## Talks earlier this year

List of speakers (in alphabetical order)
1. Goro Akagi, Traveling wave dynamics for a one-dimensional constrained Allen-Cahn equation , Monday, 13 September 2021.
2. Mark Ashbaugh, A Faber-Krahn Result for the Vibrating Clamped Plate under Compression , Monday, 28 February 2022.
3. Sandra Cerrai, Incompressible viscous fluids in the plane and SPDEs on graphs., Monday, 22 November 2021.
4. Beomjun Choi, Liouville theorem for surfaces translating by sub-affine-critical powers of Gauss curvature, Monday, 27 September 2021.
5. Chiun-Chuan Chen, Traveling wave solutions for the diffusive Lotka-Volterra system of 3 competing species, Monday,15 November 2021.
6. Florica Cirstea, Anisotropic elliptic equations with gradient-dependent lower order terms and $$L^1$$ data, Monday, 20 September 2021.
7. Cristiana De Filippis, Perturbations beyond Schauder data, Monday, 8 November 2021.
8. Serena Dipierro, Boundary behaviour of nonlocal minimal surfaces, Monday, 22 February 2021.
9. Yihong Du, Spreading rate for the Fisher-KPP nonlocal diffusion equation with free boundary , Monday, 31 May 2021.
10. Renjun Duan, Low-regularity solutions to the non-cutoff Boltzmann equation: existence, regularity and grazing limit , Monday, 28 March 2021.
11. Ilaria Fragala, Concavity properties of solutions to Robin problems , Monday, 5 July 2021.
12. Rupert Frank, Blow-up of solutions of critical elliptic equations in three dimensions , Monday, 10 May 2021.
13. Nicola Garofalo, A heat equation approach to some problems in conformal geometry., Monday, 19 July 2021.
14. Emanuela Gussetti, A pathwise stochastic Landau-Lifschitz-Gilbert equation via rough paths in 1D., Monday, 16 May 2022.
15. François Hamel, Symmetry properties for the Euler equations and semilinear elliptic equations, Monday, 12 April 2021.
16. In-Jee Jung, Ill-posedness for incompressible fluid models at critical Sobolev regularity, Monday, 26 April 2021.
17. Yoshiyuki Kagei, Stability and bifurcation analysis of the compressible Navier-Stokes equations, Monday, 8 March 2021.
18. Derek Kielty, Degeneration of the spectral gap with negative Robin parameter., Monday, 30 August 2021.
19. Minhyun Kim, Nonlocal problems with non-standard growth , Monday, 6 December 2021.
20. Sunghan Kim, Uniform regularity in homogenization problems of fully nonlinear equations , Monday, 14 March 2022.
21. Wei-Xi Li, Gevrey well-posedness of the 3D Prandtl equations without Structural Assumption , Monday, 26 July 2021.
22. Yuan Lou, On principal eigenvalues for elliptic and parabolic operators , Monday, 1 November 2021.
23. Tao Luo, Estimates and geometry for a free surface problem of fluids with heat-conductivity , Monday, 17 May 2021.
24. Yasunori Maekawa, Recent progress on the Prandtl boundary layer expansion for viscous incompressible flows , Monday, 14 June 2021.
25. Shuang Miao, On the free boundary hard phase fluid in Minkowski space-time, Monday, 15 February 2021.
26. Tatsuya Miura, Li-Yau type inequality for curves and applications, Monday, 6 September 2021.
27. Yoichi Miyazaki, A tour of Sobolev spaces by Muramatu's integral formula, Monday, 11 October 2021.
28. Monica Musso, Vortex filaments for Euler equations , Monday, 25 October 2021.
29. Toru Nogayama, Maximal regularity in Besov-Morrey spaces and its application to Keller-Segel System, Monday, 12 July 2021.
30. Aaron Palmer, Hidden Convexity in problem of Nonlinear Elasticity, Monday, 22 March 2021.
31. Naoto Shida, Bilinear pseudo-differential operators with exotic symbols, Monday, 7 March 2022.
32. Ken Shirakawa, Temperature optimization problems governed by semi-discrete phase-field models of grain boundary motions , Monday, 14 February 2022.
33. Adam Sikora, Square functions and Riesz transforms on a class of non-doubling manifolds , Monday, 21 June 2021.
34. Mitsuru Sugimoto, A constructive approach to semilinear wave equations, Monday, 25 January 2021.
35. Yutaka Terasawa, Convergence of a Nonlocal to a Local Diffuse Interface Model for Two-Phase Flow with Unmatched Densities, Monday, 10 May 2022.
36. Emmanuel Trélat, Spectral analysis of sub-Riemannian Laplacians and Weyl measure, 8, February 2021.
37. Po Lam Yung, Sobolev spaces revisited, 29, November 2021.
38. Zhifei Zhang, Linear inviscid damping and enhanced dissipation for shear flows, 24, January 2022.
39. Rongchan Zhu, Large $$N$$ Limit of the $$O(N)$$ Linear Sigma Model via Stochastic Quantization, Monday, 25 January 2021.
40. Enrique Zuazua, Inverse design for conservation laws and Hamilton-Jacobi equations, Monday, 21 March 2022.

Monday, 16 May 2022.
PhD student @ University of Bielefeld, Germany

Emanuela Gussetti is currently a Phd student at the University of Bielefeld (Germany), under the supervision of Professor Martina Hofmanová. She completed her Master degree at the University of Milan (Italy). Her main research interests are in the application of rough path for the study of stochastic PDEs.

#### Slides to the talk

A pathwise stochastic Landau-Lifschitz-Gilbert equation via rough paths in 1D

Using a rough path formulation, we investigate existence, uniqueness and regularity for the stochastic Landau-Lifshitz-Gilbert equation with multiplicative Stratonovich noise on the one dimensional torus. As a main result we show the Lipschitz continuity of the so-called Itô-Lyons map in the energy spaces $$L^\infty(0,T;H^k)\cap L^2(0,T;H^{k+1})$$ for any $$k \ge 1$$. As a consequence we then deduce a Wong-Zakai type result, a large deviation principle for the solution and a support theorem. At the end of the talk, I will discuss some recent results.

The talk is based on a joint work with Antoine Hocquet.

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Monday, 9 May 2022.
Associate Professor @ Nagoya University, Japan

Yutaka Terasawa obtained a doctor degree in Science in Hokkaido University in Japan in 2007 under supervision by Tohru Ozawa and Yoshikazu Giga. He got a JSPS Research Fellowships for Young Scientists (DC2 and PD) from 2006 to 2008, by which he collaborated with Helmut Abels in Stefan Müller's group in Max Planck Institute for Mathematics in the Applied Sciences in Leipzig. After that, he spent six months further as a postdoc fellow at the same institute, three months in Université Paris-Est-Marne-la-Vallée in Paris and three months in Charles University in Prague from 2008 to 2009. He became a research assistant in Tohoku University in 2009. In 2010, we was a specially appointed researcher at the University of Tokyo. Terasawa received the JSPS Research Fellowship for Young Scientists (PD) in 2011, and in 2013, he was appointed as assistant professor in 2013 at the University of Tokyo.

Since 2014, he is appointed as associate professor at the Graduate School of Mathematics of the Nagoya University in Japan. His main research interest is in mathematical analysis of incompressible fluids, especially diffuse interface models of two-phase flow, harmonic analysis and probability theory.

#### Slides to the talk

Convergence of a Nonlocal to a Local Diffuse Interface Model for Two-Phase Flow with Unmatched Densities

We prove convergence of suitable subsequences of weak solutions of a diffuse interface model for the two-phase flow of incompressible fluids with different densities with a nonlocal Cahn-Hilliard equation to weak solutions of the corresponding system with a standard local'' Cahn-Hilliard equation. The analysis is done in the case of a sufficiently smooth bounded domain with no-slip boundary condition for the velocity and Neumann boundary conditions for the Cahn-Hilliard equation. The proof is based on the corresponding result in the case of a single Cahn-Hilliard equation and compactness arguments used in the proof of existence of weak solutions for the diffuse interface model.

This talk is based on a recent joint work with Helmut Abels (Regensburg Univ., Germany).

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Monday, 28 March 2022.
Professor @ The Chinese University of Hong Kong, Hong Kong

Professor Duan received his PhD in 2008 at City University of Hong Kong under the supervision of Professor Tong Yang. After graduation, he spent two years as a postdoctoral fellow at RICAM, Austrian Academy of Sciences. From 2010 to present, he has been in the Chinese University of Hong Kong. He was appointed to be an Associate Professor in 2018. His research interest mainly focuses on kinetic theory, in particular, Boltzmann equation and related kinetic equations.

#### Slides coming soon

Low-regularity solutions to the non-cutoff Boltzmann equation: existence, regularity and grazing limit

The Wiener algebra is the space of all integrable functions on torus whose Fourier series are absolutely convergent. In the talk, we will present an application of the Wiener algebra to the mathematical study of the non-cutoff Boltzmann equation on torus. We develop a complete $$L^2$$ theory in the close-to-equilibrium framework for global existence, uniform Gevrey regularity and grazing collision limit of low-regularity solutions to the Cauchy problem on the non-cutoff Boltzmann equation.

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Monday, 21 March 2022.
Humboldt Professor @ Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany, Professor @ Universidad Autónoma de Madrid, Spain, Director of CCM @ University of Deusto, Spain

Enrique Zuazua Iriondo (Eibar, Basque Country – Spain, 1961) holds the Chair of Dynamics, Control and Numerics – Alexander von Humboldt Professorship at FAU- Friedrich–Alexander University, Erlangen–Nürnberg (Germany). He also leads the research project "DyCon: Dynamic Control", funded by the ERC – European Research Council at the Department of Mathematics, at UAM – Autonomous University of Madrid and Deusto Foundation, University of Deusto – Bilbao (Basque Country, Spain), where he holds secondary appointments as Professor of Applied Mathematics (UAM) and Director of CCM – Chair of Computational Mathematics (Deusto).

His research in the area of Applied Mathematics covers topics in Partial Differential Equations, Systems Control, Numerical Analysis and Machine Learning, and led to fruitful collaborations in different industrial sectors such as the optimal shape design in aeronautics, the management of electrical and water distribution networks and the design of recommendation systems. His research had a high impact (h-index 44) and he has mentored a significant number of postdoctoral researchers and coached a wide network of Science managers.

He holds a degree in Mathematics from the University of the Basque Country, and a dual PhD degree from the same university (1987) and the Université Pierre et Marie Curie, Paris (1988). In 1990 he became Professor of Applied Mathematics at the Complutense University of Madrid, to later move to UAM in 2001.

He has been awarded the Euskadi (Basque Country) Prize for Science and Technology 2006 and the Spanish National Julio Rey Pastor Prize 2007 in Mathematics and Information and Communication Technology and the Advanced Grants NUMERIWAVES in 2010 and DyCon in 2016 of the European Research Council (ERC).

He is an Honorary member of the Academia Europaea and Jakiunde, the Basque Academy of Sciences, Letters and Humanities, Doctor Honoris Causa from the Université de Lorraine in France and Ambassador of the Friedrich-Alexander University, Erlangen-Nürenberg, Germany. He was an invited speaker at ICM2006 in the section on Control and Optimization.

From 1999-2002 he was the first Scientific Manager of the Panel for Mathematics within the Spanish National Research Plan and the Founding Scientific Director of the BCAM – Basque Center for Applied Mathematics from 2008-2012. He is also a member of the Scientific Council of a number of international research institutions such as the CERFACS in Toulouse, France and member of the Editorial Board in some of the leading journals in Applied Mathematics and Control Theory.

#### Slides to the talk

Inverse design for conservation laws and Hamilton-Jacobi equations

We discuss the problem of inverse design, or time inversion, for scalar conservation laws and Hamilton-Jacobi equations. The presence of singularities in the forward evolution is an obstruction for backward uniqueness and the unilateral bounds generated by the forward dynamics establishe thresholds on the set of reachable data. In this lecture we shall present our recent works in collaboration with Thibault Liard and Carlos Esteve, characterising the set of reachable states, identifying the multiplicity of initial data leading to a final target, and the determining the role of backward entropy or viscous solutions. We also develop numerical algorithms allowing to reconstruct the set of inversions and present some numerical experiments.

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Monday, 14 March 2022.
Postdoctoral Fellow @ Uppsala University, Sweden

Dr Kim received his Phd in 2019 @ Seoul National University (Korea) under the supervision of Professor Ki-Ahm Lee. Following this, he spent one year as a postdoctoral fellow @ KTH Royal Institute of Technology in Stockholm, Sweden. Since 2021, Kim works as a postdoctoral fellow @ Uppsala University, Sweden.

#### Slides coming soon

Uniform regularity in homogenization problems of fully nonlinear equations

When two different materials are mixed in small scales, under certain patterns, the effective property of the composite material in large scales is determined in a nontrivial way. Mathematically, it involves solving a family of equations with rapidly oscillating variables parameterized by the length of the small scale and studying the behavior of the solutions and the equations at the limit. Due to certain patterns in the rapid oscillation of the variables, the equation at the limit is usually homogeneous in space. Therefore, the solution at the limit tends to behave nicely, which makes the solutions close to the limit behave more regular, uniformly in small scales, than the standard regularity theory ensures, despite the rapid oscillation of the equations at those scales. For this reason, the uniform regularity in homogenization problems has gained many interests and has contributed to the development of the regularity theory in various ways. Still, the uniform regularity has only been recently established for fully nonlinear equations.

In this talk, I am going to briefly overview the feature and history of this problem, and introduce the recent results on sharp uniform estimates for fully nonlinear equations.

This talk will be partially based on joint work with Ki-Ahm Lee.

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Monday, 7 March 2022.
Ph.D. student @ Osaka University, Japan

Naoto Shida is currently Ph.D. student @ Osaka University under the supervision of Professor Naohito Tomita. He got his Master's degree from Osaka University in 2020.

#### Slides coming soon

Bilinear pseudo-differential operators with exotic symbols

In this talk, we consider the boundedness of bilinear pseudo- differential operators with symbols

in the bilinear Hörmander class $$BS^m_{\rho, \rho}$$, $$0 \le \rho <1$$.

First, we consider the case $$\rho = 0$$.

In particular, we give an improvement of $$L^2 \times L^2 \to L^1$$ boundedness by using Besov spaces.

Furthermore, we discuss the Kato-Ponce type inequality (or fractional Leibniz type rule)

for these operators in the setting of Besov spaces.

Secondly, we give a remark on the condition $$1/p = 1/p_1 + 1/p_2$$ for $$L^{p_1} \times L^{p_2} \to L^p$$ boundedness

of those operators. This talk is partially based on a joint work with Tomoya Kato (Gunma Univ.)

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Monday, 28 February 2022.
Professor Emeritus @ University of Missouri - Columbia, United States

Professor Ashbaugh received his Ph.D. in Mathematical Physics from Princeton University in 1980, working under the direction of Barry Simon. He visited @ the University of Tennessee-Knoxville for the 2 years 1980-82 and has been @ the University of Missouri-Columbia since 1982. Ashbaugh has visited extensively in Chile, most recently as a Fulbright Fellow at the Pontificia Universidad Católica de Chile in Santiago in 2009 and at the Universidad de Concepción in 2018. Ashbaugh is now an Emeritus Professor of Mathematics, having retired from the University of Missouri in 2015.

#### Slides to the talk

Temperature optimization problems governed by semi-discrete phase-field models of grain boundary motions

We give a Faber-Krahn result for the first eigenvalue of the vibrating clamped plate under compression, that is, we show that the lowest eigenvalue of this problem for an arbitrary planar domain $$\Omega$$ is bounded below by that of a disk of the same area for sufficiently small compressions $$\kappa$$. Note that this is a result for $$n=2$$ dimensions only, and is sharp. The corresponding result for the vibrating clamped plate (i.e., when $$\kappa = 0$$) was proved by Nadirashvili in 1995 for dimension $$n = 2$$, followed quickly by an alternative proof by Benguria and the speaker that succeeds for dimensions $$n=2$$ and $$n=3$$ (Duke Math. J., 1995).

This is joint work with R. Benguria and R. Mahadevan. We take a similar approach to that used in the 1995 Ashbaugh-Benguria paper. Interestingly, the proof does not extend to any $$\kappa > 0$$ when $$n = 3$$, even though the $$\kappa = 0$$ case is known for $$n = 3$$. We explain why this is so.

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Monday, 24 January 2022.
Professor @ Chiba University, Japan

Ken Shirakawa obtained his PhD from Chiba University, Japan, in 2001. He has been studied mathematical analysis of nonlinear evolution equations, nonlinear variational problems, nonlinear PDEs, and his recent interest has been in phase field models of grain boundary motions. He has been an associate professor at Department of Mathematics, Faculty of Education, Chiba University, since Oct. 2010.

#### Slides to the talk

Temperature optimization problems governed by semi-discrete phase-field models of grain boundary motions

In this talk, we consider a class of optimal control problems which are governed by phase-field systems associated with grain boundary motions. The state-systems are time-discrete gradient flows, and the governing energies are based on the free-energy of planar grain boundary motions, proposed by [Kobayashi–Warren–Carter, Physica D 140 (2000)]. On this basis, the principal component of the control is given by the relative temperature. In the former part of this talk, we discuss about the solvability of the optimal control problems with the well-posedenss of state-systems; the first order necessary optimality conditions in regular cases of problems; and the limiting approaches to the optimality conditions in singular cases. Meanwhile, in the latter part, we focus on the 1D-case of the spatial domain. On this basis, we deal with some advanced issues, concerned with $$H^2$$-regularity of the solutions to state-systems; precise characterizations of the limiting optimality conditions.

This talk is based on recent jointwork with Harbir Antil (George Mason Univ., USA), Shodai Kubota (Chiba Univ., Japan), and Noriaki Yamazaki (Kanagawa Univ., Japan).

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Monday, 24 January 2022.
Boya Distinguished Professor @ Peking University, China

Zhifei Zhang is a Boya Distinguished Professor at the School of Mathematical Sciences, Peking University. His research interests include the interface problem of the incompressible fluids, mathematical theory of the liquid crystal, hydrodynamic stability at high Reynolds number, and other topics such as the well-posedness of the hydrodynamic equations.

#### Slides to the talk pending

Linear inviscid damping and enhanced dissipation for shear flows

The inviscid damping and enhanced dissipation play a crucial role in the hydrodynamic stability. Both stabilizing effects are due to the mixing mechanism induced by shear flows. In this talk, I will introduce many approaches developed by some joint works with Q. Chen, T. Li, D. Wei and W. Zhao, to establish the inviscid damping and enhanced dissipation for the linearized Navier-Stokes system around shear flows including the monotone shear flow and Kolmogorov flow.

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Monday, 6 December 2021.
Postdoctoral Fellow @ Bielefeld University, Germany.

Dr Kim received his PhD in 2020 from Seoul National University, Korea, where his supervisor was Prof. Ki-Ahm Lee. Following this, he accepted his first postdoctoral position at Chung-Ang University, Korea and since 2021, he is a postdoctoral research fellow at Bielefeld University, Germany.

#### Slides to the talk pending

Nonlocal problems with non-standard growth

In the calculus of variations, functionals with non-standard 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.

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Monday, 29 November 2021.
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 2010-2013, he held the Hill Assistant Professorship @ Rutgers, New Jersey. Following this, we became a Tichmarsh Fellow from 2013-2014 @ the University of Oxford and Assistant Professorship @ the Chinese University of Hong Kong from 2014-2020. 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 Gagliardo-Nirenberg 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.

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Monday, 22 November 2021.
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 Mittag-Leffler 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 long-time 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 reaction-diffusion-advection equations in the plane. I will show that as the divergence-free 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.

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Monday, 15 November 2021.
Professor @ National Taiwan University (NTU), Taiwan.
Dr. Chiun-Chuan 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 Chung-Cheng University. In 1996, he joined NTU and has been a professor there since 1998. He visited Harvard University for one year during 2007-2008. He was awarded the National Chair Professorship in 2008. His research interest mainly focuses on elliptic equations, variational problems, and reaction-diffusion equations with applications to biology.

#### Slides to the talk

Traveling wave solutions for the diffusive Lotka-Volterra system of 3 competing species

This talk concerns with the 3-species Lotka-Volterra competition system. Especially we are interested in a type of traveling wave solutions with a non-monotone 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.

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Monday, 8 November 2021.
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 G-Research 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

So-called 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.

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Monday, 1 November 2021.
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 (1995-1996) and Dickson Instructor at University of Chicago (1996-1998). 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 reaction-diffusion equations with applications to biology. He has authored 130+ papers on these topics. He served as Associate Director of Mathematical Biosciences Institute (2009-2013). Currently he is serving as Co Editor-in-Chief of Discrete and Continuous Dynamical Systems-Series 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 time-periodic 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.

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Monday, 25 October 2021.
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 3-dimension. 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 so-called "binormal curvature flow". Existence of true solutions whose vorticity is concentrated near a given curve that evolves by this law is a long-standing open question that has only been answered for the special case of a circle travelling with constant speed along its axis, the thin vortex-rings. In this talk I will discuss the construction of helical filaments, associated to a translating-rotating helix, and of two vortex rings interacting between each other, the so-called 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).

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Monday, 11 October 2021.
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 Hardy-Littlewood 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 Hölder-Zygmund 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 Gagliardo-Nirenberg inequality and its generalization which replaces the $$L^\infty$$ norm with the BMO norm or the homogeneous Besov norm, the Brezis-Gallouet-Wainger inequality, the Brezis-Wainger 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.

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Monday, 27 September 2021.
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 sub-affine-critical powers of Gauss curvature

We classify the translators to the flows by sub-affine-critical powers of Gauss curvature in $$\mathbb{R}^3$$. If $$\alpha$$ denotes the power, this is a Liouville theorem for degenerate Monge-Ampere equations $$\det D^2u = (1+|Du|^2)^{2-\frac{1}{2\alpha}}$$ for $$0<\alpha<1/4$$. For the affine-critical-case $$\det D^2u =1$$, 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.

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Monday, 20 September 2021.
Associate Professor @ University of Sydney.
A/Professor Florica Cirstea 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 gradient-dependent 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 divergence-form nonlinear anisotropic operator $$\mathcal A$$, the prototype of which is $$\mathcal A u=-\sum_{j=1}^N \partial_j(|\partial_j u|^{p_j-2}\partial_j u)$$ 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 pseudo-monotone from $$W_0^{1,\overrightarrow{p}}(\Omega)$$ into its dual, as well as a gradient-dependent 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).

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Monday, 13 September 2021.
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, Allen-Cahn and Cahn-Hilliard 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 one-dimensional constrained Allen-Cahn equation

This talk concerns a one-dimensional Allen-Cahn equation on the whole line with the positive-part function, which constrains the growth of each solution to be non-decreasing. We shall discuss traveling wave dynamics, which has been well studied for classical Allen-Cahn equations, for the constrained one. More precisely, we shall start with constructing a one-parameter 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 Allen-Cahn 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 Ken-Ichi Nakamura (Kanazawa).

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Monday, 6 September 2021.
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

Li-Yau type inequality for curves and applications

A classical result of Li-Yau 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'Acqua-Novaga-Pluda.

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Monday, 30 August 2021.
PhD Student @ University of Illinois Urbana-Champaign, United States.
Derek Kielty is a sixth-year Ph.D. student at the University of Illinois Urbana-Champaign 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.

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Monday, 26 July 2021.
Professor @ Wuhan University, China.
Wei-Xi 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 Fokker-Planck operator and related models.

#### Slides to the talk

Gevrey well-posedness of the 3D Prandtl equations without Structural Assumption

We establish the well-posedness 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 ill-posedness are not worse than the two dimensional ones. Joint work with Nader Masmoudi and Tong Yang.

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Monday, 19 July 2021.
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 Mittag-Leffler 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 1989-2013, 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 Kohn-Spencer 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 so-called 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 self-contained 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.

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Monday, 12 July 2021.
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 Besov-Morrey spaces and its application to Keller-Segel 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 non-reflexive Banach spaces are not UMD. In this talk, we discuss the maximal regularity of the heat equation in Besov--Morrey spaces which are not reflexive. As an application, we present the well-posedness results for the two dimensional Keller--Segel system.

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Monday, 5 July 2021.
Professor @ Politecnico di Milano, Italy.
1999: Researcher at Politecnico di Milano; 2000 PhD in Mathematics at University of Pisa (Advisor G. Buttazzo); 2016-today: Full professor at Politecnico di Milano. Main fields of interest: Calculus of variations, shape optimization, PDEs. Author of 80 publications on peer-reviewed journals.

#### Slides to the talk

Concavity properties of solutions to Robin problems

We present some recent results about the log-concavity of the Robin ground state and the power concavity of the Robin torsion function on convex domains in the Euclidean N-dimensional 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 Andrews-Clutterbuck-Hauer. Anyhow, many related open questions remain open.

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Monday, 28 June 2021.
Professor @ Chung-Ang 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 Chung-Ang University in Seoul.

#### Slides to the talk

On the Korteweg-de Vries limit for the Fermi-Pasta-Ulam system

The Fermi-Pasta-Ulam (FPU) system is a simple nonlinear dynamical lattice model describing a one-dimensional 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 quasi-periodic 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.

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Monday, 14 June 2021.
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 Fisher-KPP 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 $$L^p(\mathcal{M})$$.

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Monday, 31 May 2021.
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 (1988-90), and one year at Heriot-Watt University, UK,(1990-91), he joined UNE in 1991, as a postdoctoral research fellow (1991-92) 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 Heriot-Watt 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 Fisher-KPP nonlocal diffusion equation with free boundary

Propagation has been modelled by reaction-diffusion equations since the pioneering works of Fisher and Kolmogorov-Peterovski-Piskunov (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 Fisher-KPP 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.

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Monday, 17 May 2021.
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.

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Estimates and geometry for a free surface problem of fluids with heat-conductivity

In this talk, I shall discuss results on the estimates for a free surface problem of highly subsonic heat-conducting 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.

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Monday, 10 May 2021.
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 post-doctoral internship and assistant professorship @ Princeton, in 2013 he became professor @ Caltech and in 2016 at LMU Munich.

#### Slides to the talk

Blow-up 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 blow-up 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 blow-up behavior of almost minimizers (but not necessarily minimizers or solutions).

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Monday, 26 April 2021.
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

Ill-posedness 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 ill-posed at critial regularity.

Such an ill-posedness 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.

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Monday, 22 February 2021.
Professor @ Aix-Marseille Université, France
Professor Hamel received his PhD in 1996 @ Sorbonne University (Ex-Paris 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 @ Aix-Marseille 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 one-dimensional 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 two-dimensional strips, in the half-plane 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 one-dimensional symmetry results for the solutions of some elliptic equations satisfied by the stream function.

The talk in based on joint work with N. Nadirashvili.

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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.

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Monday, 8 March 2021.
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 Navier-Stokes equations

The compressible Navier-Stokes equation, which is the basic equation for compressible viscous fluids, is classified as a quasi-linear hyperbolic-parabolic 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 Navier-Stokes equation, and state some recent results on a related bifurcation phenomenon and singular limit problem.

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Monday, 15 February 2021.
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.

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On the free boundary hard phase fluid in Minkowski space-time

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 well-posedness of this model in Sobolev spaces. Second, we give a rigorous justification of the non-relativistic limit for this model as the speed of light approaches infinity.

This is joint work with Sohrab Shahshahani and Sijue Wu.

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Monday, 22 March 2021.
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 Young-Heon 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 Monge-Ampere 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.

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Monday, 25 January 2021.
Professor @ Nagoya University, Japan
Professor Sugimoto was a Research Associate @ University of Tsukuba in 1987-90 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.

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A constructive approach to semilinear wave equations

In this talk, I will explain a new attempt to construct self-similar solutions to semilinear wave equations with power nonlinearity. The existence of self-similar solutions to the same equations has been already established by Pecher (2000), Kato-Ozawa (2003), etc. based on the standard fixed point theorem. We will rediscuss it by a constructive approach using the theory of hypergeometric differential equations.

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Monday, 8 February 2021.
Head of the Laboratoire Jacques-Louis Lions and Professor @ Sarbonne Université, CNRS, Université de Paris, France
Emmanuel Trélat got his PhD in 2000 in optimal control and sub-Riemannian geometry, under the supervision of Bernard Bonnard, at Dijon University, France. He became an assistant professor at Paris-Sud 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 Jacques-Louis Lions.

#### Slides to the talk

Spectral analysis of sub-Riemannian Laplacians and Weyl measure

In collaboraton with Yves Colin de Verdière and Luc Hillairet, we study spectral properties of sub-Riemannian Laplacians, which are selfadjoint hypoelliptic operators satisfying the Hörmander condition.

Thanks to the knowledge of the small-time 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., Baouendi-Grushin, MarVnet) the Wey law reveals much more complexity. In turn, we derive quantum ergodicity properties in some sub-Riemannian cases.

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Monday, 15 March 2021.
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 mean-field singular SPDE, also proved to be globally well-posed. 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 mean-field 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.