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**Analysis, Geometry and Topology Research Group**## Department of Mathematics

# Analysis, Geometry and Topology Research Group

The Analysis, Geometry and Topology Group has strengths in differential geometry, functional analysis, harmonic analysis and topology.

### Permanent Research Staff

- Pedram Hekmati

Differential geometry, Lie theory and mathematical physics. - Rod Gover

Differential geometry and its relationship to representation theory. Applications to analysis on manifolds, Partial Differential Equation theory and mathematical physics Conformal and related structures - Sina Greenwood

Continua theory and discrete dynamical systems - Igor Klep

Real algebraic geometry - Sione Ma'u

Pluripotential theory and its applications, functions of several complex variables - Warren Moors

Functional analysis and applications of topology to analysis - Tom ter Elst

Harmonic analysis, operator theory, geometric analysis, subelliptic and degenerate operators, Partial Differential Equations - Shayne Waldron

Finite tight frames with symmetries, approximation theory, polynomial interpolation and numerical methods

### Current and recent post-doctoral researchers

- Callum Sleigh

Differential Geometry

### Seminars and recent events

- Analysis Seminar
- Geometry and Analysis Seminar
- Topology

### Current and recent visitors

- Marcus Appleby (Queen Mary, University of London)
- Wolfgang Arendt (Ulm)
- Jussi Behrndt (TU Giraz)
- Andreas Cap (University of Vienna)
- David Cox (Amherst College)
- Steve Flammia (University of Sydney)
- Paul Gartside(University of Pittsburgh)
- Markus Haase (Delft)
- Emanuele Latini (University of Zurich)
- Mariusz Lemanczyk (Torum, Poland)

- Vladimir Matveev (University of Jena)
- Primoz Moravec (University of Ljubljana)
- Vladimir Muller (Prague)
- Jean-Philippe Nicolas (University of Brest)
- Daniel Plaumann (University of Konstanz)
- Manfred Sauter (Ulm)
- Gerd Schmalz (University of New England)
- Friedrich Martin Schneider (Dresden)
- Endre Suli (Oxford)
- Marcus Tressl (University of Manchester)
- Richard Vale (University of Canterbury)
- Andrew Waldron (UC Davis)
- Lutz Weis (Karlsruhe)

- Travis Willse (ANU)
- Wei-Hsuan Yu (Michigan State)

- Valentin Zagrebnov (Marseille)

### Current and recent postgraduate students

- Abhishek Bhardwaj (Hons): Positive Polynomials and Sums of Hermitian Squares

- Sean Curry (PhD): Overdetermined natural PDE, parabolic geometry, and applications
- Tuan Chien (PhD): On the existence of d2 equiangular lines in complex vector spaces
- Sunanda Dixit (PhD): Structures on non-metrizable manifolds
- Bartek Ewertowski (PhD)
- Tan Do (PhD): Degenerate elliptic operators
- James Fletcher (Masters): Chebychev Sets
- Keegan Flood (PhD): Cartan Geometry, Manifold Decompositions, and Geometric PDE
- Alex Galicki (Hons): B rown's Approximation Theorm
- Hwan Goh (Hons): Knot Theory
- Gareth Gordon (Phd): The Dirichlet-to-Neumann operator with partial data
- Charles Hadfield (Hons): The construction of conserved quantities in geometry and GR
- Paul Harris (Masters): Topological Games

- Jesse Hart (PhD): Pluripotential Theory In C^n
- Ben Lawrence (Masters): Symmetric semialgebraic sets and orbit spaces

- Benny Lawrence (PhD)
- Michael Lockyer (PhD): Generalised inverse limits
- Yuki Maehara (Hons): Categories of generalised inverse systems

- Afshin Mardani (PhD): Set-theoretic Topology, Topology of manifolds
- Joshua Marshall (Hons): On generalised inverse limits and questions of dimention
- Caleb Moses (Hons): Potential Theory on Algebraic Curves in C2

- Roberto Panai (PhD): The conformal geometry of submanifolds and natural PDE
- Sam Porath (PhD): Conformal Geometry and its Application to General Relativity and Fundamental Physics
- Daniel Snell (PhD)
- Nazli Uresin (PhD): Abstract Dynamical Systems
- Jurij Volcic (PhD)

- Simon Youl (PhD): Generalised inverse limits

- Community for Understanding and Learning in the Mathematical Sciences (CULMS)
- Centre for Mathematical Social Science (CMSS)
- Department of Computer Science
- Department of Engineering Science
- Department of Physics
- Department of Statistics
- Auckland Bioengineering Institute
- New Zealand Journal of Mathematics

**Programmes, Centres and Partners**

- Community for Understanding and Learning in the Mathematical Sciences (CULMS)
- Centre for Mathematical Social Science (CMSS)
- Department of Computer Science
- Department of Engineering Science
- Department of Physics
- Department of Statistics
- Auckland Bioengineering Institute
- New Zealand Journal of Mathematics

**Programmes, Centres and Partners**