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UID:63d9150a37c6e2b9f2a0a484766666b8
CATEGORIES:Lie Group Quantum Mathematics Seminar
CREATED:20240307T123410
SUMMARY:Symmetric polynomials and interpolation polynomials
LOCATION:Computing Research & Education Building (CoRE)\, Room 433
DESCRIPTION:Symmetric polynomials, for example, Schur, Jack, and Macdonald polynomials,
  are classical objects in the study of algebra, representation theory, and 
 combinatorics. Interpolation polynomials are certain inhomogeneous versions
  of the classical Jack and Macdonald polynomials. In this talk, I will firs
 t review some basics of symmetric polynomials, introduce the interpolation 
 polynomials, and discuss our recent work. As an application, I will talk ab
 out a characterization of the containment partial order in terms of Schur p
 ositivity or Jack positivity. This result parallels the works of Cuttler--G
 reene--Skandera, Sra, and Khare--Tao, which characterize two other partial 
 orders in terms of Schur positivity.\nThis work is joint with my advisor, P
 rof. Siddhartha Sahi, and available on arXiv:2403.02490.\n
X-ALT-DESC;FMTTYPE=text/html:<p style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Cali
 bri, Helvetica, sans-serif; font-size: 12pt; color: #000000;">Symmetric pol
 ynomials, for example, Schur, Jack, and Macdonald polynomials, are classica
 l objects in the study of algebra, representation theory, and combinatorics
 . Interpolation polynomials are certain inhomogeneous versions of the class
 ical Jack and Macdonald polynomials. In this talk, I will first review some
  basics of symmetric polynomials, introduce the interpolation polynomials, 
 and discuss our recent work. As an application, I will talk about a charact
 erization of the containment partial order in terms of Schur positivity or 
 Jack positivity. This result parallels the works of Cuttler--Greene--Skande
 ra, Sra, and Khare--Tao, which characterize two other partial orders in ter
 ms of Schur positivity.</p><p style="font-family: Aptos, Aptos_EmbeddedFont
 , Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; col
 or: #000000;">This work is joint with my advisor, Prof. Siddhartha Sahi, an
 d available on arXiv:2403.02490.</p>
CONTACT:Hong Chen, Rutgers University
X-EXTRAINFO:(Note the special day, time and location.)
DTSTAMP:20260828T013837
DTSTART;TZID=America/New_York:20240403T114500
DTEND;TZID=America/New_York:20240403T124500
SEQUENCE:0
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