ANALYTIC NUMBER THEORY

- Non-vanishing of L-functions.
- Average values of twists of L-functions.
- Sato-Tate conjecture.
- Distribution of Fourier coefficients of modular forms.
- Lang-Trotter conjecture and generalizations.
- Families of L-functions.

ALGEBRAIC NUMBER THEORY

- Class numbers of solvable extensions.
- Effective versions of the Chebotarev density theorem.
- Growth of Selmer ranks of Abelian varieties in towers of number fields.
- Euclidean Algorithm.
- Bounded generation of Algebraic groups.

ARITHMETIC ALGEBRAIC GEOMETRY

- Conjectures on algebraic cycles (Hodge, Tate).
- Tannakian groups.
- Algebraic cycles on Shimura varieties.
- Fundamental group of Satake compactifications.

APPLICATIONS TO INFORMATION TECHNOLOGY

- Algebraic curves and cryptography.
- Explicit arithmetic on Abelian varieties over finite fields.
- Counting points on Abelian varieties over finite fields.
- Data Integrity algorithms.
- Data Compression algorithms.
- Storage Security.

GANITA LAB

- Started in January 2001, this group studies Geometry, Algebra, Number Theory and their Information Technology Applications. It was initially housed in the Department of Mathematics at St. George. As space was unavailable for growth, it moved to UTM and was there from 2001-2010. In 2010, it returned to St. George and is now housed on the 10th floor of 215 Huron Street. Over the past 12 years, GANITA has received approximately $1.5 million in funding agency and industrial grants.