Virginia Tech® home

Christina Giannitsi

Postdoctoral Associate

Postdoctoral Associate Christina Giannitsi's profile picture

Christina Giannitsi's profile picture
McBryde Room 334

460 McBryde Hall, Virginia Tech
225 Stanger Street
Blacksburg, VA 24061-1026

My research area falls under the umbrella of harmonic analysis, and mainly focuses on the discrete setting. Instead of considering functions defined on a continuum like the reals, we begin with the integer lattice. The Fourier transform in this setting is often viewed as from the integers Z to the torus T. There is a beautiful analogy between the discrete and the continuous theory. One can define averaging, maximal, Hilbert, and other operators, and for everything we know in the continuous setting, try to establish their counterpart results.

A particular sub-category of these problems is connecting them to number theory, by introducing traditional arithmetic functions, usually in the form of weights, or by moving from the traditional integer lattice, to lattices that stem from algebraic extensions of the integers. These problems can often be very involved and usually require a deep understanding of both harmonic analysis the number theory, but can be fascinating projects that produce exciting results.