1. Speaker: Jangwon Ju(Ulsan University), 10:00~11:50 Title: Universal sums of generalized polygonal numbers Abstract: The sum of generalized polygonal numbers is said to be universal if it represents all nonnegative integers. In this talk, we introduce some arithmetic method on studying representations of sums of generalized polygonal numbers. We provide effective criteria on the universalities of sums of generalized polygonal numbers with some small order. These might be considered as a generalization of the 15-Theorem of Conway and Schneeberger. 2. Speaker: Kyoungmin Kim(Hannam University), 14:00~15:50 Title: The use of modular form theory in studying quadratic forms Abstract: In this talk, we introduce some modular form theory used in studying the number of representations of integers by quadratic forms. 3. Speaker: Mingyu Kim(Sungkyunkwan University), 16:00~17:50 Title: Tight universal quadratic forms Abstract: For a positive integer n, let T(n) be the set of all integers greater than or equal to n. An integral quadratic form f is called tight T(n)-universal if the set of nonzero integers that are represented by f is exactly T (n). The smallest possible rank over all tight T(n)-universal quadratic forms is denoted by t(n). In this talk, we prove that t(n) ∈ Ω(log_2(n)) ∩ O(\sqrt(n)). Explicit lower and upper bounds for t(n) will be provided for some small integer n. We also consider the classication of all tight T(n)-universal diagonal quadratic forms. This is a joint work with Byeong-Kweon Oh.