I am a Chapman fellow in Mathematics in the Applied Mathematics and Mathematical Physics section. My research lies in the fields of Analysis of Partial Differential Equations and Probability.
I am especially interested in:
- Stochastic homogenization for elliptic operators
- Random walks in random environments and interacting particles systems
- Fluid flows in porous media
- Magnetic Schrödinger operators
Before joining Imperial College, I was an Hausdorff postdoc at the University of Bonn in the group of J.J. L. Velázquez. I received my PhD at the Max Planck Institute for Mathematics in the Sciences of Leipzig, under the supervision of F. Otto.
List of publications and preprints:
- A. Giunti, Derivation of Darcy's law in randomly punctured domains, ArXiv Preprint 2101.01046.
- A. Giunti, C. Gu and J-C. Mourrat, Quantitative homogenization of interacting particle systems, ArXiv Preprint 2011.06366.
- A. Giunti and R.M. Höfer, Convergence of the pressure in the homogenization of the Stokes equations in randomly perforated domains, ArXiv preprint 2003.04724.
- A. Giunti, Convergence rates for the homogenization of the Poisson problem in randomly perforated domains, to appear in Net. & Het. Media, ArXiv preprint 2007.13386.
- A. Giunti and J.J.L. Velázquez, Edge states for the magnetic Laplacian in domains with smooth boundary, to appear in SIAM J. Math. An., ArXiv preprint 1912.07261;
- A. Giunti and F. Otto, On the existence of the Green function for elliptic systems in divergence form, to appear in Manuscripta Mathematica,ArXiv preprint 1911.0210;
- A. Giunti and J.J.L. Velázquez, On the homogenization of random stationary elliptic operators in divergence form, to appear in Proc. of AMS, arXiv preprint 1809.06111;
- P. Bella, A. Giunti and F. Otto, Effective multipoles in random media, in Comm. PDEs, 45(6): 561-640, 2020;
- A. Giunti and R.M. Höfer, Homogenization for the Stokes equations in randomly perforated domains under almost minimal assumptions on the size of the holes, in Ann. Inst. H. Poincare'- An. Nonl., 36(7): 1829-1868, 2019;
- A. Giunti, R.M. Höfer and J.J.L. Velázquez, Homogenization for the Poisson equation in randomly perforated domains under minimal assumptions on the size of the holes, in Comm. in PDEs, 43(9): 1377-1412, 2018;
- A. Giunti, Y.Gu and J.-C. Mourrat, Heat kernel upper bounds for interacting particle systems, in Annals of Prob., 47(2): 1056-1095, 2019;
- P. Bella and A. Giunti, Green's function for elliptic systems: Moment bounds, in Net. and Het. Media, Vol.13 n.1, pp.155-176, 2018;
- A. Giunti and J.-C. Mourrat, Quantitative homogenization of degenerate random environments, in Ann. Inst. H. Poincare' Probab. Statist., Vol.54 n.1, pp.22-50, 2018;
- J. Conlon, A.Giunti and F.Otto, Green's function for elliptic systems: Existence and Delmotte-Deuschel bounds, in Calc.Var. and PDEs, Vol.56 n.6, 2017;
- P. Bella, A. Giunti and F. Otto, Quantitative stochastic homogenization: Control of local homogenization error through corrector, in Mathematics and Materials, Park City Mathematics series, pp. 299-327, 2015;