Summer School on Inclusive Paths Toward Number Theory

This summer school will introduce students to Number Theory topics being researched throughout Alberta: algebraic number theory, diophantine geometry, and analytic number theory. The goal of this event is to promote positive cooperation and collaboration amongst students, while bringing light to equity, diversity, and inclusion issues within the study of Mathematics.

The summer school is *free* and open to MSc students from a Canadian or North-West American University. In exemplary cases, upper-year undergraduate students will also be considered. Students from under-represented groups or those committed to EDI are encouraged to apply.

Speakers and Course Abstracts:

Habiba Kadiri (ULethbridge)

Prime Numbers and Riemann Zeta Function.

The Prime Number Theorem gives an estimate for the number of primes pi(x) up to an asymptotically large number x. First conjectured by Gauss, then proven by de la Vallée Poussin and Hadamard, building upon some groundbreaking ideas of Dirichlet and Riemann, this result is seminal in the field of analytic number theory. We invite the participants to discover a few notions regarding the zeros of the Riemann zeta function as well as some analytical tools to deduce the prime number theorem. Some basic notions on Fourier analysis or complex analysis are preferable (background material shall be provided).

Dang Khoa Nguyen (UCalgary)

Roth's Theorem, Subspace Theorem, and Some Applications

Roth's Theorem and especially its generalization, the Subspace Theorem, are among the milestones of diophantine geometry in the second half of the 20th century. Without the Subspace Theorem, several elementary-to-state yet surprisingly-hard-to-prove results would have remained open. The goal of this course is to introduce versions of these theorems involving only absolute values over the rational numbers. Although this limits the strength of the theorems and the scope of their application, the trade off is that only a minimal prerequisite is required. This allows us to provide these very powerful tools to students at an early stage and hope that one day they can discover many more beautiful applications of these tools. 

Renate Scheidler (UCalgary) 

An Introduction to Global Function Fields

This course represents a basic introduction to function fields and algebraic curves over finite fields from a number theoretic perspective. Topics will include some or all of the following: valuation theory, algebraic function fi elds, divisors, extensions of function fields, class groups, elliptic and hyperelliptic curves and their function fields. The course can serve as a foundation for anyone wishing to pursue research involving function fields, such as arithmetic on algebraic curves, zeta functions of curves, curve cryptography, algebraic geometry codes, Drinfeld modules and other topics.