## Summary

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 and J.J. L. Velázquez,
*Edge States for generalised Iwatsuka models: Magnetic fields having a fast transition across a curve,*ArXiv Preprint 2109.09651. - 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,
*Derivation of Darcy's law in randomly punctured domains, to appear in Calc.Var. and PDEs,*ArXiv Preprint 2101.01046. - 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;