2018-01-012024-05-18https://scholars.lib.ntu.edu.tw/handle/123456789/706956摘要：本合作計畫將構造不規則霍奇結構所構成的淡中範疇 (Tannakian category)。計畫內容包含抽象實係數不規則霍奇結構的正確定義，並找出此淡中範疇所對應的伽羅瓦群。我們也將比較此範疇與其它建構的異同並計算與算數或鏡對稱有關的許多例子。<br> Abstract: The project aims to construct the Tannakian category of irregular Hodge structures with real coefficients. This includes to find out the correct definition of the objects and then to construct the Galois group corresponding to the Tannakian category. We would compare our approach, which rely on the Mumford-Tate groups of the (real or rational) irregular Hodge structures, with the recent construction of exponential motives of Fresan-Jossen via Nori’s quivers. On the other hand, we focus on explicit calculations of interesting examples of the Mumford-Tate groups coming from the considerations of rigid local systems and Landau-Ginzburg models in mirror symmetry.霍奇理論不規則奇點淡中範疇Hodge theoryirregular singularitiesTannakian categoryMumford-Tate group