10시 - 10시 30분 : 입장 및 토의
10시 30분 - 12시 : 손재범
12시 - 13시 30분 : 점심
13시 30분 - 14시 30분 : 조시훈
14시 30분 -15시 30분 : 진석호
15시 30분 - 15시 40분 : 휴식
15시 40분 - 16시 40분 : 남하얀
손재범
Title : A survey on t-core partitions
Abstract : t-core partitions have played important roles in the theory of partitions and related areas. In this survey, we brief summarize interesting and important results on t-cores from classical results like how to obtain a generating function to recent results like simultaneous cores. Since there have been numerous studies on t-cores, it is infeasible to survey all the interesting results. Thus, we mainly focus on the roles of t-cores in number theoretic aspects of partition theory. This includes the modularity of t-core partition generating functions, the existence of $t$-core partitions, asymptotic formulas and arithmetic properties of t-core partitions, and combinatorial and number theoretic aspects of simultaneous core partitions. We also explain some applications of t-core partitions, which include relations between core partitions and self-conjugate core partitions, a t-core crank explaining Ramanujan's partition congruences, and relations with class numbers.
조시훈
Title : Properties of some Jacobi forms expressed by infinite products
Abstract : We study asymptotic formulas for the Fourier coefficients of Jacobi forms expressed by infinite products with Jacobi theta functions and the Dedekind function. We also investigate the algebraicity of the generating functions given by Gottsche for the Hilbert schemes associated to surfaces. This is a joint work with Seokho Jin.
진석호
Title : On a problem of modularity of some q-series
Abstract : Modular forms are interesting in one sense because it has many examples having interesting Fourier coefficients. The converse is also an interesting problem, i.e., to check whether a given $q$-series has a modular property or not. In this talk, I raise a problem in this direction and consider the problem from the easiest cases. This is in progress.
남하얀
Title : Results on bar-core partitions, core shifted Young diagrams, and doubled distinct cores
Abstract : Simultaneous bar-cores, core shifted Young diagrams (or CSYDs), and doubled distinct cores have been studied since Morris and Yaseen introduced the concept of bar-cores. In this talk, we give a formula for the number of these core partitions on $(s,t)$-cores and $(s,s+d,s+2d)$-cores for the remaining cases that are not covered yet.
In order to get this formula, we observe a characterization of $\overline{s}$-core partitions to obtain characterizations of doubled distinct $s$-core partitions and $s$-CSYDs. By using them, we construct $NE$ lattice path interpretations of these core partitions on $(s,t)$-cores. Also, we give free Motzkin path interpretations of these core partitions on $(s,s+d,s+2d)$-cores.