Mathematics Theses and Dissertationshttps://scholarsbank.uoregon.edu/xmlui/handle/1794/20442020-10-27T22:16:17Z2020-10-27T22:16:17ZAT-algebras from zero-dimensional dynamical systemsHerstedt, Paulhttps://scholarsbank.uoregon.edu/xmlui/handle/1794/256852020-09-25T07:24:25Z2020-09-24T00:00:00ZAT-algebras from zero-dimensional dynamical systems
Herstedt, Paul
We outline a particular type of zero-dimensional system (which we call "fiberwise essentially minimal"), which, together with the condition of all points being aperiodic, guarantee that the associated crossed product C*-algebra is an AT-algebra. Since AT-algebras of real rank zero are classifiable by K-theory, this is a large step towards a classification theorem for fiberwise essentially minimal zero-dimensional systems.
2020-09-24T00:00:00ZSome Extension Algebras of Standard Modules over Khovanov-Lauda-Rouquier Algebras of Type A, Including A-Infinity StructureBuursma, Doekehttps://scholarsbank.uoregon.edu/xmlui/handle/1794/256762020-09-25T07:24:09Z2020-09-24T00:00:00ZSome Extension Algebras of Standard Modules over Khovanov-Lauda-Rouquier Algebras of Type A, Including A-Infinity Structure
Buursma, Doeke
We give an explicit description of the category of Yoneda extensions of standard modules over KLR algebras for two special cases in Lie type A. In these two special cases, the A-infinity category structure of the Yoneda category is formal. We give an example to show that, in general, the A-infinity category structure of the Yoneda category is non-formal.
2020-09-24T00:00:00ZCombinatorics of the Double-Dimer ModelJenne, Helenhttps://scholarsbank.uoregon.edu/xmlui/handle/1794/256692020-09-25T07:23:44Z2020-09-24T00:00:00ZCombinatorics of the Double-Dimer Model
Jenne, Helen
We prove that the partition function for tripartite double-dimer configurations of a planar bipartite graph satisfies a recurrence related to the Desnanot-Jacobi identity from linear algebra. A similar identity for the dimer partition function was established nearly 20 years ago by Kuo. This work was motivated in part by the potential for applications, including a problem in Donaldson-Thomas and Pandharipande-Thomas theory, which we will discuss. The proof of our recurrence requires generalizing work of Kenyon and Wilson; specifically, lifting their assumption that the nodes of the graph be black and odd or white and even.
2020-09-24T00:00:00ZA Categorical sl_2 Action on Some Moduli Spaces of SheavesTakahashi, Ryanhttps://scholarsbank.uoregon.edu/xmlui/handle/1794/256612020-09-25T07:29:29Z2020-09-24T00:00:00ZA Categorical sl_2 Action on Some Moduli Spaces of Sheaves
Takahashi, Ryan
We study a certain sequence of moduli spaces of stable sheaves on a K3 surface of Picard rank 1 over $\mathbb{C}$. We prove that this sequence can be given the structure of a geometric categorical $\mathfrak{sl}_2$ action, a global version of an action studied by Cautis, Kamnitzer, and Licata. As a corollary, we find that the moduli spaces in this sequence which are birational are also derived equivalent.
2020-09-24T00:00:00Z