*Research in the field of pure mathematics from the Faculty of Science, University of Melbourne.*

## Researchers

**Diarmuid Crowley**
Differential topology, algebraic topology, surgery classification of manifolds.

**Jan de Gier**
Combinatorics, mathematical physics, integrable models, stochastic processes.

**Nora Ganter**
Categorification, elliptic cohomology, homotopical representation theory, monstrous moonshine.

**Jesse Gell-Redman**
Microlocal analysis, partial differential equations, differential geometry.

**David Gepner**
Homotopy theory, algebraic K-theory, algebraic geometry, higher category theory.

**Alex Ghitza**
Computational number theory, Galois representations, Shimura varieties, automorphic forms.

**Christian Haesemeyer**
K-theory, algebraic cycles, motives.

**Iva Halacheva**
Low dimensional topology, knot theory, representation theory, quantum algebra.

**Craig Hodgson**
Hyperbolic geometry, low dimensional topology, differential geometry.

**Mario Kieburg**
Harmonic analysis and group and representation theory, random matrix theory, orthogonal functions and polynomials, quantum field theory, telecommunications systems, supersymmetry & graded algebras, quantum chaos, quantum information theory.

**Deborah King**
Studies in dynamic systems, including combinatorial dynamics, and mathematics education.

**Peter McNamara**
Representation theory.

**Daniel Murfet**
Mathematical logic, algebraic geometry, topological field theories.

**Paul Norbury**
Gauge theory, mathematical physics, algebraic geometry, moduli spaces.

**Sam Povall**
Geometric group theory, singularity theory, complex hyperbolic geometry

**Thomas Quella**
Representation theory and applications, conformal field theory, quantum integrable models, topological states of matter, tensor network states, Lie (super) algebras, diagram algebras, quantum groups, quantum many-body physics.

**Arun Ram**
Combinatorial representation theory.

**Lawrence Reeves**
Geometric group theory.

**David Ridout**
Conformal field theory, vertex operator algebras, representation theory, Lie (super) algebras, integrable models.

**Marcy Roberston**
Higher category theory, operad theory, homotopy theory.

**Volker Schlue**
Partial differential equations, general relativity, geometric analysis.

**Trithang Tran**
Research in the use of algebraic topology with configuration spaces and braid groups.

**Kari Vilonen**
Representation theory, algebraic geometry, algebraic analysis.

**Chenyan Wu**
Representation theory, algebraic geometry, algebraic number theory.

**Ting Xue**
Algebraic groups, representation theory.

**Yaping Yang**
Geometric representation theory, quantum groups.

**Gufang Zhao**
Algebra, geometry, topology, representation theory, algebraic geometry.

**Paul Zinn-Justin**
Quantum integrable systems, algebraic combinatorics, Schubert calculus.

## Research centres

**Mathematical Research Institute MATRIX**

MATRIX is an international research institute that runs research programs where world lead researchers in the mathematical sciences, as well as experts from business and industry, can come together.

Research in this area is conducted in the School of Mathematics and Statistics.