Contact topology of singularities and symplectic fillings

2022-2 Rookies Pitch: Algebraic Geometry (박현준)

BK21 FOUR Rookies Pitch | 강연자 : 박현준 | 소속 : KIAS

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2022-2 Rookies Pitch: Geometric Topology (김승원)

BK21 FOUR Rookies Pitch | 강연자 : 김승원 | 소속 : 성균관대학교

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2022-2 Rookies Pitch: Probability Theory (이중경)

BK21 FOUR Rookies Pitch | 강연자 : 이중경 | 소속 : 수리과학부

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2022-2 Rookies Pitch: Probability Theory (변성수)

BK21 FOUR Rookies Pitch | 강연자 : 변성수 | 소속 : KIAS

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Towards Trustworthy Scientific Machine Learning: Theory, Algorithms, and Applications

BK21 FOUR Rookies Pitch | 강연자 : 신연종 | 소속 : KAIST

Machine learning (ML) has achieved unprecedented empirical success in diverse applications. It now has been applied to solve scientific problems, which has become an emerging field, Scientific Machine Learning (SciML). Many ML techniques, however, are very complex and sophisticated, commonly requiring many trial-and-error and tricks. These result in a lack of robustness and interpretability, which are critical factors for scientific applications. This talk centers around mathematical approaches for SciML, promoting trustworthiness. The first part is about how to embed physics into neural networks (NNs). I will present a general framework for designing NNs that obey the first and second laws of thermodynamics. The framework not only provides flexible ways of leveraging available physics information but also results in expressive NN architectures. The second part is about the training of NNs, one of the biggest challenges in ML. I will present an efficient training method for NNs - Active Neuron Least Squares (ANLS). ANLS is developed from the insight gained from the analysis of gradient descent training.

Elliptic equations with singular drifts in critical spaces

수학강연회 | 강연자 : 김현석 | 소속 : 서강대학교

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Now

현재 Contact topology of singularities and symplectic fillings

수학강연회 | 강연자 : 권명기 | 소속 : 순천대학교

For an isolated singularity, the intersection with a small sphere forms a smooth manifold, called the link of a singularity. It admits a canonical contact structure, and this turns out to be a fine invariant of singularities and provides an interesting playground to explore relationships between contact topology and singularity theory. In this talk, we briefly introduce results on contact topology of singularities in terms of exotic contact spheres, uniqueness of symplectic fillings, and Floer theory.