Seminars in March 2012

• Byungchan Kim (김병찬), The Odd Moments of Ranks and Cranks

  The Odd Moments of Ranks and Cranks

  Byungchan Kim (김병찬)
  School of Liberal Arts, Seoul National University of Science and Technology, Seoul, Korea

  2012/3/28 Wed 4PM-5PM

  By modifying the definition of moments of ranks and cranks, we study the odd moments of ranks and cranks. In particular, we prove the inequality between the first crank moment M₁(n) and the first rank moment N₁(n):</p>

  M₁(n) > N₁(n).

  We also study new counting function ospt(n) which is equal to M₁(n) – N₁(n). We will also discuss higher order moments of ranks and cranks.
  This is a joint work with G. E. Andrews and S. H. Chan.</div>

  Tags:

  • 김병찬

• HwanChul Yoo (유환철), Purity of weakly separated set families

  Purity of weakly separated set families

  HwanChul Yoo (유환철)
  School of Mathematics, KIAS, Seoul, Korea

  2012/3/14 Wed 4PM-5PM

  Weakly separated set families were first studied by Leclerc and Zelevinsky in the context of quantum flag variety. Two quantum Plücker coordinates quasi-commute whenever their indexing sets are weakly separated. It was conjectured that maximal such families always have the same size. Similar question was asked by Scott when she studied quantum Grassmannian. These conjectures were independently proved by Danilov-Karzanov-Koshevoy and Oh-Postnikov-Speyer using some planar graphs and by the author using truncation. In this talk, definitions and motivations for the weakly separated set families will be explained, including Oh-Postnikov-Speyer’s point of view on the subject. The proof of the purity conjecture using truncation will be provided, and related questions will be discussed.

  Tags:

  • 유환철