about

Aleksis Arendt

Undergraduate mathematics, Ho Chi Minh City University of Science.

Research Interests

Geometric analysis, geometric measure theory, and calculus of variations. Currently working toward a solid foundation in real analysis and functional analysis before moving into PDE theory and GMT proper.

Long-term interest in minimal surfaces, harmonic maps, mean curvature flow, and gauge theory — particularly Uhlenbeck-style Yang-Mills theory and principal fiber bundles with connections.

Current Focus

Measure TheoryFolland, Evans-Gariepy
Functional AnalysisBrezis
ODE TheoryPeano existence, Picard-Lindelöf, Lax-Milgram
Differential GeometryStarting again in summer

Academic Path

Targeting a master's program in Germany or Switzerland — Bonn, LMU Munich, or ETH Zürich — followed by a PhD in geometric analysis or GMT. The recommended path is a German master's first, then PhD application to ETH or EPFL with a strong thesis and supervisor letter.

About This Blog

These are working notes — written to consolidate understanding, not to present polished results. Each post starts from a single problem or theorem, explores it until exhausted, then connects it to the broader picture.

The writing process follows a simple rule borrowed from Halmos: don't just read — fight it. Every hypothesis questioned, every counterexample sought, every proof reproduced from scratch.