Nikolaos Tzirakis

Department of Mathematics
University of Toronto
40 St. George St.
Toronto, Ontario
Canada M5S 2E4

Office:BA 6107
Phone: (416) 946-5440
FAX: (416) 978-4107
e-mail: tzirakis@math.toronto.edu

Research

My research area is Harmonic Analysis and Partial Differential Equations (PDE). More precisely I am interested in the long time behavior of the Cauchy problem for dispersive nonlinear PDE . Most of my work is concentrated on the study of the semilinear Schrodinger equation (focusing or defocusing), especially the L^2-critical problem. I am also studying dispersive systems such as the Zakharov system and the Klein-Gordon-Schrodinger system.

Professional Information

2004, Ph.D. in Mathematics, University of Massachusetts at Amherst.
2004-2005, Institute for Advanced Study at Princeton, Member.
2005-2007, University of Toronto, Postdoctoral Fellow.
2007-\ \ \ \ , University of Illinois at Urbana-Champaign, Assistant Professor.

Recent Publications

(with J. Colliander and M. Grillakis) Improved interaction Morawetz inequalities for the cubic nonlinear Schroedinger equation in 2d. Submitted for publication, pdf file.
(with D. De Silva, N. Pavlovic and G.Staffilani) Global well-posedness and polynomial bounds for the defocusing nonlinear Schroedinger equation in 1d. Submitted for publication, pdf file.
(with D. De Silva, N. Pavlovic and G.Staffilani) Global Well-Posedness for the L^2-critical nonlinear Schroedinger equation in higher dimensions. Submitted for publication, pdf file.
(with D. De Silva, N. Pavlovic and G.Staffilani) Global well-posedness for a periodic nonlinear Schroedinger equation in 1d and 2d. To appear in Discrete and Continuous Dynamical Systems, pdf file.
(with J. Colliander and J. Holmer) Low regularity global well-posedness for the Zakharov and Klein-Gordon-Schroedinger systems. To appear in Trans. Amer. Math. Soc., pdf file.
Mass concentration phenomenon for the quintic nonlinear Schroedinger equation in one dimension. SIAM J. Math. Anal. 37 (2006), no. 6, 1923--1946, pdf file.
(with P. G. Kevrekidis)On the collapse arresting effects of discreteness. Math. Comput. Simulation 69 (2005), no. 5-6, 553--566.
The Cauchy problem for the Klein-Gordon-Schroedinger system in low dimensions below the energy space. Comm. Partial Differential Equations 30 (2005), no. 4-6, 605--641.
The Cauchy problem for the semilinear quintic Schroedinger equation in one dimension. Differential Integral Equations 18 (2005), no. 8, 947--960.
(with Arpad Benyi) Multilinear almost diagonal estimates and applications. Studia Math. 164 (2004), no. 1, 75--89.

Curriculum Vitae

Teaching

Fall 2006:

MAT 137Y. Calculus I

Spring 2007:

MAT 137Y. Calculus I