Varieties, their fibrations and automorphisms in mathematical physics and arithmetic geometry.

AMS Sectional Meetings in Raleigh,

NC, November 12--13, 2016

Organizers: Jimmy Dillies, Georgia Southern University Tony Shaska, Oakland University Enka Lakuriqi, Georgia Southern University
Overview: While there is a pretty thorough understanding of automorphisms of algebraic curves, starting with surfaces, their level of complexity increases drastically. Nevertheless, just as the skeleton of organisms helps us understand their motricity, automorphisms give us a glimpse of their geometric properties. For example, automorphisms help us give models of varieties, they can help us understand their arithmetic properties, etc. While automorphisms of surfaces have been of interest for over a century (as e.g. in the case of the lines on the cubic), they remain a very active area of research which has made incredible progress over the last five years, especially regarding K3 surfaces. Similarly, fibrations allow us to better understand varieties by decomposing them in parts of lower dimension. All in all, automorphisms and fibrations have helped us make breakthroughs in several important problems such as mirror symmetry, F-Theory or arithmetic problems. The goal of this session is to focus on the role of automorphisms and fibrations of varieties, in particular K3 surfaces and curves, in more general problems in arithmetic geometry, algebraic geometry and mathematical physics. Examples of interests are the latest developments on automorphisms of K3 surfaces and their link with mirror symmetry or the Bloch conjecture. The use of fibrations in the study of Heterotic/F-duality and so on. Topics of the session include, but are not limited to: Families, fibrations Applications of vector bundles and moduli spaces in mathematical physics Surfaces and higher-dimensional varieties in mathematical physics Limit linear series and Brill-Noether theory Pencils of genus-two curves Period integrals for higher-genus curves Aomoto-Gel’fand and GKZ systems, A-hypergeometric functions, Appell-functions K3 surfaces related to genus-two curves and to the six-line configuration Automorphisms of K3 surfaces Mirror Symmetry and automorphisms Kuga-Satake variety of Abelian surfaces Prym varieties and their moduli Mirror symmetry Seiberg-Witten curves and Dessins d’enfant others
Schedule
Organizers: Jimmy Dillies (jdillies@georgiasouthern.edu) Department of Mathematical Sciences Georgia Southern University Statesboro, GA 30460 Enka Lakuriqi (elakuriqi@georgiasouthern.edu) Department of Mathematical Sciences Georgia Southern University Statesboro, GA 30460 Tony Shaska (shaska@oakland.edu) Oakland University Rochester, MI 48386 |