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Hi there! My name is Antonio Alfieri.

I'm currently limited term associate professor at University of Georgia at Athens.

My research focus on various aspects of geometry, topology, and dynamics.

[Picture courtesy of Stefan Friedl. Oberwolfach, July 2024. ]

My research mentor at UGA is Prof. Gordana Matić. Before moving to UGA I was research associate at Stony Brook, and I was advised by Prof. Olga Plamenevskaya.

If you want to contact me, please use my gmail address: MyfamilynameMyname90(at)gmail-com. Otherwise you can come find me at the Boyd Graduate center in room 321, my door is always open!

You can also find me on MathOverflow and MathStackexchange.

Teaching and student supervision.

In my collaboration with Alfréd Rényi Institute I have a PhD student. Her name is Sarah Zampa and she is working on symplectic fillings of graph manifolds.

If you attended one of my classes and you need a recomendation letter please send an inquiry on my gmail 1-2 months in advance.

Save the date!

Me and some other people are organizing Geometry and Topology in Low Dimensions: Lasting Trends and Emerging Directions a conference to celebrate the mathematics of Andras Stipsicz and Zoltan Szabo.
I'm also organizing the contact topology section of the 2026 AMS Spring Southeastern Sectional Meeting
And participating to the organization of the 2026 Georgia Topology Conference at UGA.

Research

Interests. 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. If you have questions about my work please don't hesitate to contact me on my gmail.

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, I don't know how much that makes sense: everything is connected!

(Pseudo) Anosov flows.

Heegaard Floer theory and pseudo-Anosov flows II: Differential and Fried pants, with Chi Cheuk Tsang. 2025.
Heegaard Floer theory and pseudo-Anosov flows I: Generators and categorification of the zeta function, with Chi Cheuk Tsang. 2025.
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, 2023. Submitted.
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.
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.

Expository.

Taut folaitions and pseudo-Anosov flows: constructions, obstructions, and some conjectures. Notes from my lecture series at UGA.
An introduction to knot Floer homology and curved bordered algebras, with Jackson Van Dyke, Periodica Mathematica Hungarica, 2020.

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