I am a postdoctoral fellow in mathematics at Tsinghua University, Beijing. Previously, 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, 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。 I'm currently in Sydney, still working on maths and Chinese.

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 (and best friend of 25 years) is Nick James. We try to work on various topical problems and develop new mathematical techniques to tackle them, with many experiments.

Papers

Apart from climate change, nothing is more important than accessibility of research, education, and information. 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).

• Efficiency of communities and financial markets during the 2020 pandemic, with Nick James, 2021, submitted.

• Trends in COVID-19 prevalence and mortality: a year in review, with Nick James, 2021, submitted.

• 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, with Nick James, Physica D: Nonlinear Phenomena, 417 (2021) 132809.

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

• COVID-19 in the United States: Trajectories and second surge behavior, with Nick James, Chaos: An Interdisciplinary Journal of Nonlinear Science, 30, 091102 (2020). This was featured as an editor's pick, chosen as the cover of the issue, and accompanied by a press release.

• Cluster-based dual evolution for multivariate time series: Analyzing COVID-19, with Nick James, Chaos: An Interdisciplinary Journal of Nonlinear Science, 30, 061108 (2020). This was featured as an editor's pick and accompanied by a press release.

• Structural clustering of volatility regimes for dynamic trading strategies, with Arjun Prakash, Nick James and Gilad Francis, 2020, submitted.

• Optimally adaptive Bayesian spectral density estimation for stationary and nonstationary processes, with Nick James, 2020, submitted.

• Equivalence relations and L^p distances between time series, with Nick James, 2020, submitted.

• Semi-metric portfolio optimisation: a new algorithm reducing simultaneous asset shocks, with Nick James and Jennifer Chan, 2020, submitted.

• Novel semi-metrics for multivariate change point analysis and anomaly detection, with Nick James, Lamiae Azizi and Jennifer Chan, Physica D: Nonlinear Phenomena, 412 (2020) 132636.

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

Selected fellowships and awards

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

• G.F.A Osborn Prize for first 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.

Previous teaching

• Teaching Fellow (lecturer) for Math 1b: Calculus, Series, and Differential Equations, Harvard University, spring 2018

• Teaching Fellow (lecturer) for Math 21a: Multivariable Calculus, Harvard University, spring 2017

• Graduate Calculus Fellow (tutor) for Math 1a: Introduction to Calculus, Harvard University spring 2016

• Math Question Center tutor for Math 21b: Linear Algebra and Differential Equations, Harvard University, spring 2015

• Mentor, Advanced Mentoring Scheme, UK Mathematics Trust, 2009-2012

• Lecturer, Australian IMO Team Selection School, 2009-2011

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 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.