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

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

Zoom ID: 934 3222 0374 (ibsdimag)

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

Zoom ID: 934 3222 0374 (ibsdimag)

Organizer

Jaehoon Kim (김재훈)
Website:
https://sites.google.com/view/jaehoon-kim
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
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