Speaker I: Prof. Alexander G. Ramm, Department of Mathematics, Kansas State University, USA
Prof. Alexander G. Ramm
Kansas State University, USA
Alexander G. Ramm is an American mathematician. He has been a professor at Kansas State University since 1981 in mathematics.He is an author of more than 660 papers in math-ematical and physical Journals, of 15 monographs, and an editor of 3 books. His scientific interests include differential and integral equations, operator theory, mathematical physics, especially scattering theory and inverse problems, numerical analysis, especially methods for solving ill-posed problems, various problems of applied mathematics and theoretical engineering. Professor A.G.Ramm was awarded many honors. He received Distinguished Graduate faculty award in 1996 and received Khwarizmi International Award for mathematical research in 2004. He was a distinguished foreign professor at the Academy of Science of Mexico (1997), research CNRS professor in France (2003), distinguished visiting professor at the University of Cairo (2004, 2006), distinguished visiting professor supported by the UK Royal Academy of Engineering (2009). He was a Mercator Professor in 2007, Distinguished HKSTAM speaker (2005), London Mathematical Society speaker (2005). Ramm was a Fulbright Research Professor in Israel (Technion) in 1991–1992, an invited plenary speaker at 7th PACOM in 2009. He was a visiting professor at IMPAN in 2010, at MPI (Max Planck Institute) in 2011, at Beijing Institute of Technology (BIT) in 2013, a Fulbright Research Professor at the University of Lviv, Ukraine, in 2015. Ramm was an elected member of Electromagnetic Academy, MIT (June 1990) and a member of New York Academy of Science. He has been an associated editor of many professional journals.Title: Solution of the Millennium Problem on the Navier-Stokes EquationsAbstract: The Navier-Stokes problem in R3 consists of solving the equations: v' + (v, ∇) v = −∇p + ν∆v + f, x ∈ R3, t ≥ 0, ∇· v = 0, v(x, 0) = v0(x), where v = v(x, t) is the velocity of the incompressible viscous fluid, p = p(x, t) is the pressure, the density ρ = 1, f = f (x, t) is the force, v0 = v0(x) is the initial velocity. The aim of this talk is to explain the author’s result concerning the Navier- Stokes problem (NSP) in R3 without boundaries. It is proved that the NSP is contradictory in the following sense: If one assumes that the initial data v(x, 0) I≡ 0, ∇ · v(x, 0) = 0 and the solution to the NSP exists for all t ≥ 0, then one proves that the solution v(x, t) to the NSP has the property v(x, 0) = 0. This paradox (the NSP paradox) shows that the NSP is not a correct description of the fluid mechanics problem and the NSP does not have a solution defined on all t ≥ 0. In the exceptional case, when the data are equal to zero, the solution v(x, t) to the NSP exists for all t ≥ 0 and is equal to zero, v(x, t) ≡ 0. The results, mentioned above, are proved in –. These results solve one of the millennium problems.References1. A. G. Ramm, The Navier-Stokes problem, Morgan & Claypool Publish- ers, 2021.2. A. G. Ramm, Theory of hyper-singular integrals and its application to the Navier-Stokes problem, Contrib. Math. 2, (2020), 47-54. Open access Journal: www.shahindp.com/locate/cm; DOI: 10.47443/cm.2020.00413. A. G. Ramm, Comments on the Navier-Stokes problem, Axioms, 2021, 10, 95. Open access Journal: https://www.mdpi.com/2075-1680/10/24. A. G. Ramm, Navier-Stokes equations paradox, Reports on Math. Phys. (ROMP), 88, N1, (2021), 41-45.
Speaker II: Prof. Ovidiu Radulescu, University of Montpellier, France
Prof. Ovidiu Radulescu
University of Montpellier, France
Ovidiu Radulescu is a full professor (Professeur classe exceptionnelle), Team leader in the Laboratory of Pathogen Host Interactions (LPHI) UMR 5235, University of Montpellier, since 2009. Expert in systems and mathematical biology, most particular in deterministic and stochastic biochemical networks, model reduction and multiscale modelling of biological systems. Through many collaborations with wet lab biologists. He got his engineering degree in Solid State Physics (University of Bucharest, 1989), PhD in Theoretical Solid State Physics (Orsay, University of Paris 11, 1994), Master degree in Probability theory and analysis (University of Marne-la-Vallée, 1996), Habilitation in Applied Mathematics (University of Rennes 1, 11/12/2006). He is the expert for ERC (European Research Council), ANR (French National Research Agency), HCERES (High Council for the Evaluation of Research and Higher Education), NW0 (Netherlands Organisation for Scientific Research).Title: Mesoscale Modelling in Biology: from Genes and Cells to Tissues and OrgansAbstract: Multicellular organisms are amazing examples of complex organisation. Single cell functioning depends on the expression of tens of thousands of genes. Cells interact with each other and with the extracellular matrix in tissues and organs in a manner dependent on their current gene expression, but also on their spatial position, environmental cues, and past decisions. In physics, since Ludwig Boltzmann, many approaches have been developed for going, as described by Hilbert, “from atomistic views to laws of motion of continua”. This problem is very general and it is not surprising that Hilbert included it in his famous list of challenges for modern mathematics. Contrary to many physical systems such as gases, where atomistic fluctuations are fast, in biological systems some gene expression fluctuations can be slow. Therefore, in biology, mesoscale modelling has to cope with fluctuations and heterogeneity at multiple scales. In biological mesoscale models, cell populations are represented as distributions over multiple dimensions, including space, but potentially also tens of thousands of genes. In order to obtain tractable models, dimensionality reduction has to be employed. Single cell technologies reveal distributions of gene expression and transitions between cell types in cell populations. Single cell, single molecule and multimodal imaging techniques add quantitative precision and spatial dimension to these descriptions. The availability of such data is a unique opportunity for developing and validating new mechanistic modelling approaches that bring biology closer to physical sciences. In this talk I will discuss examples of mesoscale modelling in infectious diseases, cancer, and developmental biology.
Speaker III: Prof. Hajime Urakawa, Department of Mathematics, Graduate School of Information Sciences,Tohoku University, Japan
Prof. Hajime Urakawa
Tohoku University, Japan
Prof. Hajime Urakawa graduated at the undergraduate course at Tohoku University and at the master course at Osaka University, and has accomplished his doctoral degree of science at Nagoya University at 1977. He held an appointment at Nagoya Univ. at 1972 as an assistant professor, accepted an offer from Tohoku Univ. at 1978 as an associate professor, and became full professor at Tohoku Univ. since 1992, and professor emeritus and professor at Institute for Intern. Education, Tohoku Univ. since 2010. In 1979, he answered negatively to M. Berger’s problem by giving a family of Riemannian metrics with a fixed volume whose first eigenvalues tend to infinity. In 1982, he answered to M. Kac’s problem by giving two higher dimensional different shaped drums sounding the same tones. In 1988, he settled an equivariant Yang-Mills gauge theory in mathematical physics having an application producing a negative answer to the Atiyah-Jones conjecture. In 1993, he published “Calculus of Variations and Harmonic Maps” (251pages) in the Amer. Math. Soc. As of today, he has published 13 books and more 120 mathematical journal papers cited in Math. Sci. Net., containing more than twenty papers in the recent five years.Title: Harmonic Maps and Biharmonic Maps between Riemannian ManifoldsAbstract: A harmonic map is a critical point of the energy, half of the integral of square ofthe norm of the derivative of the mapping. This means vanishing of the tension ﬁeld.The bienergy is deﬁned by the integral of the square norm of the tension ﬁeld. Thecritical points of the bienergy are biharmonic maps by deﬁnition. Harmonic maps arebiharmonic. In 1991, B.Y. Chen asked the reverse (unsolved);Every biharmonicisometric immersion into the Euclidean space must be harmonic.In this talk, we will give a short survey on our recent results on biharmonic maps:(i) Every biharmonic map into a Riemannian manifold of non-positive with ﬁniteenergy and ﬁnite bienergy is harmonic.(ii) If the projection of a principal bundle over a Riemannian manifold of non-positivecurvature with ﬁnite energy and ﬁnite bienergy, is biharmonic, then it is harmonic.(iii) We characterize the tension ﬁeld and the bitension ﬁeld of the Riemanniansubmersion, and as its application, we give an inﬁnite series of the principal circle bundles over the projective space whose projections are biharmonic but not harmonic.(iv) For a compact Lie group G, let K and H be two compact closed subgroups of G such that G/K and G/H are symmetric spaces whose involutions are commutative. Then, we show that every K-invariant biharmonic (or minimal) hypersurface in G/Hyields an H-invariant biharmonic (or minimal) hypersurface in G/K, and vice versa.
Speaker IV: Prof. Yajun Liu, South China University of Technology, China
Prof. Yajun Liu
South China University of Technology, China
Prof. Yajun Liu is a full professor in the Professor in the School of Mechanical and Automotive Engineering, South China University of Technology (2016-at pressent). His research interests include Digital signal processing technology and its application in mechanical systems (such as hydraulic System for Energy Saving.); Intelligence control and Manufacturing Engineering. Moreover, Prof. Yajun Liu has published more than 150 papers in Journals and proceedings of international conferences. 35 patents on Mechanical System design and manufacturing.