Motivic Donaldson-Thomas invariants and Kac conjecture

We derive some combinatorial consequences from the positivity of Donaldson-Thomas invariants for symmetric quivers conjectured by Kontsevich and Soibelman and proved recently by Efimov. These results are used to prove the Kac conjecture for quivers having at least one loop at every vertex.Comment: 10 page

The Harder-Narasimhan system in quantum groups and cohomology of quiver moduli

Methods of Harder and Narasimhan from the theory of moduli of vector bundles are applied to moduli of quiver representations. Using the Hall algebra approach to quantum groups, an analog of the Harder-Narasimhan recursion is constructed inside the quantized enveloping algebra of a Kac-Moody algebra. This leads to a canonical orthogonal system, the HN system, in this algebra. Using a resolution of the recursion, an explicit formula for the HN system is given. As an application, explicit formulas for Betti numbers of the cohomology of quiver moduli are derived, generalizing several results on the cohomology of quotients in 'linear algebra type' situations.Comment: 22 page

Cultivating Research

Faculty Opportunity Awards help innovative ideas blossom into fully formed scientific and scholarly investigations. UNLV’s Faculty Opportunity Awards program provides seed funding for faculty researchers with promising ideas and a desire to pursue additional funding from government agencies, foundations, or private industry. The program has supported a wide variety of campus research projects involving multidisciplinary teams, single investigators, and other faculty working to develop intellectual property. Elizabeth Hausrath Rebecca Gill Janet Dufek Ying Tia