Hello

I am currently studying for a PhD in the Department of Mathematics and Statistics at the University of Western Australia. My research interests are in elliptic/parabolic partial differential equations (PDEs), particularly in integro-differential equations. Currently, I am working on projects in nonlocal overdetermined problems and regularity theory for nonlocal elliptic PDE. My supervisors are Enrico Valdinoci (principle supervisor), Serena Dipierro, and Lyle Noakes.

Office: G14, Mathematics building.
My contact details are availiable at the bottom of the page.

CV

Publications and preprints

Articles and preprints

  • Quantitative stability for the nonlocal overdetermined Serrin problem, pdf
    Serena Dipierro, Giorgio Poggesi Jack Thompson, Enrico Valdinoci
    Submitted, available on arXiv (2023)
  • Quantitative stability for overdetermined nonlocal problems with parallel surfaces and investigation of the stability exponents, pdf
    Serena Dipierro, Giorgio Poggesi Jack Thompson, Enrico Valdinoci
    Submitted, available on arXiv (2023)
  • Some nonlocal formulas inspired by an identity of James Simon, pdf
    Serena Dipierro, Jack Thompson, Enrico Valdinoci
    Submitted, available on arXiv (2023)
  • On the Harnack inequality for antisymmetric s-harmonic functions, pdf
    Serena Dipierro, Jack Thompson, Enrico Valdinoci
    J. Funct. Anal. 285 (2023), 109917, 49 pp
  • The role of antisymmetric functions in nonlocal equations, pdf
    Serena Dipierro, Giorgio Poggesi, Jack Thompson, Enrico Valdinoci
    To appear Trans. Amer. Math. Soc.

Theses

Awards

  • Ethel Raybould Prize in Mathematics
    Awarded to the honours student in the field of mathematics at the University of Queensland with the greatest proficiency for the year. 2020
  • Enid Russell Scholarship
    Award of $ 5 000 to a resident of St Catherine’s College who displays strong leadership qualities, academic potential, and embodies the pursuit of excellence. 2021.
  • Dean’s Commendation for Academic Excellence. Seven time recipient. 2017-2020.

Talks

Events, conferences, and seminars

  • International Conference on Nonlinear Partial Differential Equations In Honour of Professor Neil Trudinger's 80th Birthday. July 2023
  • Asia-Pacific analysis seminar. May 2023
  • Minimal surfaces and geometric flows: interaction between the local and the nonlocal worlds. January 2023.
  • AustMS Annual Meeting. December 2022.
  • Australian Geometric PDE Seminar. August 2022.
  • AustMS Annual Meeting. December 2021.

Reading courses

  • Special Solutions to Ricci Flow: Einstein Metrics and Ricci Solitons Australia Geometric PDE seminar. October 2021. Reading course on Ricci flow.
  • The Leray Projection UQ Analysis Seminar. August 2021. Slides. Reading course on the analysis of the Navier-Stokes equations.
  • An Introduction to Morse Theory and Handle Decompositions. As part of a reading course in algebraic topology. October 2020.
  • Local Estimates via the Maximum Principle for Mean Curvature Flow. UQ Analysis Seminar. August 2020. Reading course on mean curvature flow
  • Optimal Tranport: The Restriction Property. UQ Analysis Seminar. March 2020. Reading course on optimal transport.
  • Weak Convergence Methods: Concentrated Compactness. UQ Analysis Seminar. September 2019. Reading course on weak convergence methods for variational PDE.
  • Applications of the First Variation Formula for Minimal Submanifolds. UQ Analysis Seminar. April 2019. Reading course on minimal surfaces.
  • Introduction to Geodesics and Convex Neighbourhoods. Given as part of a reading course I took on Riemannain Geometry in Sem. 1, 2019.

Other Talks

  • On the Uniqueness of Conformal Metrics with Prescribed Curvature. Presentation for the fulfilment of my Honours degree. October 2020.
  • Topological Degree and its Applications to Partial Differential Equations. This was a presentation on a undergraduate research project I did in Sem. 1, 2019. June 2019.

Service

  • UWA Maths Union Postgraduate Representative 2023
  • Co-organiser UWA research talks
    July 2022 - Ongoing. A weekly seminar series targeted at first and second year undergraduate students in Maths and Physics with the intention of inspiring students to pursue higher level research and to provide an opportunity for students to interact with postgraduate students and staff.

Teaching

I am currently an assistant lecturer at the University of Western Australia. Previously, I've worked as a teaching assistant at the University of Western Australia and the University of Queensland.

Assistant lecturer at the University of Western Australia

  • Semester 2, 2022: MATH1012 Mathematical Theory and Methods
  • Semester 1, 2022: MATH1012 Mathematical Theory and Methods

Teaching assistant at the University of Western Australia

  • 2023 Semester 2: MATH1012 Mathematical Theory and Methods
  • 2023 Semester 1: MATH1011 Multivariable Calculus, MATH1013 Mathematical Analysis, MATH1700 Forensic Mathematics
  • 2022 Semester 1: MATH1012 Mathematical Theory and Methods
  • 2021 Semester 2: MATH3032 Topology and Analysis, MATH1012 Mathematical Theory and Methods (two classes)
  • 2021 Semester 1: MATH1011 Multivariable Calculus, MATH1721 Mathematics Foundations: Methods

Teaching assistant at the University of Queensland

  • 2021 Semester 1: MATH2001 Calculus & Linear Algebra II (two online classes)
  • 2020 Semester 2: MATH3405 Differential Geometry, MATH1061 Discrete Mathematics
  • 2020 Semester 1: STAT3004 Probability Models & Stochastic Processes (two classes), STAT2003 Mathemtical Probability, MATH2000 Linear Algebra II
  • 2019 Semester 2: MATH1061 Discrete Mathematics
  • 2019 Semester 1: MATH1071 Advanced Calculus & Linear Algebra