I am interested in low-dimensional topology and geometry, with a focus on knot theory. My research up to now has been centered around knot homologies, quantum invariants, and their applications. I am currently working (also in collaboration) on various projects concerning Khovanov-Rozansky sl(N)-homologies and their deformations, the study of knot and link concordance from different perspectives,  combinatorial invariants of links, and virtual knots. Here is a small list of some topics I am interested in. 

1. Properties of Khovanov-Rozansky homologies and their deformations;

2. Combinatorial and homological invariants of graphs;

3. Finite-type invariants;

4. Combinatorial invariants of links;

5. Concordance of knots and links, obstructions to sliceness, slice genus computations and slice-torus invariants;

6. Computability and categorification of quantum invariants for links and 3-manifolds;

7. Invariants for surfaces in four dimensional spaces;

8. Invariants for graphs in three dimensional spaces;

9. Invariants for transverse knots and links arising from link homologies, their properties, and their applications to the study of braids;

10. Link homologies for virtual knots, and applications to the study of virtual concordance;

11. Properties of links with special symmetries;

12. Spacification of link homologies and their properties.

Conference Talks

Oct. 2023 - Weight systems and quantum states, LIT Workshop, Pisa, Italy

Mar. 2023 - Weight systems which are quantum states, Geometric/Topological Quantum Field Theories and Cobordisms, Abu Dhabi, UAE

Feb. 2023 -  Some obstructions to positivity conditions for knots and links, Winter Braids XII, Tours, France

Mar. 2019 - Symmetric union knots and how to distinguish them, Chekanov-Eliashberg algebra and knot invariants, Budapest, Hungary

Jan. 2018 - On combinatorial bounds for Rasmussen’s s-invariant, Khovanov Homotopy Type, Budapest, Hungary

Feb. 2017 - Contact Invariants from Khovanov-type homologies, PRIN Workshop, Pisa, Italy

Jun. 2015 - Invariants for transverse knots from Khovanov-type homologies, ECSTATIC, London, U.K.

Seminar Talks

May 2024 - Legendrian knots and strong inversions, Séminaire de Géométrie et Topologie de Marseille, Université de Aix-Marseille, Marseille, FR

Feb. 2024 - Groebner methods and magnitude (co)homology, Seminario di Geometria, Dipartimento di Matematica, La Sapienza Università di Roma, Roma, Italy

Feb. 2024 - Groebner methods and magnitude (co)homology, AATRN Seminar, Online

Dec. 2023 - Strongly Invertible Legendrian Links, Seminario di Geometria, Dipartimento di Matematica, Pisa, Italy

Nov. 2023 - Multipath: Homology and Homotopy, Topology Seminar, Aberdeen University, Aberdeen, UK 

Nov. 2022 - Multipath Cohomology and Path Poset ,OS Complexity Theory, Model Theory, Set Theory,Universitat Konstanz, Konstanz, Germany 

Apr. 2022 -  Some Obstructions to Positivity Conditions for Knots and Links, Baby-Geometri, Pisa, Italy

Jan. 2022 - Multipath Cohomology and Path Poset (in Italian), Seminario PRIN2017, Pisa, Italy (Online)

Oct. 2021 - Multipath Cohomology of Directed Graphs, Geometry, Topology, and Physics Seminar, NYUAD, Abu Dhabi, UAE

May 2021 - On Slice-Torus Invariants and Positivity Conditions, Algebraic Geometry and Differential Topology Seminar, Alfréd Rényi Institute, Budapest, HU (Online)

Dec. 2019 - Splitting numbers, Seminario di Geometria, Pisa, Italy

Jul. 2019 - Spin models and Symmetric knots, Seminari di Geometria, Firenze, Italy

May 2019 - Slice-torus link invariants and applications, Oberseminar Geometrie und Globale Analysis, Regensburg, Germany

May 2019 - An introduction to the sl(3)-link homology, LKS Seminars, Regensburg, Germany

Jan. 2019 - Bracket polynomial: applications and generalisations, GATEAWAY Seminar, Warwick, U.K.

Dec. 2018 - Transverse invariants from the deformations of Khovanov sl(3)-homology , Seminari di Geometria e Analisi Complessa, Florence, Italy

Nov. 2018 - On slice-torus invariants and applications, G & T Seminar, Glasgow, U.K.

Oct. 2018 - Transverse invariants from the deformations of Khovanov sl(3)-homology, Seminario di Geometria, Pisa, Italy

Oct. 2018 -  Slice-torus link invariants, G & T Seminar, Durham, U.K.

May 2018 -  Sice-torus link invariants and Whitehead doubles, Seminario di Geometria,  Pisa, Italy

Mar. 2018 - Two lectures on Khovanov’s sl(3)-homology via foams and its deformations, Alfréd Rényi Institute, Budapest, Hungary

Feb. 2018 -  On concordance and related problems, Baby-Geometri, Pisa, Italy

Feb. 2017 -  On a Bennequin-type inequality from Bar-Natan homology, LKS Seminars, Regensburg, Germany

Mar. 2016 - Combinatorial invariants of knots, Seminari di Geometria,  Cagliari, Italy

Mar. 2015 -  Topological Quantum Field Theories ,Baby-Geometri, Pisa, Italy

Mar. 2014 -  Quandles and minimal colourings of knots ,Baby-Geometri, Pisa, Italy

Nov. 2012 -  Handle decomposition of Lefschetz fibrations, Baby-Geometri, Pisa, Italy

Posters

Feb. 2020 - Transverse invariants in link homologies, WinterBraids X, Pisa, Italy

Sep. 2022 - Multipath cohomology of directed graphs, Topology of Data in Rome, Rome, Italy