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.
Properties of Khovanov-Rozansky homologies and their deformations;
Combinatorial and homological invariants of graphs;
Finite-type invariants;
Combinatorial invariants of links;
Concordance of knots and links, obstructions to sliceness, slice genus computations and slice-torus invariants;
Computability and categorification of quantum invariants for links and 3-manifolds;
Invariants for surfaces in four dimensional spaces;
Invariants for graphs in three dimensional spaces;
Invariants for transverse knots and links arising from link homologies, their properties, and their applications to the study of braids;
Link homologies for virtual knots, and applications to the study of virtual concordance;
Properties of links with special symmetries;
Spacification of link homologies and their properties.
with L. Caputi & S. Di Trani
with L. Caputi & S. Di Trani
Apr. 2025 - Gröbner methods and graph homologies, Manifolds and Groups in Bologna III, Bologna, Italy
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.
Feb 2025 - Uberhomology, combinatorics and the Mayer-Vietoris spectral sequence, AATRN, online
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
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
Links in Dimensions 3 and 4, ICERM - Brown University, Providence, US (12.05.2024 - 16.05.2025)
Manifolds and groups in Bologna III, Università di Bologna, Bologna, Italy (14.04.2025 - 16.04.2025)
WinterBraids XIV, Bordeaux, France (03.02.20255 - 06.02.2025)
Combinatorial and Gauge theoretical methods in low dimensional topology and geometry, Centro De Giorgi, Pisa, IT (03.06.2024 - 07.06.2024)
Manifolds and groups in Bologna II, Università di Bologna, Bologna, Italy (17.04.2024 - 19.04.2024)
WinterBraids XIII, Institut Montpelliérain Alexander Grothendieck, Montpellier, France (06.02.2024 - 09.02.2024)
Leaning into Topology (LIT) Workshop, Università di Pisa, Pisa, Italy (18.09.2023 - 19.09.2023)
Swiss Knots 2023, Universität Regensburg, Regensburg, Germany (06.09.2023 - 08.09.2023)
The Low-Dimensional Workshop, Alfréd Rényi Institute, Budapest, Hungary (27.03.2023 - 31.03.2023)
Non-positive curvature in manifolds and groups, Università di Bologna, Bologna, Italy (24.03.2023)
Manifolds and groups in Bologna, Università di Bologna, Bologna, Italy (22.03.2023 - 23.03.2023)
Geometric/Topological Quantum Field Theories and Cobordisms, NYUAD, Abu Dhabi, UAE (15.03.2023 - 18.03.2023)
WinterBraids XII, Université de Tours , Tours, France (21.02.2023 - 24.02.2023)
Topology of Data in Rome, Università di Roma "Tor Vergata", Roma, Italy (15.09.2022-16.09.2022)
Perspectives on quantum link homology theories, Universität Regensburg, Regensburg, Germany (Online - 09.08.2021 - 15.08.2021)
WinterBraids X, Centro di Ricerca Ennio de Giorgi, Pisa, Italy (17.02.2020 - 21.02.2020)
M-theory and Mathematics, NYUAD, Abu Dhabi, UAE (27.01.2020 - 30.01.2020)
SwissKnots 2019, ETH Zurich, Zurich, Swizzerland (16.06.2019-19.06.2019)
Workshop on Chekanov-Eliashberg algebra and knot invariants, Alfréd Rényi Institute, Budapest, Hungary (08.03.2019 - 10.03.2019)
WinterBraids IX, Université de Reims Champagne-Ardenne, Reims, France (04.03.2019 - 07.03.2019)
Gauge theory and applications, Universität Regensburg, Regensburg, Germany (17.07.2018 - 27.07.2018)
Khovanov Homotopy Type, Alfréd Rényi Institute Budapest, Hungary (18.01.2018 - 21.01.2018)
Categorification, representation theory and symplectic geometry, Hausdorff Institute for Mathematics, Bonn, Germany (19.11.2017-25.11.2017)
Thematic School on Quantum Topology and Geometry, CIMI, Toulouse, France (08.05.2017 - 13.05.2017)
SMI course "Kähler-Einstein metrics", Palazzone, Cortona, Italy (30.04.2017 - 06.05.2017)
PRIN Workshop on Geometry, Topology and Harmonic Analysis, Scuola Normale Superiore, Pisa, Italy (20.02.2017 - 22.02.2017)
Floer theories and low dimensional topology, Universität Regensburg, Regensburg, Germany (19.07.2016 - 22.07.2016)
CEU Summer school in low-dimensional Topology, Alfréd Rényi Institute, Budapest, Hungary (04.07.2016 - 08.07.2016)
ECSTATIC II, Imperial College, London, United Kingdom (13.06.2016 - 14.06.2016)
WinterBraids VI, Université de Lille, Lille, France (22.02.2016 - 25.02.2016)
ECSTATIC, Imperial College, London, United Kingdom (10.06.2015 - 11.06.2015)
Perspectives in Lie Theory, Centro di Ricerca Ennio de Giorgi, Pisa, Italy (09.12.2014 - 28.02.2015)
WinterBraids V, Université de Pau et Pays de l'Adour, Pau, France (16.02.2015 - 20.02.2015)
The 10th William Rowan Hamilton Geometry and Topology Workshop, Trinity College, Dublin, Ireland (24.08.2014 - 31.08.2014)
Intensive Period on Teichmüller Theory and Surfaces in 3-Manifolds, Università di Pisa, Pisa, Italy (26.05.2014 - 20.06.2014)
Master Class Around Thurston-Groethendieck-Teichmüller Theories, Université de Strasbourg, Strasbourg, France (08.05.2014 -18.05.2014)
Journées d'Algébre: Categorification et invariants de Noeuds, Université de Caen, Caen, France (27.03.2014 - 28.03.2014)
Secondo Workshop su Varietà Reali e Complesse, Scuola Normale Superiore, Pisa, Italy (20.02.2014 - 22.02.2014)