Hi there! My name is Antonio Alfieri.
My research focus on various aspects of geometry, topology, and dynamics.
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[Picture courtesy of Stefan Friedl. Oberwolfach, July 2024. ]
I work in low-dimensional topology and its related fields, more specifically:
3- and 4-manifold topology, knot theory
Heegaard Floer and Instanton Floer homology
singularity theory, lattice cohomology
symplectic topology and contact topology
foliations and (pseudo) Anosov flows
All my preprints are available on the arXiv.
In recent years my research mentors have been Prof. Gordana Matić and Prof. Olga Plamenevskaya.
What's new
What's new
I recently posted a preprint with Connor Novak in which we explore the limits of large language models (LLMs) in tackling a problem in symplectic topology. This work is part of the First Proof initiative.
Here are the slides of a talk I recently gave at MIT regarding my new work in collaboration with Chi Cheuk Tsang
My student Sarah Zampa just uploaded a paper about the unknotting number of strongly invertible knots. Go check it out!
Publication list.
Since my PhD I worked on a variety of different topics, using some very different techniques. Below you can find my papers grouped by thematic areas.
(Pseudo) Anosov flows.
Heegaard Floer theory and pseudo-Anosov flows II: Differential and Fried pants, with Chi Cheuk Tsang. 2025. Submitted.
Heegaard Floer theory and pseudo-Anosov flows I: Generators and categorification of the zeta function, with Chi Cheuk Tsang. 2025. Submitted.
Gluing Ansov flows via convex surface theory, with Federico Salmoiraghi.
Partial open book decompositions and Anosov flows, with Gordana Matić and Chi Cheuk Tsang. In preparation.
Contact topology.
Holomorphic curves in Stein domains and the tau-invariant, with Alberto Cavallo, 2023. Submitted.
Graph manifolds bounding Stein rational balls, and the twisting number of special knots, in collaboration with my PhD student Sarah Zampa.
Instanton Floer homology.
Involutions and the Chern-Simons filtration in instanton Floer homology, with Irving Dai, Abhishek Mallick, Masaki Taniguchi. To appear in Journal of Differential Geometry.
Instanton Floer homology of almost-rational plumbings, with John Baldwin, Irving Dai, and Steven Sivek, Geometry & Topology, 2021.
Heegaard Floer homology.
Is the geography of Heegaard Floer homology restricted or is the L-space conjecture false?, with Fraser Binns, 2024. Submitted.
Deformations of lattice cohomology and the upsilon invariant, 2020. Submitted.
Connected Floer homology of covering involutions, with Sungkyung Kang and András Stipsicz, Mathematische Annalen, 2019
A note regarding L-space surgeries on chainmail links. In preparation.
Knot theory.
Strongly invertible knots, invariant surfaces, and the Atiyah-Singer signature theorem, with Keegan Boyle, Michigan Math. Journal, 2021.
Upsilon invariants from cyclic branched covers, joint with Daniele Celoria and András Stipsicz, Studia Scientiarum Mathematicarum Hungarica, 2021.
An introduction to knot Floer homology and curved bordered algebras, with Jackson Van Dyke, Periodica Mathematica Hungarica, 2020.
On sums of torus knots concordant to alternating knots, with Paolo Aceto, Bulletin of the London Mathematical Society, 2018.
Upsilon type concordance invariants, Algebraic & Geometric Topology, 2018.
REU 2025: algorithmic and machine learning methods in algebraic geometry
REU 2025: algorithmic and machine learning methods in algebraic geometry
In the summer of 2025 I directed a Research Experience for Undergraduates. Our topic was algorithmic methods in algebraic geometry, and applications of machine learning in pure mathematics.
Here is the reading list we followed:
Chapters 1 through 5 from Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra
three classic papers arXiv:1406.1078, arXiv:1409.0473 and arXiv:1706.03762 about recursive neural networks, and transformers
and a paper about Gröbner basis and transformers
Here are some of my lecture notes:
gradient descent more details are in these notes
neural networks and RNNs
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