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Raleigh 2016

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

Saturday morning


9:00-9:20         Lubjana Beshaj 14-17

Minimal models for superelliptic curves with extra automorphisms.


9:30-9:50         Patrick Clarke 51-297

Deformed T-duality.


*10:00-10:50    Frank Thorne 11-105

Levels of distribution for prehomogeneous vector spaces.


Saturday afternoon


3:00-3:20 Milagros Izquierdo 14-22

Riemann Surfaces with 4g Automorphisms.


3:30-3:50 Marco Aldi 14-155

Invertible Hypersurfaces over a Finite Field and Mirror Symmetry.


4:00-4:20 Tolga Karayayla 14-6

Finite groups which act freely on smooth Schoen threefolds.


4:30-4:50 Jimmy Dillies  14-277

Models of automorphisms and fibrations


Sunday morning


*9:00-9:45   Andrew Obus 14-325

Good reduction of three-point Galois covers


10:00-10:20 Jim Wolper  14-371

Distribution of Periods of Macbeath's Curve


10:30-10:50 Justin Sawon 14-92

Lagrangian fibrations on holomorphic symplectic manifolds.



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)
Department of Mathematics and Statistics

Oakland University

Rochester, MI 48386

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