Algebra & topology

Algebra & topology

We work on problems of central interest in mathematics.

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About

We work on problems of central interest in mathematics. Our primary research areas include number theory, representation theory, low-dimensional topology, algebraic geometry, algebraic topology, homological algebra, geometric group theory, cluster algebras, and symplectic geometry. We also have strong ties with other parts of the Mathematical Sciences Institute, and we collaborate regularly with researchers in mathematical physics, geometry, and applied topology. In addition to the ongoing research of our continuing staff, we support undergraduate, honours, masters and PhD students. We also host a steady stream of postdoctoral and visiting scholars.

Capabilities

  • Vigleik Angeltveit: Algebraic Topology, stable homotopy theory, algebraic K-theory, Ramsey theory.
  • Asilata Bapat: Geometric representation theory, homological algebra.
  • Jim Borger: Number theory and algebraic geometry.
  • Anand Deopurkar: Algebraic geometry and its connections to number theory, representation theory, and mathematical physics. Homological algebra.
  • Ian Le: Representation theory and algebraic combinatorics. Cluster theory.
  • Joan Licata: Low-dimensional topology and contact geometry. Knot theory and Floer theoretic invariants.
  • Amnon Neeman: Algebraic K-theory, algebraic geometry, topology, homological algebra.
  • Uri Onn: Representation theory. Analytic and Algebraic groups.
  • Brett Parker: Symplectic geometry and Gromov-Witten and related invariants using exploded manifolds.
  • Adam Piggott: Geometric group theory. Rewriting systems, automorphisms of the free group.
  • James Tener: Operator algebras, functional analysis, and representation theory. Mathematical foundations of quantum field theory.
  • Katharine Turner: Computational topology. Topological data analysis.
  • Bryan Wang: Geometric properties of moduli spaces in symplectic topology. Gauge theory.

Reasons to work with us

We are one of the largest and broadest mathematical research groups at ANU. We support an active, collaborative research and learning environment. Our regular topics courses, seminars, and learning groups aimed at fostering interactions between mathematicians at all levels, from undergraduates through to continuing faculty. Our mathematicians are international leaders in their fields, and we maintain active collaborations with mathematicians all over the world.

Projects

Depending on student interest and background I can supervise a variety of topics related to algebraic topology.

Student intake

Open for Bachelor, Summer scholar students

People

Arithmetic algebraic geometry

Student intake

Open for Summer scholar students

People

How many solutions does the equation x2+y2 = z2 have if x, y, z are taken from Z/pZ? How many square-free polynomials of degree n are there with coefficients in Z/pZ? Questions of this kind have deep and seemingly unexpected connections with the arithmetic and geometry of algebraic varieties.

Student intake

Open for Honours, Masters, PhD students

People

Combinatorial and Geometric Group Theory

Student intake

Open for Honours, Masters, PhD students

People

Homotopy groups are extremely difficult to compute, and even the homotopy groups of spheres are only understood through some small range of degrees.

Student intake

Open for Honours, Masters students

People

Can one write a computer program to decide whether two given rings are isomorphic? Or whether a given group is the trivial group? Or whether a given CW complex is a sphere? These are questions on the inteface of logic, theoretical computer science, and mathematics with fascinating results and open problems.

Student intake

Open for Honours, Masters, PhD students

People

Members

Convenor

James Borger

Associate Director (Education)
Associate Professor

Associate Professor
Honours Convener

Emeritus

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Emeritus Professor

Researcher

Vigleik Angeltveit

International students convenor
Senior Lecturer

Asilata Bapat

Lecturer

Anand Deopurkar

Senior Lecturer

Tony Licata

Professor
PhB Convenor

Amnon Neeman

Emeritus Professor

Uri Onn

Professor

Brett Parker

Senior Lecturer
MSI Colloquium Organiser

Associate Professor

Senior Lecturer

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Senior Lecturer

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Honorary Professor

Bryan Wang

Associate Professor
HDR Convenor

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Honorary Fellow

Retired Fellow

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Retired Fellow

Student

News

MATRIX launches Australia's first all-women residential research program in the mathematical Sciences

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Congratulations to Associate Professor Anthony Licata who was awarded the 2017 AustMS medal at the opening of the Annual AustMS meeting at Macquarie University in Sydney. 

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