Alexander Woo
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Registered User
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May 12 |
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(semi-)Small resolutions of Peterson varieties I would love to be contradicted, but my educated guess is that this is not known. |
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Apr 11 |
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Does there exist a topology for a set X which is compact and Hausdorff? A silly solution: Pick one element x. Declare every finite set NOT containing x to be open. Declare the COMPLEMENT of every finite set NOT containing x to be open. This is a compact Hausdorff topology. |
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Apr 10 |
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Syzygies of determinantal varieties: Looking for English text You have the right reference. Lascoux's paper isn't a complete solution; he has to assume some constants he constructs are nonzero, but does not prove that the constants actually are nonzero. (This is acknowledged in the paper; it was the best that could be done at the time.) The paper that finishes off this problem in characteristic zero is by Pragacz and Weyman in the late 80s; I don't have the reference offhand but you'll find it in Weyman's book. |
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Apr 8 |
awarded | ● Nice Answer |
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Mar 31 |
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On mentioning recommenders' names in cover letter for postdoctoral applications their research statement, which helped since we were hiring specifically in applied algebra. Some applicants also used part of their cover letter to convince us they were interested teaching our population of students; they couldn't do so in their teaching statement since that was used for a much broader range of types of schools. |
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Mar 31 |
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On mentioning recommenders' names in cover letter for postdoctoral applications I strongly disagree with what you have written about the cover letter. Beyond having a reasonable number of publications, what I looked for in our search this year was an indication that the applicant fit our position, and the easiest place to see this was the one paragraph synopses of research and teaching in the cover letter. (The research and teaching statements are too long for a first screening.) Customization of cover letters clearly made a difference. Some relatively pure algebraists made a case for their involvement with applications in their cover letter that they did not in... |
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Mar 28 |
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3D generalizations of permutations, RSK correspondence, contingency tables, etc. There are papers on "permutation arrays" by Eriksson and Linusson which might be useful; there is a paper by Billey and Vakil using this to solve Schubert problems. |
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Feb 13 |
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A “known” Pythagorean identity in algebra? To be more specific, this is Equation 2.2 in Section 2 of Chapter I, found on p. 19 of the 2nd edition. |
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Feb 13 |
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A “known” Pythagorean identity in algebra? What's the complete homogeneous symmetric function analogue? I might recognize that more easily. I get the feeling this is standard or at least a routine application of something standard in symmetric function theory. The right hand sides look like the squares of Cauchy kernels. |
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Jan 12 |
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Is the quasisymmetric expansion of the inner product of two Schur functions known? Send me an e-mail if you want suggestions of whom to ask (but I don't want to publicly put people on the spot). |
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Jan 8 |
awarded | ● Yearling |
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Dec 19 |
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Why is there a unique increasing maximal path in any Bruhat interval under any reflection order? Michael: Many people who might have an answer to your question (myself included) don't remember the details of the increasing-Bruhat-path interpretation of $R$-polynomials and are too lazy to reach for their copy of Bjorner--Brenti to find it. (In my case, it's not just laziness; I'm about 1000 miles away from my office at the moment.) Providing some partial explanation might help you get an answer. |
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Dec 18 |
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Triality of Spin(8) You ask for an explicit construction of these automorphisms. Unfortunately, there are a number of different ways to understand Spin(8) explicitly, and without knowing how you understand Spin(8) explicitly, we can't really figure out how to answer your question in a way that's useful to you. |
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Dec 14 |
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For a Weyl group, what is the connection between its exponents and lengths of its elements? Yes this is true. Unfortunately I can't remember a proof or a good reference at the moment. (I believe the fact because the covariant ring is the cohomology ring of the flag variety which has a basis of Schubert classes.) |
