ALGANT - Algebra, Geometry and Number Theory University of Padua

Overview

Since its launch, the ALGANT - Algebra, Geometry and Number Theory program at University of Padua admitted more than 250 students, from over 30 countries as diverse as Australia, Belgium, Canada, China, Colombia, Ecuador, Ethiopia, France, India, Indonesia, Iran, Israel, Italy, Lebanon, Malaysia, Mexico, Montenegro, Nepal, Netherlands, Nigeria, Peru, Russia, Senegal, Serbia, South Africa, Syria, Taiwan, Turkey, Ukraine, United States of America, Venezuela, Vietnam.

General presentation

Traditionally number theory used the methods of algebra and analysis, to solve problems such as finding the number of integral of solutions of equations. In recent times geometric methods have been playing a more important role. Also, number theory has important applications in areas such as cryptography, theoretical computer science, and numerical mathematics. These led to a unification of number theory. The ALGANT course aims at introducing students into the latest developments of this fascinating subject.

Main focus on ALgebra, Geometry And Number Theory.

The Master Course is built on wider Master programs in mathematics and our course allows for the choice of optional courses in other areas of mathematics, physics, computer science, and the history and philosophy of science. Still the main focus is on Algebra, Geometry and Number Theory because:

• these are subjects that have a much greater tradition in Europe than anywhere else in the world;
• some of the most important recent advances in mathematics have taken place in our field and our staff is perfectly in synch with these advances: our departments have a worldwide reputation in these fields;
• Number Theory is a "royal way" into higher, contemporary mathematics, thus permitting to attract good students who might not have had the necessary formal training at the bachelor level; starting with classical, "concrete" problems, such students will be quickly introduced to the more sophisticated algebraic and geometric techniques that lie at the foundations of so much current work;
• as is well-known, but still unexpected few years ago, the most recent advances in Algebraic Geometry have led to important applications (cryptography, error correcting codes, etc.); we offer training towards employment in areas were expertise in these fields is necessary for the development of applications