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Jaiung Jun (전재웅), On the Hopf algebra of multi-complexes

Thursday, December 17, 2020 @ 10:00 AM - 11:00 AM KST

Zoom ID: 869 4632 6610 (ibsdimag)

Speaker

Jaiung Jun (전재웅)
Department of Mathematics, SUNY New Paltz
https://sites.google.com/site/jaiungjun0915/

In combinatorics, Hopf algebras appear naturally when studying various classes of combinatorial objects, such as graphs, matroids, posets or symmetric functions. Given such a class of combinatorial objects, basic information on these objects regarding assembly and disassembly operations are encoded in the algebraic structure of a Hopf algebra. One then hopes to use algebraic identities of a Hopf algebra to return to combinatorial identities of combinatorial objects of interest.

In this talk, I introduce a general class of combinatorial objects, which we call multi-complexes, which simultaneously generalizes graphs, hypergraphs and simplicial and delta complexes. I also introduce a combinatorial Hopf algebra obtained from multi-complexes. Then, I describe the structure of the Hopf algebra of multi-complexes by finding an explicit basis of the space of primitives, which is of combinatorial relevance. If time permits, I will illustrate some potential applications.

This is joint work with Miodrag Iovanov.

Details

Date:
Thursday, December 17, 2020
Time:
10:00 AM - 11:00 AM KST
Event Category:
Event Tags:
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Venue

Zoom ID: 869 4632 6610 (ibsdimag)

Organizer

Jaehoon Kim (김재훈)
View Organizer Website
IBS 이산수학그룹 Discrete Mathematics Group
기초과학연구원 수리및계산과학연구단 이산수학그룹
대전 유성구 엑스포로 55 (우) 34126
IBS Discrete Mathematics Group (DIMAG)
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
E-mail: dimag@ibs.re.kr, Fax: +82-42-878-9209
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