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research [2018/05/29 14:03] ckoehler |
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| ====== Research program ====== | ====== Research program ====== | ||
| - | The aim of this International Research Training Group is to advance Mathematics in a joint initiative between Bielefeld University and Seoul National University. The focus will be on the mathematical analysis of problems which exhibit singular features or the in uence of randomness. Our research program is structured into the following four research areas: | + | The aim of this International Research Training Group is to advance Mathematics in a joint initiative between Bielefeld University and Seoul National University. The focus will be on the mathematical analysis of problems which exhibit singular features or the influence |
| * **A. Analysis of differential and integro-differential equations** \\ Nonlinear dispersive equations, singular integrals, nonlocal generators of jump processes | * **A. Analysis of differential and integro-differential equations** \\ Nonlinear dispersive equations, singular integrals, nonlocal generators of jump processes | ||
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| **Principal Researchers: | **Principal Researchers: | ||
| - | **Scientific Partners:** Kyeong-Hun Kim (Korea University), | + | **Scientific Partners:** Kyeong-Hun Kim (Korea University), |
| The aim of this project is to study notoriously difficult Cauchy problems. We investigate nonlinear dispersive equations and systems, as well as integro-differential equations. Concerning nonlinear dispersive equations, such as nonlinear Schrödinger and Wave equations, well-posedness problems for initial data in Sobolev spaces of low regularity will be studied using methods from harmonic analysis. With regard to integro-differential operators, research projects will be offered that extend the theory for the fractional Laplace operator to anisotropic and/or nonlinear nonlocal operators. Characteristic properties of the aforementioned problems can often be described in terms of the underlying scaling behavior, e.g., when studying the interplay between dispersion and nonlinearity or the impact of singularities | The aim of this project is to study notoriously difficult Cauchy problems. We investigate nonlinear dispersive equations and systems, as well as integro-differential equations. Concerning nonlinear dispersive equations, such as nonlinear Schrödinger and Wave equations, well-posedness problems for initial data in Sobolev spaces of low regularity will be studied using methods from harmonic analysis. With regard to integro-differential operators, research projects will be offered that extend the theory for the fractional Laplace operator to anisotropic and/or nonlinear nonlocal operators. Characteristic properties of the aforementioned problems can often be described in terms of the underlying scaling behavior, e.g., when studying the interplay between dispersion and nonlinearity or the impact of singularities | ||
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| **Principal Researchers: | **Principal Researchers: | ||
| - | **Scientific Partners:** Seung-Yeal Ha (SNU), Ki-Ahm Lee (SNU)\\ | + | **Scientific Partners:** Seung-Yeal Ha (SNU), Ki-Ahm Lee (SNU), Insuk Seo (SNU)\\ |
| In this project, we will study various aspects of the dynamics of interacting systems in deterministic and random media.\\ | In this project, we will study various aspects of the dynamics of interacting systems in deterministic and random media.\\ | ||
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| **Principal Researchers: | **Principal Researchers: | ||
| - | **Scientific Partners:** Nam-Gyu Kang (KIAS), Ji Oon Lee (KAIST)\\ | + | **Scientific Partners:** Nam-Gyu Kang (KIAS), Ji Oon Lee (KAIST), Insuk Seo (SNU)\\ |
| Random Matrix theory is an extremely active and exciting research area in Mathematics and Mathematical Physics. It connects for example Analysis, Probability Theory and Combinatorics in various ways. The area is characterized by emerging universal laws for spectral statistics, which apply to surprisingly many phenomena ranging from Number Theory to Quantum Field Theory. \\ | Random Matrix theory is an extremely active and exciting research area in Mathematics and Mathematical Physics. It connects for example Analysis, Probability Theory and Combinatorics in various ways. The area is characterized by emerging universal laws for spectral statistics, which apply to surprisingly many phenomena ranging from Number Theory to Quantum Field Theory. \\ | ||