Research

Stochastic Search Strategies on Manifolds

Geodesic Lévy Flight and Expected Time for Random Searches Bonthonneau, Chaubet, Lefeuvre, Tzou;

A Counterexample to the L\’evy Flight Foraging Hypothesis in the Narrow Capture Framework, L.Tzou, J.C. Tzou, Physical Review Research (to appear)

The narrow capture problem on Riemannian surfaces Nursultanov, Trad, Tzou, Tzou;

Narrow escape problem in the presence of the force field Nursultanov, Trad, Tzou; Mathematical Methods in Applied Sciences (to appear)

On the Mean First Arrival Time of Brownian Particles on Riemannian Manifolds Nursultanov, Tzou, Tzou; Journal de Mathématiques Pures et Appliquées 2021

Numerical Simulation of Reaction-Diffusion on Manifolds

Analysis of Spot Patterns on a Coordinate-Invariant Model for Vegetation on a Curved Terrain Tzou, Tzou; SIAM Journal on Applied Dynamical Systems 19 (4), 2500-2529, 2020

Spot patterns of the Schnakenberg reaction–diffusion system on a curved torus, Tzou, Tzou; Nonlinearity 33 (2), 643, 2019

Image Recovery Using Nonlinearity

An Inverse Problem for General Minimal Surfaces Lassas, Liimatainen, Carstea, Tzou; Preprint

Determining Lorentzian Manifold from Non-Linear Wave Observations at a Single Point Nursultanov, Oksanen, Tzou; Preprint.

Determining Riemannian manifolds from nonlinear wave observations at a single point Tzou; Inverse Problems (to appear).

Inverse Problems for Semilinear Elliptic PDE with Measurements at a Single Point Salo, Tzou; Proceedings of AMS (to appear).

Geometric Scattering

Inverse scattering for Dirac operators on surfaces with Euclidean ends Tzou; Journal of Mathematical Analysis and Applications 491 (1), 124 -232, 2020

Inverse Scattering for the Magnetic Schrödinger Operator on Surfaces with Euclidean Ends, Pohjola, Tzou; Communications in Mathematical Physics 356 (1), 107-142, 2017

Inverse scattering at fixed energy on surfaces with Euclidean ends, Guillarmou, Salo, Tzou; Communications in mathematical physics 303 (3), 761-784, 2011

Dynamics Systems and Integral Geometry

A General Support Theorem for Analytic Double Fibration Transforms Mazzucchelli, Salo, Tzou;

Boundary and lens rigidity for non-convex manifolds Guillarmou, Mazzucchelli, Tzou; American Journal of Mathematics 143 (2), 533-575, 2021

X-ray transform in asymptotically conic spaces Guillarmou, Lassas, Tzou; International Mathematics Research Notices (2020)

Asymptotically Euclidean metrics without conjugate points are flat Guillarmou, Mazzucchelli, Tzou; Journal of Geometric Analysis 2022

Impedance Tomography

Stability estimates for the magnetic Schr\” odinger operator with partial measurements, Potenciano-Machado, Ruiz, Tzou; JDE 321, 475-521, 2022

Semilinear Calderon problem on Stein manifolds with Kahler metric, Ma, Tzou; Bulletin of the Australian Mathematical Society 103 (1), 2020

Partial data inverse problem with 𝐿^{𝑛/2} potentials, Chung, Tzou; Transactions of the American Mathematical Society, Series B 7 (4), 97-132, 2020

Uniqueness for the inverse boundary value problem with singular potentials in 2D, Blåsten, Tzou, Wang; Mathematische Zeitschrift, 1-15, 2019

The linearized Calderón problem on complex manifolds Guillarmou, Salo, Tzou; Acta Mathematica Sinica, English Series 35 (6), 1043-1056, 2019

Partial data inverse problems for Maxwell equations via Carleman estimates Chung, Ola, Salo, Tzou; Annales de l’Institut Henri Poincaré C, Analyse non linéaire 35 (3), 605-624, 2018

The reflection principle and Calderón problems with partial data, Tzou; Mathematische Annalen 369 (1), 913-956, 2017

Partial data inverse problems for the Hodge Laplacian Chung, Salo, Tzou; Analysis & PDE 10 (1), 43-93, 2017

Stability for a magnetic Schrödinger operator on a Riemann surface with boundary, Andersson, Tzou, Inverse problems & Imaging, 2016

Inverse problems and invisibility cloaking for FEM models and resistor networks, Lassas, Salo, Tzou; Mathematical Models and Methods in Applied Sciences 25 (02), 309-342, 2015

Inverse boundary problems for systems in two dimensions, Albin, Guillarmou, Tzou, Uhlmann; Annales Henri Poincaré 14 (6), 1551-1571, 2013

The Calderón inverse problem in two dimensions, Guillarmou, Tzou; Inverse problems and applications: Inside Out. II, 119-166, 2013

Identification of a connection from Cauchy data on a Riemann surface with boundary, Guillarmou, Tzou; Geometric and Functional Analysis 21 (2), 393-418, 2011

Calderón inverse problem with partial data on Riemann surfaces, Guillarmou, Tzou; Duke Mathematical Journal 158 (1), 83-120, 2011

Inverse problems with partial data for a Dirac system: a Carleman estimate approach, Salo, Tzou; Advances in Mathematics 225 (1), 487-513, 2010

Calderon inverse problem for the Schrödinger operator on Riemann surfaces Guillarmou, Tzou; The AMSI–ANU Workshop on Spectral Theory and Harmonic Analysis, 129-141, 2010

Carleman estimates and inverse problems for Dirac operators, Salo, Tzou; Mathematische Annalen 344 (1), 161-184, 2010

Stability estimates for coefficients of magnetic Schrödinger equation from full and partial boundary measurements, Tzou; Communications in Partial Differential Equations 33 (11), 1911-1952 2008

Variational PDE

Anti-selfdual Lagrangians II: Unbounded non self-adjoint operators and evolution equations, Ghoussoub, Tzou; Annali di Matematica Pura ed Applicata 187 (2), 323-352, 2008

Iterations of anti-selfdual Lagrangians and applications to Hamiltonian systems and multiparameter gradient flows, Ghoussoub, Tzou; Calculus of Variations and Partial Differential Equations 26 (4), 511-534, 2006

A variational principle for gradient flows, Ghoussoub, Tzou; Mathematische Annalen 330 (3), 519-549, 2004