We introduce concepts of parameterized complexity, especially, kernelization. Kernelization is a polynomial-time preprocessing algorithm that converts a given instance for a problem to a smaller instance while keeping the answer to the problem. Delicate kernelization mostly boosts the speed of solving the problem. We explain standard techniques in kernelizations, for instance, the sunflower lemma. Most optimization problems can be reformulated in the Hitting Set problem format, and the sunflower lemma gives us a simple yet beautiful kernelization for the problem. We further introduce our recent work about the Hitting Set problem on sparse graph classes.

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Discipline of talk: Graph Theory, Complexity Theory / Advisor: 엄상일 (Sang-il Oum)

In this talk, we present a formula for the degree of the 3-secant variety of a nonsingular projective variety embedded by a 3-very ample line bundle. The formula is provided in terms of Segre classes of the tangent bundle of a given variety. We use the generalized version of double point formula to reduce the calculation into the case of the 2-secant variety. Due to the singularity of the 2-secant variety, we use secant bundle as a nonsingular birational model and compute multiplications of desired algebraic cycles.

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Discipline of talk: Algebraic geometry / Advisor: 이용남 교수님 ( Yong nam, Lee)

In this seminar, we will talk about the chemotaxis model, which is a diffusion model for biological dispersion. Chemotaxis is the movement of biological organisms in response to chemical stimuli. The chemotaxis model has nonlinear diffusion with no reaction term and has been extensively studied in the sense of a diffusion model for heterogeneous media. The nonlinear diffusion alone makes it possible to allow us to observe various spatial patterns. We will see what kind of pattern formation the model provides and what mathematical problems this model can be applied to. Language : Korean but English if it is requested

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Discipline of talk: Analysis / Advisor: 김용정 (Yongjung Kim )