My CV

PERSONAL INFORMATION

Name: Alessandro Audrito.

Date of Birth: 21 February 1990.

Nationality: Italian.

Civil Status: Married, two children. 

Languages: English, Spanish, Italian (native).

CURRENT POSITION

December 2022 - present: Tenure track position (RTDB) at the Department of Mathematics DISMA of Politecnico di Torino (Italy). 

PREVIOUS POSITIONS

• September 2022 - November 2022: post-doctoral-teaching assistant position at the DMath of ETH Zürich (Switzerland).

Supervisor: Prof. Joaquim Serra. 

• September 2020 - August 2022: post-doctoral position at the DMath of ETH Zürich (Switzerland), under the MSC IF 2019 No. 892017 (project acronym: LNLFB-Problems).

Supervisor: Prof. Joaquim Serra.

• October 2019 - August 2020: post-doctoral-teaching assistant position at the Department of Mathematics of Universität Zürich (Switzerland).  

Supervisor: Prof. Xavier Ros-Oton.

• January 2018 - September 2019: post-doctoral-teaching assistant position at the Department of Mathematics DISMA of Politecnico di Torino (Italy). 

Supervisor: Prof. Enrico Serra and Prof. Paolo Tilli.

• November 2014 - July 2018: Ph.D. program in Pure and Applied Mathematics at Università degli Studi di Torino (Italy). International Co-tutela Program with the PhD Program in Mathematics at Universidad Autónoma de Madrid (Spain).

Supervisor: Prof. Susanna Terracini and Prof. Juan Luis Vázquez.

STUDIES

• September 2012 - December 2015:  Advanced studies program at Scuola di Studi Superiori dell'Università di Torino (SSST), Università degli Studi di Torino (Italy).  

• September 2012 - July 2014: Master's Degree in Mathematics (Laurea Magistrale in Matematica), Università degli Studi di Torino (Italy). 

• September 2009 - July 2012: Bachelor's Degree in Mathematics (Laurea Triennale in Matematica), Università degli Studi di Torino (Italy). 

PREPRINTS

• A. Audrito, G. Fioravanti, S. Vita. Schauder estimates for parabolic equations with degenerate or singular weights, Arxiv preprint, arXiv:2401.06038 (2024).

• A. Audrito, G. Fioravanti, S. Vita. Higher order Schauder estimates for parabolic equations with degenerate or singular weights, Arxiv preprint, arXiv:2403.08575 (2024).

PUBLICATIONS

• A. Audrito, S. Terracini. On the nodal set of solutions to a class of nonlocal parabolic equations, to appear in Memoirs AMS, pp.99.

• A. Audrito, T. Sanz-Perela. Elliptic regularization of some semilinear parabolic free boundary problems, Interfaces Free Bound. 26 (2024), 135-159.

• A. Audrito, T. Kukuljan. Regularity theory for fully nonlinear parabolic obstacle problems, J. Funct. Anal. 285 (2023), 1-57.

• A. Audrito. On the existence and Hölder regularity of solutions to some nonlinear Cauchy-Neumann problems, J. Evol. Equ. 23 (2023), 1-45.

• A. Audrito, A. Garriz, F. Quiros. Convergence in relative error for the Porous Medium equation in a tube, Ann. Mat. Pura Appl. 203 (2023), 149-171.

• A. Audrito, J.-C. Felipe-Navarro, X. Ros-Oton. The Neumann problem for the fractional Laplacian: regularity up to the boundary, Ann. Sc. Norm. Super. Pisa Cl. Sci. 24 (2023), 1155-1222.

• A. Audrito, J. Serra. Interface regularity for semilinear one-phase problems, Adv. Math 403 (2022), 1-51. 

• A. Audrito, E. Serra, P. Tilli. A minimization procedure to the existence of segregated solutions to parabolic reaction-diffusion systems, Comm. Partial Differential Equations  46 (2021), 2268-2287. 

• A. Audrito, X. Ros-Oton. Nonlocal Dirichlet problems with $C^{0,\alpha}$ exterior data, Proc. Amer. Math. Soc. 148 (2020), 4455-4470. 

• A. Audrito, J. L. Vázquez. Travelling wave behaviour arising in nonlinear diffusion problems posed in tubular domains,  J. Differential Equations 269 (2020), 2664-2696. 

• A. Audrito. Bistable reaction equations with doubly nonlinear diffusion, Discrete Contin. Dyn. Syst. - A 39 (2019), 2977-3015.

• A. Audrito, J. L. Vázquez. The Fisher-KPP problem with doubly nonlinear "fast" diffusion, Nonlinear Anal. 157 (2017), 212-248. 

• A. Audrito, J. L. Vázquez. The Fisher-KPP problem with doubly nonlinear diffusion, J. Differential Equations 263 (2017), 7647-7708.

SELECTED TALKS

• Seminar: Elliptic regularization of some semilinear free boundary problems, Università di Milano, Italy, March 2024.

• Seminar: Il problema dell'ostacolo parabolico con diffusione fully nonlinear, UMI congress, Pisa, Italy, September 2023.

• Seminar: Free boundary regularity for the Stefan problem with fully nonlinear diffusion, Politecnico di Milano, Italy, November 2022.

• Online seminar: The parabolic obstacle problem with fully nonlinear diffusion, Purdue University, USA, November 2022.

• Seminar: The parabolic obstacle problem with fully nonlinear diffusion, Universidad Autónoma de Madrid, Madrid, June 2022.

• Online seminar: A rigidity result for a class of elliptic semilinear one-phase problems, University of California San Diego, San Diego, USA, January 2022.

• Seminar: A variational approach to a class of nonlinear Cauchy-Neumann problems, Università di Pisa, Italy, October 2021.

• Seminar: Interface regularity for semilinear one-phase problems, Levico Terme, Italy, September 2021.

• Online seminar: The Neumann problem for the fractional laplacian, SIAM annual meeting, July 2021.

• Online seminar: The Neumann problem for some nonlocal elliptic operators: Regularity up to the boundary, ETHZ, Zürich, Switzerland, 24/11/2020.

• Seminar: Travelling wave behaviour for nonlinear flows in tubes, Università degli Studi di Torino, Torino, Italy, February 2020.

• Seminar: Existence of segregated solutions to a class of parabolic systems: a variational approach, Castelló, Spain, January 2020.

• Seminar: Hölder regularity of solutions to a class of nonlocal Dirichlet problems, Valencia, Spain, July 2019.

• Seminar: Asymptotic behaviour of nonlinear flows in tubular domains, Università di Roma ``La Sapienza'', Roma, Italy, March 2019.

• Seminar: On the nodal set of solutions to some nonlocal parabolic reaction  diffusion-equations, Universidade de Lisboa, Lisboa, Portugal, October 2018.

• Online seminar: On the nodal set of solutions to a nonlocal heat equation, ``Nonlocal interactions in partial differential equations and geometry'', Mittag-Leffler Institute, Stockholm, Sweden, May 2018.

• Seminar: Blow-up classification and nodal properties for solutions to some nonlocal parabolic equations, La Sapienza Università di Roma, Roma, Italy, February 2018.

• Seminar: Blow-up classification for some parabolic equations with singular-degenerate diffusion, Spa, Belgium, December 2017.

• Seminar: Large time asymptotics for reaction-diffusion equations with doubly nonlinear diffusion, Mathematical Research Institute MATRIX, Creswick, Australia, October 2017.

• Seminar: Large time behaviour for the Fisher-KPP problem with doubly nonlinear diffusion, Università degli Studi di Milano-Bicocca, Milano, Italy, June 2017.

• Seminar: The FKPP problem with doubly nonlinear diffusion, Politecnico di Milano, Italy, November 2016.

SELECTED CONFERENCES, SCHOOLS and WORKSHOPS

• "Regularity for nonlinear diffusion equations. Green functions and functional inequalities", Universidad Autónoma de Madrid, Madrid, Spain, 13 - 17 June 2022.

• "Analytical Methods in Quantum and Continuum Mechanics", Torino, Italy, 29 November - 3 December 2021.

• "Regularity Theory for Free Boundary and Geometric Variational Problems", Levico Terme, Italy, 06-10 September 2021.

• "V Congreso de Jóvenes Investigadores 2020", Castelló, Spain, 27-31 January 2020

• "Geometric Measure Theory and Applications: From Geometric Analysis to Free Boundary Problems", Fondazione Cime, Cetraro, Italy, 02-06 September 2019.

• "Recent developments in the analysis of nonlocal operators" ICIAM 2019, Valencia, Spain, 15-19 July 2019.

• "Intensive week of PDE@Cogne", Cogne, Valle d'Aosta, Italy, 03-07 June 2019.

• "Topics in Nonlinear Analysis: Calculus of Variations and PDEs", Universidade de Lisboa, Lisboa, Portugal, 10-12 October 2018.

• "Interactions between PDE and probability", Summer Course UIMP, Santander, Spain, 13-17 August 2018.

• "Young PDE's @ Roma", La Sapienza Universit\`a di Roma, Roma, Italy, 19-22 February 2018.

• "Intensive Week of PDEs at SPA", Radisson Hotel, Spa, Belgium, 11-15 December 2017.

• "Elliptic Partial Differential Equations Of Second Order: Celebrating 40 Years Of Gilbarg And Trudinger's Book", Mathematical Research Institute MATRIX, Creswick, Australia, 16-20 October 2017.

• "Equadiff 2017", Department of Mathematics and Descriptive Geometry, Slovak University of Technology, Bratislava, Slovakia, 24-28 July 2017.

• "Existence and regularity for the Plateau problem", SMI Summer Course, Palazzone della Scuola Normale Superiore, Cortona, Italy, 17-29 July 2016.

• "Nonlocal and nonlinear diffusions and interactions: new methods and directions", Fondazione Cime, Cetraro, Italy, 04-08 July 2016.

• "Conference on Qualitative Aspects of the Theory of Nonlocal Equations", Fields Institute, Toronto, Canada, 16-20 May 2016.

• "Frontiers of Mathematics and Applications IV", Summer Course UIMP, Santander, Spain, 20-24 July 2015.

FELLOWSHIPS and AWARDS

• June 2020: I have been awarded with the "Premio Vicent Caselles 2020" for PhD thesis, Real Sociedad Matemática Española and Fundación BBVA (Spain).

• February 2020: I have been awarded with a "Marie Sklodowska-Curie IF 2019". Project title: "Local and Nonlocal Free Boundary Problems" (LNLFB-Problems). EU Project Contract No: 892017.

• November 2017: I have been awarded with the "Premio Qualità 2017" for PhD thesis, Politecnico di Torino (Italy).

PROJECTS

• May 2023 - present: I am the coordinator of the project "Teoria della regolarità per problemi ellittici e parabolici con diffusione anisotropa e pesata", GNAMPA, Italy. 

• September 2020 - August 2022: I have co-directed the project "Local and Nonlocal Free Boundary Problems}" (LNLFB-Problems, Marie Sklodowska-Curie IF 2019, EU Project Contract No: 892017). Supervisor: Joaquim Serra (ETHZ).

TEACHING ACTIVITIES

• Lecturer for the PhD course "Geometrical Aspects of PDEs" (part I and II), Università degli Studi di Torino, co-held with A. Iacopetti, N. Soave and S. Terracini, 2023-24.

• Lecturer for the course "Mathematical Analysis 1", 1st year of Undergraduate Studies in Politecnico di Torino, PoliTo, 2022-2023. 

• Lecturer for the PhD course "Reaction-diffusion equations: traveling fronts and long-time behaviour", ETHZ (2021-2022).

• Teaching assistant for the course/seminar "Classical Theory of Elliptic Partial Differential Equations", Undergraduate and Postgraduate Studies at ETHZ (2020-2021).

• Lecturer/Responsible for the course/seminar "Reaction-diffusion equations in Biology", Undergraduate and Postgraduate Studies at UZH (2019-2020).

• Teaching assistant for the course "Lineare Algebra", 1st year of Undergraduate Studies at UZH (2019-2020).

• Teaching assistant for the course "Algebra Lineare" (MATLAB laboratory), 1st year of Undergraduate Studies at PoliTo (2018-2019).

• Teaching assistant for the course "Analisi II", 2nd year of Undergraduate Studies in Computer Engineering (Ingegneria Informatica), PoliTo (2017-2018, 2018-2019). 

• Lecturer for the problem solving activity "Attività di risoluzione di esercizi di alto livello matematico", 3th year of Undergraduate Studies in Mathematics, UniTo (2016-2017).

• Teaching assistant for the course "Analisi II", 2nd year of Undergraduate Studies in Biomedical Engineering (Ingegneria Biomedica), PoliTo (2016-2017).

• Lecturer for the course "Precorso di Geometria", 1st year of Undergraduate Studies in Physics, UniTo (2016-2017).

• Teaching assistant for the course "Matemàticas 1", 1st year of Undergraduate Studies in Chemical Engineering, UAM (2015-2016). 

• Teaching assistant for the course "Variable real", 4st year of Undergraduate Studies in Mathematics, UAM (2015-2016).

SCIENTIFIC POPULARIZATION, COMMUNICATION ACTIVITIES

• Online seminar: Some Wonderful PDEs, Science is Wonderful 2021, November 2021.

• Organizer of the workshop "Zome and soap bubbles'", 2021 European Researcher's Night, Torino, Italy, September 2021.

• Speaker in the online workshop "MSCA - Postdoctoral fellowships in Horizon Europe", UniTo, July 2021.

• Seminar: MSCA Proposal Preparation: some hints, in the online workshop "Online Applicants Training for MSC Individual Fellowships", ETHZ, June 2020.

• Organizer of the workshop "Estrategias Ganadoras", XV Edition of ``Semana de la Ciencia'', UAM, November 2015.

MENTORING and SUPERVISION 

• PhD Thesis: Regularity theory for solutions to a class of weighted parabolic PDE's and applications (provisional title), Gabriele Fioravanti (co-advised with S. Terracini and S. Vita), UniTo-PoliTo, November 2022-present.

• Master Thesis: A variational problem for the spatial segregation of reaction-diffusion systems, Patrik Rosa Ferreira (co-advised with J. Serra).

ORGANIZATION

• Organizer of the PhD course "Topics in Geometric Analysis", Dipartimento di Scienze Matematiche DISMA, Politecnico di Torino, Torino, Italy, June 2024.

• Organizer of the workshop "Free boundary problems and related topics", DMATH ETHZ, Zurich, Switzerland, July 2022.

• Organizer of the conference "Intensive week of PDE@Cogne", Cogne, Valle d'Aosta, Italy, June 2019.

• Organizer of the workshop "Topics in Nonlinear Analysis and Calculus of Variations'", Dipartimento di Matematica, UniTo, Torino, Italy, April 2019.

• Organizer of the of seminars "Seminari Dottorandi" for the academic year 2016/17, Dipartimento di Matematica, UniTo, Torino, Italy.