CMC Algebra Seminar

CMC Algebra Seminar

2023. 6. 12. (Mon) 10:30-12:00 Room 1424
Dohoon Choi (Korea University)

Newman's conjecture on the partition function

ABSTRACT. Let p(n) be the partition function. Erdős conjectured that for each integer m, there exists a positive integer n such that p(n) = 0 (mod m). Later, Newman conjectured that for each integer m and r, there are infinitely many positive integers n such that p(n) = r (mod m). In this talk, I will talk about known results on Newman's conjecture on the partition function and our recent progress on the conjecture. This is a joint work with Youngmin Lee.
2023. 6. 5. (Mon) 10:30-12:00 Room 1424
Jaebum Sohn (Yonsei University)

Core partition and numerical semigroup

ABSTRACT. In this talk, we'll introduce the t-core partition. The generating function and modularity will be mentioned along with some results and applications of the t-core partition. Recent results on simultaneous core partitions will also be presented. At the end of the talk, we'll introduce numerical semigroup and give some connections between numerical semigroup (numerical sets) and partitions. Some problems related to these topics will be given.
2023. 6. 1. (Thu) 10:30-12:00 Room 8101
Bo-Hae Im (KAIST)

Topics in Multiple Zeta Values

ABSTRACT. In this talk, the zeta values and multiple zeta values are introduced and their linear independence and their Hopf algebra structure will be discussed. In particular, the classical setting and the function field setting of Zagier-Hoffman's conjectures will be introduced. The results on Zagier-Hoffman's conjectures in positive characteristic and the Hopf algebra structures of AMZV's are joint works with H. Kim, K. N. Le, T. Ngo Dac, and L. H. Pham.
2023. 5. 18. (Thu) 10:30-12:00 Room 1424
Jae-Hoon Kwon (Seoul National University)

Quantum affine algebras and super duality

ABSTRACT. We introduce a new approach to finite-dimensional representations of the quantum affine superalgebra of type A motivated by the theory of super duality for classical Lie superalgebras. The first half of this talk will be a brief introduction to the representation theory of simple Lie and Lie superalgebras.
2023. 4. 27. (Thu) 10:30-12:00 Room 1424
Sangjib Kim (Korea University)

Polynomial constructions of modules over gl(n, C)

ABSTRACT. Group representation theory studies vector spaces with linear actions of a group. For a Lie group, such vector spaces become modules over a corresponding Lie algebra. One of main questions in representation theory is how to construct them explicitly. We will discuss some classical constructions of modules over the complex general linear Lie algebra using polynomials.
2023. 4. 17. (Mon) 10:30-12:00 Room 1424
Dae-Yeoul Kim (Jeonbuk National University)

Iterated stable number and amicable pairs derived from restricted divisor functions

ABSTRACT. The results of this talk are elementary. It can be seen that various values can be obtained by iterating the restricted divisor functions. If we consider iteration of t-free divisor functions, then the values of them sees four cases, that is, stable, amicable pair, sociable, unpredictable sequence. Based on the results calculated with Mathematica 12.3, problems with statble numbers and the simplest case of t=2 are introduced. Finally, we introduce problems related to Mersenne primes. Most of this talk is in https://doi.org/10.1002/mma.7555
2023. 4. 6. (Thu) 10:30-12:00 Room 1424
Euiyong Park (University of Seoul)

Categorification and cluster algebras

ABSTRACT. In this talk, I will explain about the notion of categorification using module categories. I will deal with quantum group examples to explain how cluster algebra structures arise in the categorification setting. The monoidal seeds and their mutations, which can be viewed as lifts of usual seeds and mutations, will be explained with examples using quantum groups and quiver Hecke algebras. If time permits, then I will explain recent research results on categorification of quantum groups.

Past Seminars

2024 Seminars

ORGANIZERS Young-Hoon Kiem - Korea Institute for Advanced Study
Chan-Ho Kim - Korea Institute for Advanced Study
Chul-hee Lee - Korea Institute for Advanced Study