colloquium

Algebraic & Differential Geometry

The Algebraic & Differential Geometry research area brings together expertise across geometry, algebra, and analysis to study fundamental questions in the areas of differential geometry, symplectic geometry, geometric partial differential equations, geometric evolutions, noncommutative geometry, algebraic geometry, number theory, and mathematical physics.

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About

The Algebraic & Differential Geometry research area brings together expertise across geometry, algebra, and analysis to study fundamental questions in the areas of differential geometry, symplectic geometry, geometric partial differential equations, geometric evolutions, noncommutative geometry, algebraic geometry, number theory, and mathematical physics.

Capabilities

  • Ben Andrews: geometric partial differential equations (including mean curvature flow and Ricci flow), geometric variational problems (including isoperimetric problems and eigenvalue inequalities), and geometric approaches to the analysis of differential equations.
  • Asilata Bapat: geometric and categorical representation theory, homological algebra, with connections to topology, combinatorics, and algebraic geometry.
  • James Borger: algebra, especially number theory and algebraic geometry.
  • Anand Deopurkar: algebraic geometry and its connections to number theory, representation theory, and mathematical physics, homological algebra.
  • Mat Langford: Ricci flow, mean curvature flow and flows of hypersurfaces by nonlinear functions of their curvature, related nonlinear elliptic and parabolic PDE, and applications to topology, geometry and general relativity
  • Ian Le: representation theory and algebraic combinatorics, cluster theory.
  • Brett Parker: symplectic geometry, Gromov-Witten and related invariants using exploded manifolds.
  • Bryan Wang: geometric properties of moduli spaces in symplectic topology, gauge theory.

Reasons to work with us

We are a broad mathematical research groups connected to a wide variety of research topics in modern mathematics. 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

Arithmetic algebraic geometry

Student intake

Open for students

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Potential

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Investigate the relation between group theory and repeating 'crystal' patterns in 1, 2, and 3 dimensions.

Student intake

Open for Bachelor students

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The curve shortening flow is a simple and beautiful example of a geometric heat flow, the family of equations which includes the Ricci flow used by Perelman to prove the Poincare conjecture as well as many other interesting examples. 

Student intake

Open for Bachelor, Summer scholar students

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Clifford algebras and Clifford modules; Spin structures and Dirac operators, their geometric properties, and some examples, possibly including Witten's proof of the positive mass theorem.

Student intake

Open for Bachelor, Honours, Masters students

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On a (compact) Riemannian manifold there is a natural differential operator on functions, the Laplacian. The eigenvalues of this operator are important invariants of the manifold, and there are many interesting results which relate the eigenvalues to other geometric quantities...

Student intake

Open for Bachelor, Summer scholar students

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People

Explorations in Geometry and Mathematical Physics: From Symplectic Geometry to String Theory

Student intake

Open for Bachelor, Honours, Masters, PhD students

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Potential

People

Members

Emeritus

John Hutchinson

Emeritus Professor

Amnon Neeman

Emeritus Professor

Neil Trudinger

Emeritus Professor

John Urbus

Emeritus Professor

Xu-Jia Wang

Honorary Professor

Researcher

Ben Andrews

Professor
Associate Director (Research)

Asilata

Senior Lecturer
ARC DECRA Fellow

Jim Borger

Associate Professor

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MSI Fellow

Anand Deopurkar in 2022 in Hawaii

Senior Lecturer

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Postdoctoral Fellow

Mat Langford

MSI Fellow
ARC Future Fellow

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Senior Lecturer
PhB Convenor

Svetlana Makarova

MSI Fellow

Leonardo Maltoni

Postdoctoral Fellow

Brett Parker

Senior Lecturer
MSI Colloquium Organiser

Student