Algebraic geometry has a long history. Its origins are the geometry of the set of solutions to systems of polynomial equations in several variables. While such down-to-earth problems remain the focus of algebraic geometry today, the language and techniques have changed enormously.
One of the advantages of algebraic geometry over other types of geometries is its ability to handle singularities and its computability. This is because its roots lie in algebra, as opposed to differential equations.
The Algebraic Geometry group at the University of Melbourne is broad, with interests in number theory, representation theory, K-theory, moduli theory and elsewhere.
Algebraic geometry is part of the Pure Mathematics Research Group
Academic Staff
Prof Christian Haesemeyer
Professor
Motives, algebraic cycles, K-theory
A/Prof Jack Hall
Associate Professor and ARC Future Fellow
Algebraic stacks, moduli spaces, formal and analytic geometry, deformation theory
Dr Johanna Knapp
Senior Lecturer and ARC Future Fellow
String theory, algebraic geometry, Gauge theory
Dr Peter McNamara
Senior Lecturer
Representation theory
Dr Daniel Murfet
Lecturer
Mathematical logic, algebraic geometry, topological field theories
Prof Paul Norbury
Professor
Gauge theory, mathematical physics, algebraic geometry, moduli spaces
Prof Arun Ram
Professor
Combinatorics, Representation Theory, algebraic geometry, number theory,
algebraic topology and mathematical physics
Prof Kari Vilonen
Professor and ARC Laureate Fellow
Representation theory, algebraic geometry, algebraic analysis
Dr Chenyan Wu
Senior Lecturer
Representation theory, algebraic geometry, algebraic number theory
Postdocs
Dr Scott Mullane
ARC DECRA Fellow (2023 – present)
Algebraic geometry and the geometry of moduli spaces
Dr Dougal Davis
Research Fellow (2022 – present)
Algebraic geometry and representation theory
Dr Lance Gurney
Research Fellow (2021 – present)
Number theory, arithmetic geometry, cohomology
Dr June Park
Research Fellow (2022 – present)
Arithmetic theory of algebraic varieties and moduli spaces
Graduate Researchers
Oliver Li (Hall)
Fei Peng (Hall)
Affiliates
A/Prof Alex Ghitza
Associate Professor
computational number theory, Galois representations, Shimura varieties, Automorphic forms
Dr Yaping Yang
Senior Lecturer
Geometric representation theory, Quantum groups
Dr Gufang Zhao
Senior Lecturer
Algebra, Geometry & Topology
Previous Members
Dr Mehdi Tavakol
Research Fellow (2018-2021)
Moduli and Stacks Learning Seminar, 2023
Semester 2, 2023: Alper–Halpern-Leinster–Heinloth
Organizer: Fei Peng
Time: Wednesdays 2-3pm, Peter Hall 162
The topic of the seminar is to work through Existence of moduli spaces for algebraic stacks.
Semester 1, 2023: The Picard Stack
Organizer: Jack Hall and Fei Peng
Time: Tuesdays, 3:15-4:15pm, Peter Hall 162
The topic of this seminar is to prove that the Picard stack and functor are algebraic.
Arithmetic Geometry Seminar, 2021
If you would like to attend or be added to the mailing list please email lance.gurney@unimelb.edu.au.
Semester 2, 2021: oo-categories
Organiser: Lance Gurney
Time: Fridays 5-6pm.
The topic of the seminar is to work through the foundations of oo-categories.
Semester 1, 2021: Prismatic Cohomology
Organisers: Lance Gurney, Jack Hall, Christian Haesemeyer
Time: Fridays 3:15pm-5:00pm
The topic of the seminar is the recent prismatic cohomology of Bhatt-Scholze and its interpretation via stacks due to Drinfeld here and here. [At some point this paper by Kisin will probably pop-up].
The talks will hopefully have notes posted afterwards. A more detailed reference for some things will be found in the evolving notes on prisms (draft) which also covers the case of DVRs other than Zp.
21 May Jack Hall Lefschetz theorems via localization
I will discuss a new approach to Lefschetz style hyperplane theorems using localizations of triangulated categories. The approach is also applicable to the Fargues–Fontaine curve, an object of recent interest in arithmetic geometry.
14 May Lance Gurney Prismatization Notes
The aim is to define prismatization and (time permitting) prismatic cohomology.
7 May Lance Gurney Some computations Notes
I gave an explicit description of the divisor in Sigma and of fibre products over Sigma.
30 April Lance Gurney What is a prism? (continued) Notes
24 April Lance Gurney What is a prism? Notes
I will begin with some motivational remarks about prismatic cohomology. After this I’ll explain the definition of a prism and of Drinfeld’s stack $\Sigma$. Time permitting some associated analogies from the theory of curves over finite fields (and shtukas).
Previous Seminars
Please contact a member of our group if you are interested in an MSc project in Algebraic Geometry.
Relevant Coursework
Semester 1
MAST90136 Algebraic Number Theory (even years)
MAST90023 Algebraic Topology (even years)
Semester 2
MAST90068 Groups, Categories & Homological Algebra (even years)
MAST90097 Algebraic Geometry (even years)
MAST90056 Riemann Surfaces and Complex Analysis (odd years)
MAST90017 Representation theory (odd years)
Current MSc Students
Adam Monteleone (Hall-Davis)
Matthew Bowkett (Hall)
Previous MSc Students
Bowen Hafey (Hall, 2022)
Fei Peng (Hall, 2022)
FT210100405
Integral transforms and moduli theory (Hall)
DP210103397
Moduli, invariants, and algebraisation (Gepner, Haesemeyer, Hall, Neeman)
DP180103891
Frobenius Manifolds From A Geometrical And Categorical Viewpoint (Murfet, Norbury)
DP180101445
Real Groups, Hodge Theory, And The Langlands Program (Vilonen)
DP170102328
Algebraic Invariants Of Singularities (Haesemeyer)