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Roma, Italia.

Research

I am currently a PhD student at The University of Adelaide under the supervision of Finnur Larruson and David Baraglia. My research is on holomorphic flexibility properties of character varieties and their related moduli spaces.

I completed my MPhil at The University of Queensland (Brisbane, Australia), under the supervision of Masoud Kamgarpour and Ole Warnaar. My thesis was about the arithmetic geometry of additive character varieties.

My honours degree at UQ was under the supervision of Masoud Kamgarpour and Sam Jeralds. In my honours thesis, I describe the ring of invariants for a class of non-reductive groups.

Seminars

I am organising a reading group on Gathmann's notes in Algebraic Geometry. See the website for more details.
University of Melbourne graduate course (run by Dougal Davis) on Hodge theory and its applications to algebraic geometry.
UQ Rep theory reading group: The Geometry of Schemes (Eisenbud & Harris). Here are my notes.
Weekly seminar reading group: on the Arithmetic and representation theory of wild character varieties.
WiSe Seminar attendee.
UQ Rep Theory Seminar: Quiver Varieties.
UQ Rep Theory Seminar: Hyperplane Arrangements.
Sydney Mathematical Research Institute: D-modules Course.
UQ Rep Theory Seminar (Konstantin Jacob): Mini Course on The Springer Correspondence.

Papers/preprints

Counting points on character varieties (joint with Masoud Kamgarpour, Gyeonghyeon Nam, and Bailey Whitbread).

Past Academic Events/Work

8th Australian Algebra Conference attendee
Ramifications in geometric Langlands and non-abelian Hodge theory (Heidelberg University, Germany)
Number Theory Down Under at UQ
Attendee of the AMSI winter school in Representation Theory 2022
ANU research workshop (14th-18th Feb, 2022) attendee: Character varieties, E-polynomials and Representation zeta functions.
UQ Maths workshop on Character Variety (18th -24th Dec, 2021)
Summer Research Project supervised by Peter van Heijster on the Generalised FitzHugh-Nagumo Model
Research Project in Nonlinear Brain Dynamics under James Roberts
Summer Research Project supervised by Qian Qian Yang on Fractional Dynamic Models for MRI

Awards

B.H. Neumann Prize at the 2024 joint meeting of NZMS, AustMS and AMS for my talk on Counting points on character varieties (honourable mention)

Awards night, AustMS 2024.

Tutoring Work

I have tutored the following courses at Adelaide University:

MATHS 1012 - Calculus and Linear algebra

I have tutored the following courses at UQ:

MATH3303 (Abstract Algebra & Number Theory)
MATH2301 (Linear & Abstract Algebra & Number theory)
MATH2401 (Mathematical Analysis and Advanced Topics)
MATH2010 (Analysis of ODEs)
MATH1061 (Discrete Mathematics)
MATH1052 (Multivariate Calculus and ODEs)
MATH1051 (Calculus & Linear Algebra I)
MATH1050 (Mathematical Foundations II)
MATH1040 (Mathematical Foundations I)

I have also been working with the Indigenous Tutorial Assistance and Retention program (ITAR).

Talks

I gave a talk at the Adelaide University Differential Geometry Seminar on The geometry of character varieties.
I gave a talk at the NZMS, AustMS and AMS meeting on Counting points on character varieties
Arithmetic Geometry of Additive Character Varieties - Australian Algebra Conference
Riemann-Hilbert correspondence via examples - UQ Rep Theory group.
The Geometry of Additive Character Varieties - Australian Mathematical Society (AustMS) Conference 2023.
What is Hilbert's 14th Problem? - Australian Postgrad Algebra Colloquium (APAC).
Invariant ring of Unipotent Groups (2022)- UQ Maths Honours talks.
De Rham Cohomology - Riemannian Geometry Reading Group (2022).
Quiver Representations (2021).

Other Activities/Hobbies

I played in the Men's Football National Premier League in Queensland (2021).
I play blitz chess on Chess.com and obtained a rating of 2227. See my profile.
Member at Movement Health Club.

Notes

Here are my solutions to some exercises in The Geometry of Schemes (Eisenbud & Harris).

Email: stefano.giannini556@gmail.com

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