Kumar Murty
Professor Kumar Murty is in the Department of Mathematics at the University of Toronto. His research fields are Analytic Number Theory, Algebraic Number Theory, Arithmetic Algebraic Geometry and Information Security. He is the founder of the GANITA lab, co-founder of Prata Technologies and PerfectCloud. His interest in mathematics ranges from the pure study of the subject to its applications in data and information security.

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.

Tags: Vijayakumar Murty, V. Kumar Murty

CONTEXT(Help)
-
EIDM  »EIDM 
People »People
Kumar Murty
MfPH – People »MfPH – People
University of Toronto »University of Toronto
Centre de recherches mathématiques (CRM) »Centre de recherches mathématiques (CRM)
National Research Council of Canada »National Research Council of Canada
Pacific Institute for Mathematical Sciences (PIMS) »Pacific Institute for Mathematical Sciences (PIMS)
Public Health Agency of Canada »Public Health Agency of Canada
Vaccine and Infectious Disease Organization »Vaccine and Infectious Disease Organization
OMNI – People »OMNI – People
01 Contact Mixing and Optimal Decision Making »01 Contact Mixing and Optimal Decision Making
02 Integrative Modelling »02 Integrative Modelling
MfPH – Scientific Advisory Committee »MfPH – Scientific Advisory Committee
Fields Institute »Fields Institute
Atlantic Association for Research in Mathematical Sciences (AARMS) »Atlantic Association for Research in Mathematical Sciences (AARMS)
08 Contact tracing »08 Contact tracing
Covid-19 »Covid-19
230928 Emergency Operations Center Exercise Event »230928 Emergency Operations Center Exercise Event
CIHR Variants of Concern Study »CIHR Variants of Concern Study
Schools »Schools
Nonpharmaceutical Interventions (NPIs) »Nonpharmaceutical Interventions (NPIs)
+Comments (0)
+Citations (6)
+About