The Wronski Map for Flag Varieties

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Tezin Türü: Yüksek Lisans

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, Türkiye

Tezin Onay Tarihi: 2021

Tezin Dili: İngilizce

Öğrenci: EMRE GÜNGÖR

Danışman: Ali Ulaş Özgür Kişisel

Özet:

In this thesis, we studied flag varieties, the Grassmann variety G(d, n) and their behavior under the Wronski map. We begin with introducing algebraic, topological and geometric tools that are required to define flag varieties as a projective variety. Schubert calculus is introduced in order to understand the cohomology of the Grassmannian and flag varieties. We described Young tableaux which is a helpful tool that makes some combinatorial computations, in particular of Littlewood-Richardson coefficients, easier and studied it extensively. Finally, we studied the Wronski map which sends a set of polynomials to their Wronski determinant which is given by the polynomials and their derivatives.