Murat Akman · Mathematics

Analysis · Geometry · Partial differential equations

Murat Akman, surrounded by mathematical equations, level curves, convex bodies and boundary diagrams.

01 / About

Understanding equations
through geometry.

I am a Senior Lecturer in Mathematics at the University of Essex, working across harmonic analysis, partial differential equations, potential theory and geometric measure theory.

My work brings together questions about nonlinear equations, the geometry of rough boundaries, and the ways in which harmonic measures capture that geometry.

I am part of the Analysis and Mathematical Physics research theme in the School of Mathematics, Statistics and Actuarial Science, where I also serve as Director of Research.

University profile Google Scholar

02 / Research

Three connected
directions.

From the local behaviour of solutions
to the global geometry of a domain.

An interplay of geometry and potential.

Equations & regularity

Variational methods for elliptic and parabolic equations. Regularity and free boundary problems in non-smooth domains.

div(|∇u|^p−2∇u) = 0

II.

Measure & geometry

How harmonic, p-harmonic and elliptic measures reflect the geometry and rectifiability of a boundary.

ω · ∂Ω · ℋⁿ⁻¹

III.

Convexity & capacity

Brunn–Minkowski inequalities, their stability, and Minkowski-type problems for nonlinear elliptic equations.

λK + (1−λ)L

03 / Publications & preprints

A body of work.

On Google Scholar

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04 / Teaching & supervision

Sharing ideas.
Asking questions.

I teach analysis and differential equations, and supervise research at the interface of PDEs and geometry.

Teaching history & course materials

Real analysis

Limits, continuity and the foundations of analysis.

Complex variables

Functions of a complex variable and their applications.

Differential equations

Tools for understanding change, from ODEs to PDEs.

Research supervision

Working together.

Ariel Aguas Barreno

PhD · 2023–2026

Shirsho Mukherjee

Postdoctoral researcher · 2022–2024

Research opportunities

05 / Mathematical community

Mathematics,
together.

All conferences & seminars

Coming up · Cambridge

2027

6 January–30 April

Isaac Newton Institute

Frontiers in harmonic analysis, elliptic and parabolic PDEs, and GMT

I am co-organising this four-month research programme at the Isaac Newton Institute for Mathematical Sciences.

Explore the programme

PDEs @ Essex

A series connecting analysis, geometry and partial differential equations at the University of Essex since 2022. Explore the three most recent meetings below.