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Jeff and "lexness"
Nov. 12th, 2005 08:43 pmToday I got to meet Jeff, whom I've known via mutual friends and the Internet for, hmm, seven years now; he came to present at the American Mathematical Society Fall Western Section meeting, which was held on the Univ. of Oregon campus. I was going to register for the conference, as it seemed quite a novel thing to do and would only have cost me $5, but when I stopped by the room he was going to present in, 45 minutes early, he was already there, so I just stayed put, chatting with him then listening to another guy's talk then his.
Jeff's field is called "commutative algebra," and what he was doing was "proving the lex-plus-powers conjecture for graded ideals containing the squares of the variables," which involves Betti numbers, whatever they may be. I thought Jeff had a nice presence while standing up there explaining things and writing on the chalkboard. I didn't learn anything beyond that, other than that there are numbers (I think) that can have properties such as "squarefree" and "lex" and "Borel"; that this involves "ideals" (which apparently are sets of numbers) and Hilbert functions; and that an early step in his proof involved using "mapping cones" and a later step involved "compression." "Lex" was a property that was quite important to the first presenter's talk as well; he had concluded by saying that some numbers were "almost lex" or "lex enough."
Meanwhile, R., D., DH, and DH's wife and step-daughter had been to breakfast in the morning, then drove up the McKenzie, then had ice cream and toured some houses for sale. We ate nice pizzas and watched the Oregon State game on TV.
Jeff's field is called "commutative algebra," and what he was doing was "proving the lex-plus-powers conjecture for graded ideals containing the squares of the variables," which involves Betti numbers, whatever they may be. I thought Jeff had a nice presence while standing up there explaining things and writing on the chalkboard. I didn't learn anything beyond that, other than that there are numbers (I think) that can have properties such as "squarefree" and "lex" and "Borel"; that this involves "ideals" (which apparently are sets of numbers) and Hilbert functions; and that an early step in his proof involved using "mapping cones" and a later step involved "compression." "Lex" was a property that was quite important to the first presenter's talk as well; he had concluded by saying that some numbers were "almost lex" or "lex enough."
Meanwhile, R., D., DH, and DH's wife and step-daughter had been to breakfast in the morning, then drove up the McKenzie, then had ice cream and toured some houses for sale. We ate nice pizzas and watched the Oregon State game on TV.