I am a third year PhD student at the University of Melbourne.
I am currently thinking about tensor-triangular geometry, and classifying t-structures and localising subcategories of triangulated categories (with motivating examples being derived categories of schemes, algebraic spaces, algebraic stacks, and categories of motives). Previously, for my Masters thesis, I was thinking about the period-index problem, and motivic homotopy theory.
Email: apclark at student.unimelb.edu.au
Student Talks
2022, December - AustMS: Classifying t-structures on tensor-triangulated categories
2022S1 - Topology Seminar: Tensor-triangular geometry and the classification of t-structures
2020S2 - MCS: Talk 1: The Category of Finite Correspondences, Talk 4: The Intersection Product Part 1, Talk 5: The Intersection Product Part 2 and preservation of rational equivalence by proper pushforward and flat pullback
2020S1 - MTT: Models for an Obstruction Theoretic Approach to the Period-Index Problem
2019S2 - GTS: Adams Operations and the Adams Conjecture
2019S1 - GTS: Homotopy Theory of DGAs
2019S1 - GTS: Minimal Models for Differential Graded Algebras
2018S2 - GSS: Abelian Objects and the Abelianisation Functor - (in the context of Alg_R/A and simplicial sAlg_R/A)
2018S1 - RTA: Categories of D-modules
2018S1 - QFT: The Crystal B(∞)
2018S1 - RTA: Lie algebroids, and Scheme Theory
2017S2 - QFT: Nilpotent orbits and Slodowy slice
2017S2 - MSS: A Fine Variety of Ideal Geometries - (Introducing affine varieties to second and third year students.)
2017S1 - QFT: Ribbon Hopf algebras
2016S2 - QFT: Free field and Boson-Fermion Correspondence
2016S2 - MSS: Roots and Fields - (Introducing field extension, subgroup lattice correspondence, to second and third year students.)
2016S1 - QFT: Verma Modules
QFT refers to the Quantum Field Theory seminar, and MSS refers to the Mathematics Student Society. The MSS talks are intended to be accessible to second and third year students. The QFT talks run weekly and are 90 minutes long, including a 10 minute break. RTA refers to the Rep Theory and Algebra Student Seminar.
GTS refers to the graduate topology seminar (Unimelb). GSS refers to the graduate student seminar (Unimelb)
MCS refers to the Motivic Cohomology Seminar that I'm running.
Reading groups and student seminars
2021:
Mirror Symmetry reading group
\infty-Category Seminar
2020:
Motivic Cohomology Seminar
Perfectoid Spaces Seminar
Reading group working through the proof of the Weil conjectures
2019:
Graduate Student Topology Seminar (Sem 1: Rational homotopy theory, Sem 2: Genetics of Homotopy Theory and the Adams Conjecture)
Representation Theory Seminar (Langlands)
Topological Cyclic Homology (reading: https://arxiv.org/abs/1803.10897 )
Topology Seminar
Number Theory Seminar
Homotopy Theory Student Group (Looking at Luries higher topos theory, etc)
2018:
Representation theory and Algebra, Students Seminar
D-modules, see the schedule.
With Marielle Ong, Aiden Suter, Adam Walsh and Sam Weatherhog
2017:
Representation theory and Algebra, Students Seminar - With Seamus Albion, Joseph Fyfield, Marielle Ong, Aiden Suter, and Sam Weatherhog
Algebraic Groups (Humphreys) - With Marielle Ong and Sam Weatherhog
2016:
Noncommutative Algebra (Farb and Dennis) - With Harrison Carsley
Tutoring
The University of Queensland
2018S1: MATH1061 - Discrete Mathematics
2018S1: MATH1051 - Calculus & Linear Algebra I
2017S3: MATH1052 - Calculus & Differential Equations
2017S2: MATH1061
2017S1: MATH1061
2016S3: MATH1052
2016S2: MATH1061
2016S1: MATH1051