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As a material scientist, I have recently constructed algorithms for solving ground state of arbitrary cluster interactions models and prepared publications in the field of physics and material science. Indeed, I wish to further develop my theory (either in algorithm sense or even construct a brand new representation in terms of groups) in mathematical aspect and I am wondering whether there might be some sites that I could look for possible collaborations with mathematician. Thank you:)

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What do you mean by "sites"? I would suggest looking at mathematicians working on related fields, and emailing. Alternately, you can cross-post your arXiv.org papers to the appropriate math fields. Maybe then they will email you :)

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Actually, I mean websites or forums:) Sorry for my ignorance, usually people in material science (at least in our group) don't quite publish papers in archive, and where shall I make the posting? Thank you:) –  user40780 2 hours ago

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