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Mathematical Artificial Intelligence and Scientific Machine LearningIn our research lab, we conduct theory of computation and applied research in the field of artificial intelligence. Particularly, we aim beyond isolated case studies or simple performance impr…
VALENTIN BUCIUMAS: RESEARCH INTRODUCTIONRepresentation theory studies how algebraic objects like groups and Lie algebras act onvector spaces. When the vector spaces are finite-dimensional, the elements of the algebraicobject act by matrices, which allows one t…
Professor Jae Choon Cha studies geometric topology and related algebraic topology, algebra, and analysis. In particular, he is interested in topology of manifolds and knots, focusing on the study of 4-manifolds and low dimensional topology, disk embedding prob…
Number Theory and Arithmetic Geometry.My current interest is - Interpretation of orbital integrals via smootheningProfessor Sungmun Cho studies number theory. In particular, he is interested in integrals over a p-adic field (which is an avatar of the set of re…
My field of research lies at the intersection of differential geometry and the analysis of Partial Differential Equations (PDEs), an area broadly referred to as geometric analysis. Some fundamental questions in geometry and topology, such as the Calabi-Yau con…
Professor YoungJu Choie is a number theorist who specializes in research on integers using the theory of modular forms. Modular forms theory, and more broadly automorphic representation theory, plays a central role in understanding L-functions, which are close…
My research focuses on the mathematical analysis of partial differential equations (PDEs) that arise from various physical phenomena. In particular, within the field of kinetic theory, I am contributing to the understanding of numerous kinetic PDEs. My researc…
My researchareaisthetopologyandgeometryof3-manifolds.Theprimaryobjectiveintopology(orgeometry)istoclassifymanifoldsbasedontheirinvariants.Forexample,closedorientablesurfacesareclassiedbytheirgenera. Inthecaseof3-dimmanifolds,W.Thurston'sgroundbreakingwork,init…
Mathematical data science and machine learning - through the lens of approximation theory- Jae-Hun JungMy primary research interests are centered around numerical analysis and scientific computing, with a specific focus on numerical partial differential equati…
My research area lies in the field of probability theory within mathematics, specifically, I am studying stochastic partial differential equations (SPDEs).SPDEs usually refer to partial differential equations (PDEs) perturbed by noise (random fields) where noi…
Our research group primarily focuses on probability theory and mathematical biology. Mathematical biology, which analyzes and predicts biological phenomena mathematically, has undergone significant changes over the past two decades. This shift originated from …
KWEON'S RESEARCH FIELDS1. Research fieldI think, mathematics is a scheme or a tool or a logical(reversible) mod-elling for formulating the unknowns or the curiosities or the ideas in ourscientific or industrial life activities. Specifically I am concerned with…
A brief summary of my researchHello, this is Kyoung-Seog Lee who is going to join POSTECH in the near future. I am happy to have this chance to introduce my research works.I am studying algebraic geometry and related fields. Traditionally, algebraic geometry i…
Kinetic TheoryLet's assume a sparse gas particle system (such as air, plasma, etc.), as we commonly envision. To simplify the system, we consider all particles to be extremely tiny spheres, and we assume that these particles undergo completely elastic collisio…
Qirui Li's research interests lie in Number Theory and Arithmetic GeometryQirui Li's research interests lie in Number Theory and Arithmetic Geometry.Number Theory originated with the discovery of integers through counting, yet its essence extends far beyond in…
Symplectic/contact topology, mirror symmetry and mathematical physicsMy research description (Yong-Geun Oh)Yong-Geun Oh’s research aims to establish and develop the emerging field of symplectic and contact topology through the tools of symplectic geometry, dyn…
Geometry of Fano varietiesAlgebraic geometry is a discipline that studies geometric objects known as algebraic varieties, which consist of solutions to systems of multivariable polynomial equations.These geometric objects encompass familiar examples such as li…
Research Highlight of Prof. Sunyoung ShinIn the era of artificial intelligence where big data can make significant contributions to science and society, we are inundated with numerous machine learning approaches and techniques. As a statistician and data scien…
Ergodic theory and its applications to number theory and combinatoricsResearch descriptionErgodic theory, originating from statistical and celestial mechanics, describes the behavior of complex evolving systems and finds applications in various mathematical fi…
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