[collari]

Postdoc, Università di Pisa

**Email:** *carlo.collari AT dm.unipi.it*

I am interested in both low-dimensional topology and geometry - with a focus on knot theory, and combinatorial algebraic topology - with a focus on graph homologies. My research up to now has been mostly 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, quantum invariants for knots and links, and Legendrian and transverse knots. Recently, I started working also around graph homologies, simplicial complexes associated to graphs, and their applications.

**Home-page:** https://sites.google.com/view/carlocollari/home

**arxiv id:** 0000-0003-0034-0702

**orcid id:** 0000-0003-0034-0702

- L. Caputi - C. Collari - S. Di Trani (preprint)

Multipath matroids, digraph colourings, and the Tutte polynomial (2024) - L. Caputi - D. Celoria - C. Collari (preprint)

Bridging between überhomology and double homology (2024) - L. Caputi - C. Collari - E. Ramos (preprint)

The weak categorical quiver minor theorem and its applications: matchings, multipaths, and magnitude cohomology (2024) - C. Collari - P. Lisca (preprint)

Strongly Invertible Legendrian Links (2023) - L. Caputi - C. Collari (
*Bulletin of the London Mathematical Society*)

On finite generation in magnitude (co)homology, and its torsion (2023) - L. Caputi - D. Celoria - C. Collari (
*Proceedings of the Royal Society of Edinburgh. Section A: Mathematics*)

From the Mayer-Vietoris spectral sequence to überhomology (2023) - L. Caputi - C. Collari - S. Di Trani - J. P. Smith (
*Mathematika*)

On the homotopy type of multipath complexes (2022) - L. Caputi - D. Celoria - C. Collari (
*Homology, Homotopy and Applications*)

Monotone cohomologies and oriented matchings (2022) - L. Caputi - D. Celoria - C. Collari (
*Journal of Pure and Applied Algebra*)

Categorifying connected domination via graph überhomology (2022) - C. Collari (
*Canadian Mathematical Bulletin*)

A note on weight systems which are quantum states (2022) - L. Caputi - C. Collari - S. Di Trani (Accepted Paper:
*Algebraic & Geometric Topology*)

Multipath cohomology of directed graphs (2021) - A. Cavallo - C. Collari - A. Conway (
*Proceedings of the AMS*)

A note on the weak splitting number (2021) - L. Caputi - C. Collari - S. Di Trani (
*Journal of Algebraic Combinatorics*)

Combinatorial and Topological Aspects of Path Posets, and Multipath Cohomology (2021) - C. Collari (
*Bulletin of the London Mathematical Society*)

Slice-torus link invariants, combinatorial invariants, and positivity conditions (2020) - C. Collari (
*Journal of Knot Theory and its Ramifications*)

On transverse invariants from Khovanov-type homologies (2019) - C. Collari (
*Michigan Mathematical Journal*)

A Bennequin-type inequality and combinatorial bounds (2019) - C. Collari - P. Lisca (
*Osaka Journal of Mathematics*)

On symmetric equivalence of symmetric union diagrams (2019) - C. Collari - P. Lisca (
*Canadian Mathematical Bulletin*)

Symmetric union diagrams and refined spin models (2018) - A. Cavallo - C. Collari (
*Canadian Journal of Mathematics*)

Slice-torus concordance invariants and Whitehead doubles of links (2018) - C. Collari (
*Algebraic & Geometric Topology*)

Transverse link invariants from the deformations of Khovanov $\mathfrak{sl}_{3}$-homology (2018)

*18 jan 2022:*Multipath homology and the path poset.*12 dec 2019:*Splitting numbers*10 jul 2019:*Spin models and Symmetric knots*11 dec 2018:*Transverse invariants from sl_3 homologies*4 oct 2018:*Transverse invariants from the deformations of Khovanov sl_3 homology*9 may 2018:*Slice-torus link invariants and Whitehead doubles*22 feb 2018:*On concordance and related problems*8 mar 2017:*On a Bennequin-type inequality*24 may 2016:*Invarianti trasversi e di concordanza in omologie di nodi*11 mar 2015:*Topological Quantum Field Theories

*1 oct 2024 - 4 oct 2024:*Combinatorial Algebraic Topology and Applications II*27 nov 2023 - 28 nov 2023:*Combinatorial Algebraic Topology and Applications