Mr Max Auer
Mr

Max Auer

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Background

I am a mathematician working in dynamical systems and ergodic theory, with a focus on probabilistic limit theorems and rare events in deterministic and random systems. My research investigates how statistical laws emerge from complex long-term behaviour.

My work sits at the intersection of:

  • Ergodic theory

  • Dynamical systems

  • Random dynamical systems

  • Probability theory

  • Limit theorems (e.g. central limit theorem, stable laws)

I study when deterministic or randomly driven systems exhibit classical probabilistic behaviour, such as the central limit theorem, as well as non-standard limit laws and heavy-tailed distributions. I have a particular interest in limit theorems governing rare and extreme events.

More broadly, my work bridges dynamical systems and probability theory, clarifying when complex systems behave “as if random” and when fundamentally different statistical phenomena arise.

Availability

Mr Max Auer is:
Available for supervision

Qualifications

  • Bachelor of Mathematics, Universität Wien
  • Masters (Coursework) of Mathematics, Universität Wien
  • Doctor of Philosophy of Mathematics, University of Maryland-College Park
  • Member, Australian Mathematical Society, Australian Mathematical Society

Research interests

  • Limit Theorems in Dynamical Systems

    I study probabilistic limit theorems for deterministic and random dynamical systems, including the central limit theorem, stable laws, and non-standard distributional limits. My work investigates when dynamical systems exhibit classical statistical behaviour and when different limiting distributions arise. I aim to identify structural conditions that determine the type of statistical law observed.

  • Rare and Extreme Events

    I investigate limit laws governing rare and extreme events in dynamical systems. This includes heavy-tailed distributions, return-time statistics, and distributional limits associated with atypical fluctuations. My research seeks to clarify how extreme behaviour emerges from deterministic or randomly driven dynamics.

  • Random Dynamical Systems

    I study dynamical systems influenced by randomness and analyse their long-term statistical properties. My work examines how noise or random driving affects limit theorems and the emergence of statistical regularity. I am particularly interested in comparing statistical behaviour in deterministic and random settings.

Research impacts

My research strengthens the mathematical foundations used to analyse complex systems with uncertainty. By developing rigorous statistical limit theorems for deterministic and random dynamical systems, I contribute to the theoretical tools that underpin modern stochastic modelling and risk assessment.

A particular focus of my work is understanding rare and extreme events, including heavy-tailed behaviour and non-standard limit laws. These phenomena play an important role in areas where extreme outcomes matter, such as environmental risk, financial modelling, and infrastructure reliability.

Beyond specific applications, my research supports long-term capability building by advancing core mathematical theory and training researchers in advanced probabilistic and analytical methods. This contributes to more reliable modelling and improved decision-making in settings involving uncertainty and complex dynamics.

Availability

Mr Max Auer is:
Available for supervision

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Enquiries

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