[collari]

Carlo 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

Available papers (20):

• 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)

Seminars:

• 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

Organizer:

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