On different notions of tameness in arithmetic geometry

Basic Notions of Geometry and Euclidean Geometry

Miscellaneous preliminaries on arithmetic geometry

One definition of a hyperelliptic curve is a curve C over an algebraically closed field k whose function field K is a degree 2 extension of a purely transcendental extension of k. 1. (a) Show that every hyperelliptic curve is birational to a curve of the form y 2 = f (x) where f ∈ k[x] is a monic squarefree polynomial. (b) Conversely, show that every squarefree f ∈ k[x] gives rise to a hyperell...

On Three Different Notions of Monotone Subsequences

We review how the monotone pattern compares to other patterns in terms of enumerative results on pattern avoiding permutations. We consider three natural definitions of pattern avoidance, give an overview of classic and recent formulas, and provide some new results related to limiting distributions.

Arithmetic in Geometry

I thank Dean Martin for his very flattering introduction. I thank the College for bestowing a chair to me and the Mathematics Department for providing a wonderful atmosphere for my work. I thank Don Lewis and my current and former colleagues for their support. I take this opportunity to also thank my family, friends, and collaborators. My mathematical horizon has widened considerably after join...

the impact of e-readiness on ec success in public sector in iran the impact of e-readiness on ec success in public sector in iran

acknowledge the importance of e-commerce to their countries and to survival of their businesses and in creating and encouraging an atmosphere for the wide adoption and success of e-commerce in the long term. the investment for implementing e-commerce in the public sector is one of the areas which is focused in government‘s action plan for cross-disciplinary it development and e-readiness in go...