 states that such a curve must evolve by the socalled "binormal curvature flow". Existence of true solutions whose vorticity is concentrated near a given curve that evolves by this law is a longstanding open question that has only been answered for the special case of a circle travelling with constant speed along its axis, the thin vortexrings. In this talk I will discuss the construction of helical filaments, associated to a translatingrotating helix, and of two vortex rings interacting between each other, the socalled leapfrogging. The results are in collaboration with J. Davila (U. of Bath), M. del Pino (U. of Bath) and J. Wei (U. of British Columbia). 
Professor @ Nihon University, Japan, Japan.
Yoichi Miyazaki was a doctoral student of Professor Tosihusa Kimura at the
University of Tokyo, focusing on spectral asymptotics of elliptic
operators. He became a research associate at Nihon University in 1988,
and received his Ph.D. (Mathematical Sciences) from the University of
Tokyo in 1993. He was promoted to an associate professor in 2013, and a
professor in 2016.
Slides to the talk 
A tour of Sobolev spaces by Muramatu's integral formula
In the study of Sobolev spaces Muramatu’s integral formula is very useful. It enables us to prove easily almost all theorems in the theory of Sobolev spaces, if we combine it with basic tools in analysis such as Hölder’s inequality, Minkowski’s inequality, Young’s inequality, and the HardyLittlewood maximal function. Here is a list of the theorems that can be obtained by Muramatu’s integral formula: the Sobolev inequality, the refined Sobolev inequality which involves the homogeneous Besov norm of negative order, the embedding theorem into HölderZygmund spaces, Trudinger’s inequality for the critical case, the embedding theorem into the BMO or VMO space for the critical case, the trace theorem, the GagliardoNirenberg inequality and its generalization which replaces the \(L^\infty\) norm with the BMO norm or the homogeneous Besov norm, the BrezisGallouetWainger inequality, the BrezisWainger inequality which is related to almost Lipschitz continuity. In this talk I will focus on how to use Muramatu’s integral formula for some of the theorems listed above. Bio: Yoichi Miyazaki was a doctoral student of Professor Tosihusa Kimura at the University of Tokyo, focusing on spectral asymptotics of elliptic operators. He became a research associate at Nihon University in 1988, and received his Ph.D. (Mathematical Sciences) from the University of Tokyo in 1993. He was promoted to an associate professor in 2013, and a professor in 2016. 
Professor @ Dept. of Mathematics, Postech, Korea.
2021.07 to present: POSTECH, Assistant Professor 2021.05 to 2021.06: KIAS, CMC Fellow 2019.08 to 2021.04: University of Toronto, Postgraduate Fellow Slides to the talk 
Liouville theorem for surfaces translating by subaffinecritical powers of Gauss curvature
We classify the translators to the flows by subaffinecritical powers of Gauss curvature in \(\mathbb{R}^3\). If \(\alpha\) denotes the power, this is a Liouville theorem for degenerate MongeAmpere equations \(\det D^2u = (1+Du^2)^{2\frac{1}{2\alpha}}\) for \(0<\alpha<1/4\). For the affinecriticalcase \(\det D^2u =1\), the classical result by Jorgens, Calabi and Pogorelov shows the level curves of given solution are homothetic ellipses. In our case, the level curves converge asymptotically to a round circle or a curve with \(k\)fold symmetry for some \(k>2\). More precisely, these curves are closed shrinking curves to the \(\frac {\alpha}{1\alpha}\)curve shortening flow that were previously classified by B. Andrews in 2003. This is a joint work with K. Choi and S. Kim. 
Associate Professor @ University of Sydney.
A/Professor Florica Cîrstea graduated with a PhD from Victoria University in April 2005.
From April 2005 to April 2009, she held an ARC Australian Postdoctoral Fellowship (APD).
The teaching (25%) was funded by the Department of Mathematics at the Australian National University and the research (75%) was funded by the Australian Research Council. In July 2008, she transferred her fellowship to the University of Sydney to take up a lectureship position in April 2009. She is an Associate Professor at the University of Sydney since January 2017.
Slides to the talk 
Anisotropic elliptic equations with gradientdependent lower order terms and \(L^1\) data
Given a bounded open subset \(\Omega\) of \(\mathbb R^N\), we prove the existence of a weak solution for a general class of Dirichlet anisotropic elliptic problems including \(\mathcal Au+\Phi(x,u,\nabla u)=\mathfrak{B}u+f\) in \(\Omega\), where \(f\in L^1(\Omega)\) is arbitrary. The principal part is a divergenceform nonlinear anisotropic operator \(\mathcal A\), the prototype of which is \(\mathcal A u=\sum_{j=1}^N \partial_j(\partial_j u^{p_j2}\partial_j u)\) with \(p_j>1\) for all \(1\leq j\leq N\) and \(\sum_{j=1}^N (1/p_j)>1\). As a novelty, our lower order terms involve a new class of operators \(\mathfrak B\) such that \(\mathcal{A}\mathfrak{B}\) is bounded, coercive and pseudomonotone from \(W_0^{1,\overrightarrow{p}}(\Omega)\) into its dual, as well as a gradientdependent nonlinearity \(\Phi\) with an “anisotropic natural growth" in the gradient and a good sign condition. This talk is based on joint work with Barbara Brandolini (Università degli Studi di Palermo). 
Professor @ Tohoku University, Japan.
Goro Akagi received a Ph.D from Waseda University in 2004 and his former supervisor is Prof. Mitsuharu Otani. He has been studying evolution equations,
variational problems, nonlinear diffusion equations, AllenCahn and CahnHilliard equations, and so on. He has been a full professor of Mathematical Institute and Graduate School of Science, Tohoku University since Apr 2016.
Slides to the talk 
Traveling wave dynamics for a onedimensional constrained AllenCahn equation
This talk concerns a onedimensional AllenCahn equation on the whole line with the positivepart function, which constrains the growth of each solution to be nondecreasing. We shall discuss traveling wave dynamics, which has been well studied for classical AllenCahn equations, for the constrained one. More precisely, we shall start with constructing a oneparameter family of "degenerate" traveling wave solutions (identified when coinciding up to translation) and investigate their properties. Furthermore, the traveling wave dynamics turns out to be relevant to a free boundary problem with a peculiar motion equation for the boundary through an analysis on a regularity issue for the constrained AllenCahn equation, and then, such a viewpoint enables us to prove exponential stability of degenerate traveling waves with some basin of attraction, although they are unstable in a usual sense. This talk is based on a joint work with Christian Kuehn (Muenchen) and KenIchi Nakamura (Kanazawa). 
Assoc. Professor @ Tokyo Institute of Technology, Japan.
Tatsuya Miura obtained his PhD from the University of Tokyo in 2017. After Postdoctoral Fellow at the Max Planck
Institute for Mathematics in the Sciences around 2018, he was appointed as Assistant Professor in 2019 at the
Tokyo Institute of Technology, where he got promoted to Associate Professor in 2021. He was awarded the MSJ
Takebe Katahiro Prize for Encouragement of Young Researchers in 2017, the JSPS Ikushi Prize in 2018, and
the Inoue Research Award for Young Scientists in 2019.
Slides to the talk 
LiYau type inequality for curves and applications
A classical result of LiYau asserts an optimal relation between the bending energy (also known as the Willmore energy) and multiplicity of a closed surface in Euclidean space, and is used as a fundamental tool for many studies. In this talk we obtain an analogue for curves in a general form, and observe new phenomena due to low dimensionality. We also discuss its applications to elastic flows, networks, and knots, in particular resolving an open problem posed by Dall'AcquaNovagaPluda. 
PhD Student @ University of Illinois UrbanaChampaign, United States.
Derek Kielty is a sixthyear Ph.D. student at the University of Illinois UrbanaChampaign advised by Richard Laugesen. Most recently he has worked on various problems related to spectra gaps of the Robin Laplacian and Schrodinger operators.
Slides to the talk 
Degeneration of the spectral gap with negative Robin parameter.
The spectral gap of the Neumann and Dirichlet Laplacians are each known to have a sharp positive lower bound among convex domains of a given diameter. Between these cases, for each positive value of the Robin parameter an analogous sharp lower bound on the spectral gap is conjectured. In this talk we show the extension of this conjecture to negative Robin parameters fails by proving that the spectral gap of double cone domains are exponentially small, for each fixed parameter value. 
Professor @ Wuhan University, China.
WeiXi Li is currently a professor at Wuhan University. He received PHD in 2008 from Wuhan University. The research of W.X.Li is microlocal analysis and its application in kinetic and fluid mechanics equations, with special focus on mathematical analysis of boundary layer system and kinetic equations, spectral analysis of FokkerPlanck operator and related models.
Slides to the talk 
Gevrey wellposedness of the 3D Prandtl equations without Structural Assumption
We establish the wellposedness in Gevrey function space with optimal class of regularity 2 for the three dimensional Prandtl system without any structural assumption. The proof combines in a novel way a new cancellation in the system with some of the old ideas to overcome the difficulty of the loss of derivatives in the system.This shows that the three dimensional instabilities in the system leading to illposedness are not worse than the two dimensional ones. Joint work with Nader Masmoudi and Tong Yang. 
Professor of Mathematics @ University of Padova, Italy.
Nicola Garofalo is Professor of Mathematics at the University of Padova. He received his Ph.D. in Mathematics from the University of Minnesota in 1987 under the supervision of Eugene Fabes. He has held positions at the University of Bologna, Northwestern University and Purdue University. He has been invited visiting professor at the Institute H. Poincare’, Paris, invited visiting fellow at the I. Newton Institute for Mathematical Sciences, Cambridge, and invited visiting professor at the MittagLeffler Institute, Stockholm. He has also been Distinguished Visiting Professor of Mathematics at the Ohio State University, Visiting Professor of Mathematics at The Johns Hopkins University and Visiting Professor of Mathematics at the University of Maryland. He has received uninterrupted funding from the US National Science Foundation during the years 19892013, and was the recipient of the 2012 Ruth and Joel Spira Award for excellence in graduate teaching.
Slides to the talk 
A heat equation approach to some problems in conformal geometry.
The Heisenberg group plays an ubiquitous role in analysis, geometry and mathematical physics. Such Lie group is equipped with a natural second order pdo L, the real part of the KohnSpencer sublaplacian, that is hypoelliptic (but fails to be elliptic at every point). It is of interest to study two different families of fractional powers of L, L^s and L_s, and their socalled extension problems. While the former has a purely analytical content, the pseudodifferential operators L_s play a critical role in conformal CR geometry. In this selfcontained talk I plan to show that, notwithstanding their substantial differences, these two classes of nonlocal operators can be treated in a unified way by a systematic use of the heat equation and suitable modifications of the latter. Such approach leads to some intertwining formulas related to conformal geometry that are instrumental in inverting the relevant nonlocal operators, as well as in constructing explicit solutions of some nonlocal Yamabe problems. This is joint work with G. Tralli. 
Postdoctoral fellow @ Tokyo Metropolitan University, Japan
Toru Nogayama obtained his PhD @ Tokyo Metropolitan University, Japan,
in 2021.
He was a JSPS Research fellow DC @ Tokyo Metropolitan University in 2020.
Since 2021, he is a JSPS Research fellow PD @ Tokyo Metropolitan
University.
Slides to the talk 
Maximal regularity in BesovMorrey spaces and its application to KellerSegel system
Maximal regularity is an important tool in the theory of nonlinear differential equations. Furthermore, from the viewpoint of harmonic analysis, it is also a very interesting subject. The maximal regularity for parabolic equations is established within the general framework on Banach spaces that satisfy the unconditional martingale differences (called UMD). Meanwhile, we need to treat differently the maximal regularity on Banach spaces which do not satisfy UMD. In particular, it is well known that nonreflexive Banach spaces are not UMD. In this talk, we discuss the maximal regularity of the heat equation in BesovMorrey spaces which are not reflexive. As an application, we present the wellposedness results for the two dimensional KellerSegel system. 
Professor @ Politecnico di Milano, Italy.
1999: Researcher at Politecnico di Milano; 2000 PhD in Mathematics at University of Pisa (Advisor G. Buttazzo); 2016today: Full professor at Politecnico di Milano. Main fields of interest: Calculus of variations, shape optimization, PDEs. Author of 80 publications on peerreviewed journals.
Slides to the talk 
Concavity properties of solutions to Robin problems
We present some recent results about the logconcavity of the Robin ground state and the power concavity of the Robin torsion function on convex domains in the Euclidean Ndimensional space. The results are valid for smooth domains, and for sufficiently large value of the parameter: the threshold for concavity turns out to depend on the space dimension and on the geometry of the domain, precisely on its diameter and boundary curvatures. In particular, this answers positively a conjecture set in 2020 by AndrewsClutterbuckHauer. Anyhow, many related open questions remain open. 
Professor @ ChungAng University, Seoul, Korea
Professor Hong received his PhD in Mathematics from Brown University, United States, in 2013. After this, he accepted a position as Instructor at the University of Texas at Austin, where he stayed until 2016. From 2016 until February 2018, he was a Postdoctoral researcher at Yonsei University Seoul, South Korea. Since March 2018, Hong is Assistant Professor at ChungAng University in Seoul.
Slides to the talk 
On the Kortewegde Vries limit for the FermiPastaUlam system
The FermiPastaUlam (FPU) system is a simple nonlinear dynamical lattice model describing a onedimensional chain of vibrating strings with nearest neighbor interactions. This model was introduced by Fermi, Pasta and Ulam in 1955. It was anticipated at that time that chaotic nonlinear interactions would lead to thermalization. Surprisingly however, numerical simulations showed the opposite behavior – it exhibited quasiperiodic motions. This phenomena is known as the FPU paradox. This puzzle has been solved by Zabusky and Kruskal by discovering a formal convergence to the Kortewegde Vries equation, and the convergence has been rigorously justified. We revisit this convergence problem, and show how to put it into the dispersive PDE framework. This talk is based on joint work with Chulkwang Kwak and Changhun Yang. 
Associate Professor @ Macquarie University, Australia.
Adam Sikora obtained his PhD from the Polish Academy of Science in 1994.
Between 1995 and 2001 he was a visiting fellow at the Australian National University.
Then he worked as Assistant Professor @ New Mexico State University (United States)
before joining Macquarie University in 2009.
Slides to the talk 
Spreading rate for the FisherKPP nonlocal diffusion equation with free boundary
We consider a class of manifolds \(\mathcal{M}\) obtained by taking the connected sum of a finite number of \(N\)dimensional Riemannian manifolds of the form \((\mathbb{R}^{n_i}, \delta) \times (\mathcal{M}_i, g)\), where \(\mathcal{M}_i\) is a compact manifold, with the product metric. The case of greatest interest is when the Euclidean dimensions \(n_i\) are not all equal. This means that the ends have different `asymptotic dimensions', and implies that the Riemannian manifold \(\mathcal{M}\) is not a doubling space.We completely describe the range of exponents \(p\) for which the Riesz transform and vertical square function on \(\mathcal{M}\) are bounded operators on \(L^p(\mathcal{M})\). 
Professor @ Kyoto University.
Professor Maekawa received his PhD @ Hokkaido University on 30 September 2007
under the supervision of Professor Yoshihiro Tonegawa. Following his Phd, he
received first a JSPS Research Fellow (PD), while he was appointed as Assistant
Professor @ Kyushu University (20082009). From 20092010, Maekawa accepted a
Lecturer position @ Kobe University, where he was promoted to Associate
Professor in 2010. He was appointed as Associate Professor @ Tohoku University
from 20132016 and Associate Professor @ Kyoto University from 20162019. Since
2019 until current, Maekawa is Professor @ Kyoto University.

Recent progress on the Prandtl boundary layer expansion for viscous incompressible flows
Determining the behavior of viscous incompressible flows at small viscosity is one of the most fundamental problems in fluid mechanics. In the region away from the boundary the flow is expected to behave as the inviscid flow, while the boundary layer appears in general when the nontrivial physical boundary is present and the classical noslip boundary condition is imposed. In 1904 Ludwig Prandtl proposed the formal expansion describing the behavior of the flows at small viscosity, however, the mathematical justification of this expansion is known as a difficult problem. In this talk we review the recent progress on the mathematical analysis of this problem. 
Professor @ University of New England, Australia.
Yihong obtained his PhD in 1988 from Shandong University (China). After spending two years at Shandong University as a Lecturer (198890),
and one year at HeriotWatt University, UK,(199091), he joined UNE in 1991, as a postdoctoral research fellow (199192) working with Prof. E.N. Dancer.
He became a Lecturer at UNE in 1993 and was promoted to a Professor in 2008. While at UNE, he visited HeriotWatt University (UK), the Chinese Academy
of Science (1999, 2001), the University of Tokyo and Waseda University (2006), and the Institute of Mathematics and Applications at the University of Minnesota (2012).
Slides to the talk 
Spreading rate for the FisherKPP nonlocal diffusion equation with free boundary
Propagation has been modelled by reactiondiffusion equations since the pioneering works of Fisher and KolmogorovPeterovskiPiskunov (KPP). Much new developments have been achieved in the past several decades on the modelling of propagation, with traveling wave and related solutions playing a central role. In this talk, I will report some recent results obtained with several collaborators on the FisherKPP equation with free boundary and "nonlocal diffusion". A key feature of this nonlocal equation is that the propagation may or may not be determined by traveling wave solutions. There is a threshold condition on the kernel function which determines whether the propagation rate is linear or superlinear in time, also known as accelerated spreading in the latter case, where the rate of spreading is not determined by traveling waves. For some typical kernel functions, sharp estimates of the spreading rate will be presented. 
Professor @ City University of Hong Kong.
Professor Luo received his PhD from Chinese Academy of Sciences in 1995 under the
supervision of Prof. Ling Hsiao. He held positions at Georgetown University and
University of Michigan before joining the City University of Hong Kong in 2016,
where he is holding a position of professor.
Slides to the talk 
Estimates and geometry for a free surface problem of fluids with heatconductivity
In this talk, I shall discuss results on the estimates for a free surface problem of highly subsonic heatconducting inviscid flow. The issues on the loss of derivatives and the coupling of interior solutions and evolving boundary geometry will be addressed. This talk is based on a joint work with Prof. Huihui Zeng at Tsinghua University. 
Professor @ Caltech University, United States, and @ Ludwig Maximilian University of Munich, Germany.
He defended his PhD thesis in 2007 @ the Royal Institute of Technology in Stockholm under the supervision of Ari Laptev. After a postdoctoral internship and assistant professorship @ Princeton, in 2013 he became professor @ Caltech and in 2016 at LMU Munich.
Slides to the talk 
Blowup of solutions of critical elliptic equations in three dimensions
We describe the asymptotic behavior of positive solutions \(u_\varepsilon\) of the equation \[\Delta u + au = 3\,u^{5\varepsilon}\qquad \textrm{in \(\Omega\subseteq\,\mathbb{R}^3\)}\] with a homogeneous Dirichlet boundary condition. The function \(a\) is assumed to be critical in the sense of Hebey and Vaugon and the functions \(u_\varepsilon\) are assumed to be an optimizing sequence for the Sobolev inequality. Under a natural nondegeneracy assumption we derive the exact rate of the blowup and the location of the concentration point, thereby proving a conjecture of Brézis and Peletier (1989). Similar results are also obtained for solutions of the equation \[\Delta u + (a+\varepsilon V) u = 3\,u^5\qquad\textrm{ in \(\Omega\).}\] For the variational problem corresponding to the latter problem we also obtain precise energy asymptotics and a detailed description of the blowup behavior of almost minimizers (but not necessarily minimizers or solutions). 
Assistant Professor @ Seoul National University, South Korea.
Professor Jung received his PhD in 2017 from Princeton University, United States,
under the supervision of Professor Yakov Sinai. He became a Research Fellow @ the
Korean Institute of Advanced Study (KIAS) in 2017, where he was promoted to KIAS
Fellow in 2019. Since March 2023, Jung is Assistant Professor @ Seoul National University.
Slides to the talk 
Illposedness for incompressible fluid models at critical Sobolev regularity
We consider the incompressible fluid equations including the Euler and SQG equations in critical Sobolev spaces, which are Sobolev spaces with the same scaling as the Lipschitz norm of the velocity. We show that initial value problem for the equations are illposed at critial regularity. Such an illposedness result can be used to prove enhanced dissipation for the dissipative counterpart. The proof relied on the Key Lemma of Kiselev and Sverak, which allows to compute the main term of the velocity gradient. This is based on joint works with Tarek Elgindi, Tsuyoshi Yoneda, and Junha Kim. Video of the talk not yet released. 
Professor @ AixMarseille Université, France
Professor Hamel received his PhD in 1996 @ Sorbonne University
(ExParis VI) under the supervision of Henri Berestycki. Before he
had the privilege to be a student @ the École Normale
Supçrieure de Paris (ENS), later to be a researcher @ CNRS from
1995 until 2001. Since 2001, François Hamel is professor @
AixMarseille Université. He was a Visiting professor @ MIT,
United States and member of the Institut Universitaire de France
from 2009 until 2014.
Slides to the talk 
Symmetry properties for the Euler equations and semilinear elliptic equations
In this talk, I will discuss radial and onedimensional symmetry properties for the stationary incompressible Euler equations in dimension 2 and some related semilinear elliptic equations. I will show that a steady flow of an ideal incompressible fluid with no stagnation point and tangential boundary conditions in an annulus is a circular flow. The same conclusion holds in complements of disks as well as in punctured disks and in the punctured plane, with some suitable conditions at infinity or at the origin. I will also discuss the case of parallel flows in twodimensional strips, in the halfplane and in the whole plane. The proofs are based on the study of the geometric properties of the streamlines of the flow and on radial and onedimensional symmetry results for the solutions of some elliptic equations satisfied by the stream function. The talk in based on joint work with N. Nadirashvili. See the video of the talk
on our YouTube Channel.

Professor and Head of the Department of Mathematics and Statistics @ the University of Western Australia.
Serena Dipierro took her PhD in Mathematical Analysis @ the International School for Advanced Studies
(SISSA, Trieste) in 2012. After PostDoc positions @ the Universidad de Chile and University of Edinburgh,
and a Humboldt Fellowship, she held permanent positions @ the University of Melbourne and the Università di Milano.
In August 2018 she moved @ the University of Western Australia, where she is now Professor and Head of the
Department of Mathematics and Statistics.
Slides to the talk 
Boundary behaviour of nonlocal minimal surfaces
In this talk we present a peculiar behaviour of nonlocal minimal surfaces (i.e. local minimisers of a nonlocal perimeter functional), namely the capacity, and the strong tendency, of adhering to the boundary of the reference domain. This characteristic is in contrast not only with the boundary behaviour of classical minimal surfaces but also with the pattern produced by solutions of linear equations. We will discuss this phenomenon and present some recent results. See the video of the talk
on our YouTube Channel.

Professor @ Tokyo Institute of Technology.
Professor Kagei received his Doctor of Science from Hiroshima University in 1994.
He was research fellow of the Alexander von Humboldt Foundation from 1997 until 1998 @
the University of Bayreuth, Germany. In 1998, Kagei becam Associate Professor @ Kyushu University in Japan,
where he got promoted to Professor in 2006. Since 2019, Kagei is Professor @ the Tokyo Institute of Technology. He
was awarded in 1998 with the prestigeous MSJ Takebe Katahiro Prize of the Mathematical Society of Japan and
in 2012 with the Analysis Prize of the Mathematical Society of Japan.

Stability and bifurcation analysis of the compressible NavierStokes equations
The compressible NavierStokes equation, which is the basic equation for compressible viscous fluids, is classified as a quasilinear hyperbolicparabolic system. Due to the hyperbolic and parabolic aspects of the sysytem, solutions exhbit iinteresting behavior. In this talk, I will review the stability and bifurcation analysis of the compressible NavierStokes equation, and state some recent results on a related bifurcation phenomenon and singular limit problem. See the video of the talk
on our YouTube Channel.

Professor @ Wuhan University, China.
Professor Miao received his PhD in July 2013 @ the University of Chinese Academy of Sciences
under the supervision of Prof. Demetrios Christodoulou and Prof. Ping Zhang. Before he accepted the
professorship @ Wuhan University, he held several postdoc positions @ University of Michigan, @ ETH Zurich,
and @ EPFL in Switzland.
Slides to the talk 
On the free boundary hard phase fluid in Minkowski spacetime
I will present a recent work on the free boundary hard phase fluid model with Minkowski background. The hard phase model is an idealized model for a relativistic fluid where the sound speed approaches the speed of light. This work consists of two results: First, we prove the wellposedness of this model in Sobolev spaces. Second, we give a rigorous justification of the nonrelativistic limit for this model as the speed of light approaches infinity. This is joint work with Sohrab Shahshahani and Sijue Wu. See the video of the talk
on our YouTube Channel.

Postdoctoral Fellow @ University of British Columbia, Canada.
Palmer received his PhD in mathematics @ Cornell University in 2016 under the supervision of Tim Healey
on a topic of nonlinear elasticity. Currently, he is working as a postdoctoral fellow @ the University of British Columbia jointly
with Nassif Ghoussoub and YoungHeon Kim on topics related to optimal transport.
Slides to the talk 
Hidden Convexity in problem of Nonlinear Elasticity
Problems in elasticity / solid mechanics have been essential to the development of the theory of partial differential equations and Calculus of Variations. However, fundamental questions regarding the regularity of equilibria in nonlinear elasticity remain largely unanswered. The theory of optimal transport has had a lot of recent success in the analysis of nonlinear PDE, ranging from the MongeAmpere equation to kinetic gas equations. In a recent work, we introduced techniques from optimal transport to problems of nonlinear elasticity and uncover a hidden convexity. I will discuss the connection between optimal transport and nonlinear elasticity, and our results on when equilibria in nonlinear elasticity correspond to minimizers of an optimal transport problem. This is joint work with Nassif Ghoussoub and Hugo Lavenant. See the video of the talk
on our YouTube Channel.

Professor @ Nagoya University, Japan
Professor Sugimoto was a Research Associate @ University of Tsukuba in 198790 and received his Ph.D. there in 1992. He worked @ Osaka University from 1990 until 2008, and is now a Professor @ Nagoya University since 2008.
Slides to the talk 
A constructive approach to semilinear wave equations
In this talk, I will explain a new attempt to construct selfsimilar solutions to semilinear wave equations with power nonlinearity. The existence of selfsimilar solutions to the same equations has been already established by Pecher (2000), KatoOzawa (2003), etc. based on the standard fixed point theorem. We will rediscuss it by a constructive approach using the theory of hypergeometric differential equations. See the video of the talk
on our YouTube Channel.

Head of the Laboratoire JacquesLouis Lions and Professor @ Sarbonne Université,
CNRS, Université de Paris, France
Emmanuel Trélat got his PhD in 2000 in optimal control
and subRiemannian geometry, under the supervision of Bernard
Bonnard, at Dijon University, France. He became an assistant
professor at ParisSud University (Orsay) in 2001, then professor at
Orléans University in 2006, and he moved to Pierre
et Marie Curie University (now named Sorbonne University) at Paris in 2011.
He is the head of Laboratoire JacquesLouis Lions.
Slides to the talk 
Spectral analysis of subRiemannian Laplacians and Weyl measure
In collaboraton with Yves Colin de Verdière and Luc Hillairet, we study spectral properties of subRiemannian Laplacians, which are selfadjoint hypoelliptic operators satisfying the Hörmander condition. Thanks to the knowledge of the smalltime asymptotics of heat kernels in a neighborhood of the diagonal, we establish the local and microlocal Weyl law. When the Lie bracket configuration is regular enough (equiregular case), the Weyl law resembles that of the Riemannian case. But in the singular case (e.g., BaouendiGrushin, MarVnet) the Wey law reveals much more complexity. In turn, we derive quantum ergodicity properties in some subRiemannian cases.
See the video of the talk
on our YouTube Channel.

Professor @ the Beijing Institute of Technology.
Rongchan Zhu got her Phd in 2021 @ Chinese Academy of Science and Bielefeld University. Now, she is professor @ the Beijing Institute of Technology.
Slides to the talk 
Large \(N\) Limit of the \(O(N)\) Linear Sigma Model via Stochastic Quantization
In this talk, I will discuss large \(N\) limits of a coupled system of \(N\) interacting \(\Phi^4\) equations posed over \(\mathbb{T}^{d}\) for \(d=1,2,3\), known as the \(O(N)\) linear sigma model. Uniform in \(N\) bounds on the dynamics are established, allowing us to show convergence to a meanfield singular SPDE, also proved to be globally wellposed. Moreover, I show tightness of the invariant measures in the large \(N\) limit. For large enough mass, they converge to the (massive) Gaussian free field, the unique invariant measure of the meanfield dynamics, at a rate of order \(1/\sqrt{N}\) with respect to the Wasserstein distance. I will also consider fluctuations and obtain tightness results for certain \(O(N)\) invariant observables, along with an exact description of the limiting correlations in \(d=1,2\). This talk is based on joint work with Hao Shen, Scott Smith and Xiangchan Zhu. See the video of the talk
on our YouTube Channel.
