I am an assistant professor (US tenure-track equivalent) in mathematics at the Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, affiliated with Tsinghua University, Beijing. Previously, I was a postdoctoral fellow in the Yau Mathematical Sciences Center, also at Tsinghua. Before that, I received my PhD in pure maths at Harvard University. My undergraduate education comprised a BA in pure maths (the mathematical tripos) and an MMath degree (Part III) from Trinity College, University of Cambridge. My permanent email address is max.menzies at alumni.harvard.edu; my WeChat ID is max-menzies. My Chinese name is 孟思哲。

Research

I am interested in both pure and applied mathematics. In pure maths, I spent my undergraduate and graduate years studying algebraic number theory and arithmetic geometry, particularly p-curvature. In applied maths, my primary collaborator is Nick James of the University of Melbourne. We try to work on various topical problems and develop new mathematical techniques to tackle them, with many experiments. We have concluded a body of work on COVID-19, and have ongoing interest in various topics, including financial markets, cryptocurrencies, gun violence, terrorism, environmental topics, and statistical methodology.

Papers

I encourage all academics to submit their work to an open access repository such as arXiv. All my papers can be found on my personal arXiv page (see links below).

• Portfolio diversification with varying investor abilities, submitted, 2023.

• Collective infectivity of the pandemic over time and association with vaccine coverage and economic development, Chaos, Solitons & Fractals 176, 114139 (2023).

• An exploration of the mathematical structure and behavioural biases of 21st century financial crises, Physica A: Statistical Mechanics and its Applications 630, 129256 (2023).

• Collective dynamics, diversification and optimal portfolio construction for cryptocurrencies, Entropy 25, 931 (2023).

  I was invited to submit this paper with a full waiver of the typical article processing charge (APC).

• Semi-metric portfolio optimization: a new algorithm reducing simultaneous asset shocks, Econometrics 11, 8 (2023).

  I was invited to submit this paper with a full waiver of the typical APC.

• Distributional trends in the generation and end-use sector of low-carbon hydrogen plants, Hydrogen 4, 174-189 (2023).

  I was invited to submit this paper with a full waiver of the typical APC.

• Equivalence relations and L^p distances between time series with application to the Black Summer Australian bushfires, Physica D: Nonlinear Phenomena 448, 133693 (2023).

• Geometric persistence and distributional trends in worldwide terrorism, Chaos, Solitons & Fractals 169, 113277 (2023).

• Global and regional changes in carbon dioxide emissions: 1970-2019, Physica A: Statistical Mechanics and its Applications 608, 128302 (2022).

• Dual-domain analysis of gun violence incidents in the United States, Chaos: An Interdisciplinary Journal of Nonlinear Science 32, 111101 (2022).

  This was featured as an editor's pick and accompanied by a press release.

• Economic state classification and portfolio optimisation with application to stagflationary environments, with Nick James and Kevin Chin, Chaos, Solitons & Fractals 164, 112664 (2022).

• On financial market correlation structures and diversification benefits across and within equity sectors, with Nick James and Georg Gottwald, Physica A: Statistical Mechanics and its Applications 604, 127682 (2022).

• Optimally adaptive Bayesian spectral density estimation for stationary and nonstationary processes, Statistics and Computing 32, 45 (2022).

• Spatio-temporal trends in the propagation and capacity of low-carbon hydrogen projects, International Journal of Hydrogen Energy 47, 16775-16784 (2022).

• In search of peak human athletic potential: a mathematical investigation, Chaos: An Interdisciplinary Journal of Nonlinear Science 32, 023110 (2022).

• Comparing the dynamics of COVID-19 infection and mortality in the United States, India, and Brazil, Physica D: Nonlinear Phenomena 412, 133158 (2022).

• Structural clustering of volatility regimes for dynamic trading strategies, with Arjun Prakash, Nick James and Gilad Francis, Applied Mathematical Finance 28, 236-274 (2022).

• Estimating a continuously varying offset between multivariate time series with application to COVID-19 in the United States, The European Physical Journal Special Topics 231, 3419-3426 (2022).

• Collective correlations, dynamics, and behavioural inconsistencies of the cryptocurrency market over time, Nonlinear Dynamics 107, 4001-4017 (2022).

• A new measure between sets of probability distributions with applications to erratic financial behavior, Journal of Statistical Mechanics: Theory and Experiment, 123404 (2021).

• Understanding spatial propagation using metric geometry with application to the spread of COVID-19 in the United States, with Nick James and Howard Bondell, EPL (Europhysics Letters) 135, 48004 (2021).

• Efficiency of communities and financial markets during the 2020 pandemic, Chaos: An Interdisciplinary Journal of Nonlinear Science 31, 083116 (2021).

• Trends in COVID-19 prevalence and mortality: a year in review, Physica D: Nonlinear Phenomena 425, 132968 (2021).

• COVID-19 second wave mortality in Europe and the United States, with Nick James and Peter Radchenko, Chaos: An Interdisciplinary Journal of Nonlinear Science 31, 031105 (2021).

  This was featured as an editor's pick and accompanied by a press release.

• Association between COVID-19 cases and international equity indices, Physica D: Nonlinear Phenomena 417, 132809 (2021).

• Changes to the extreme and erratic behaviour of cryptocurrencies during COVID-19, Physica A: Statistical Mechanics and its Applications 565, 125581 (2021).

• COVID-19 in the United States: Trajectories and second surge behavior, Chaos: An Interdisciplinary Journal of Nonlinear Science 30, 091102 (2020).

  This paper was chosen as the cover of the journal issue, featured as an editor's pick, and accompanied by a press release.

• Novel semi-metrics for multivariate change point analysis and anomaly detection, Physica D: Nonlinear Phenomena 412, 132636 (2020).

• Cluster-based dual evolution for multivariate time series: Analyzing COVID-19, Chaos: An Interdisciplinary Journal of Nonlinear Science 30, 061108 (2020).

  This was featured as an editor's pick and accompanied by a press release.

• The p-curvature conjecture for the non-abelian Gauss-Manin connection, 2019, PhD thesis.

Selected fellowships and awards

• Postdoctoral fellowship completion with Distinction, Tsinghua University, 2021. In China, postdocs are treated a little like degrees, with a final thesis submission, defence, etc.

• Fellowship of the Higher Education Academy (FHEA), Advance HE, 2021. Home website.

• Frank Knox Memorial Fellowship, Harvard University, 2013. Home website.

• G.F.A Osborn Prize for first place in second year mathematics, Trinity College, Cambridge, 2011.

• T.G. Room Award for first in Extension 2 mathematics, NSW, 2009. Archived website. It looks like MANSW abandoned their website, but there's some nice history there.

• International Mathematical Olympiad silver medal, 2007 and 2008. Historical website.

Useful links

There's a nice function on arXiv to create a personal author page, where all your papers are lined up together. It's more reliable than searching by an author's name in the search bar. My personal arXiv page is here.

I like the Mathematics Genealogy Project. Here is my personal page.

I also like ORCID ID's, and encourage everyone to sign up for one. It's really quick (much quicker than getting a MGP profile...). Here is my page.

Finally, I'm a big fan of open source end-to-end encrypted applications. Signal is an alternative to WhatsApp that is actually encrypted rather than likely not, and its call quality is much better. Jitsi is an alternative to Zoom that is superior in every way. It is completely free, open source, encrypted, easier to use, and requires no sign-up to create a meeting.