Talks

Invited Talks at International Conferences and Workshops

  • DOCToR (Duality, Order, (Co)algebras, Topology, and Related topics). Online.
    Unit intervals of unital commutative distributive -monoids.
    July 2021.
    Abstract

    Given a commutative distributive -monoid (M; , , +, 0) and an invertible element u 0 in M, we equip the set of elements of M between 0 and u with the MV-flavored operations , , , , 0, 1. For the algebras arising in this manner, we provide an axiomatization that is both equational and finite, and we name these algebras MV-monoidal algebras.

    From a categorical perspective, we establish an adjunction that restricts to an equivalence between commutative distributive l-monoids with strong order-unit and MV-monoidal algebras. The equivalence can be further restricted to the celebrated equivalence between Abelian -groups with strong order-unit and MV-algebras.

    Slides.

  • Third Algebra Week. University of Siena, Italy. (Cancelled due to COVID-19 pandemic.)
    Equivalence à la Mundici for lattice-ordered monoids.
    June 2020.

Contributed Talks at Peer-Reviewed Conferences

  • XXVII Incontro di logica. Università della Campania "L. Vanvitelli", Caserta, Italy.
    Duality for metrically complete Abelian -groups.
    13 September 2022.
    Abstract, Slides.

  • TACL 2022. University of Coimbra, Portugal.
    An approach à la de Vries for compact Hausdorff spaces and closed relations.
    24 June 2022.
    Abstract, Slides.

  • Category Theory 20->21. Università di Genova, Italy.
    The opposite of the category of compact ordered spaces is monadic over the category of sets .
    September 2021.
    Abstract, Slides.

  • BLAST 2021. New Mexico State University, Las Cruces, USA, Online.
    The opposite of the category of compact ordered spaces as an infinitary variety.
    June 2021.
    Abstract, Slides.

  • AAA99. University of Siena, Italy.
    Priestley duality above dimension zero: algebraic axiomatisability of the dual of compact ordered spaces.
    February 2020.
    Abstract, Slides.

  • Topology, Algebra, and Categories in Logic 2019. University of Nice, France.
    Norm-complete Abelian -groups: equational axiomatization.
    June 2019.
    Abstract, Slides.

  • PhDs in Logic XI. University of Bern, Switzerland.
    Stone-Gelfand duality for groups.
    April 2019.
    Abstract, Slides.

  • BLAST 2018. University of Denver, USA.
    Operations that preserve integrability, and truncated Riesz spaces.
    August 2018.
    Abstract, Slides.

Talks at Local Seminars

  • Lectures on Logic and its Mathematical Aspects (LLAMA seminar). Institute for Logic, Language and Computation, University of Amsterdam, Online.
    A generalization of the De Vries duality to compact Hausdorff spaces with closed relations.
    May 2022.
    Abstract

    Stone’s representation theorem for Boolean algebras gives a bridge between algebra and topology in the form of a categorical duality. In his PhD thesis, de Vries generalized this duality to a duality between compact Hausdorff spaces and what are nowadays called de Vries algebras, which are structures that encode the set of regular open sets of a given compact Hausdorff space. One drawback of the category of de Vries algebras is that the composition of morphisms is not function composition. We propose to work with relations (rather than functions) as morphisms between de Vries algebras: this has the advantage that the composition of morphisms is usual relation composition. Moreover, this approach allows for an extension of de Vries duality to a duality for the category of compact Hausdorff spaces and closed relations between them.

    Slides.

  • Algebra seminar. New Mexico State University, NM, USA.
    Free extension for universal algebras.
    March 2022.
    Abstract

    Given an equational class of algebras (such as groups, Boolean algebras, etc.), and a fixed sublanguage of this class (such as monoid operations, lattice operations, etc.), we can show the equivalence of two properties. The first, which is called free extension property, is more semantic: it concerns extensions of certain partial functions to homomorphisms. Whereas the second, called expressibility of equations, is concerned with terms and identities, thus being more syntactic.

    Slides.

  • University of Caserta, Italy.
    Positive MV-algebras.
    Februrary 2022.
    Abstract

    The Boolean terms that are order-preserving in each argument (when thought of as functions from {0,1}n to {0,1}) are precisely those expressible in the signature {∨, ∧, 0, 1}. It is known that the subreducts of Boolean algebras with respect to the signature {∨, ∧, 0, 1} are precisely the bounded distributive lattices.

    We make a similar investigation replacing Boolean algebras by MV-algebras - the structures that provide the algebraic semantics of Łukasiewicz logic. The MV-terms that are order-preserving in each argument (when thought of as functions from [0,1]n to [0,1]) are precisely those expressible in the signature {⊕, ⊙, ∨, ∧, 0, 1}. In this talk we address the following question:

    Is there a nice axiomatization of the subreducts of MV-algebras with respect to the signature {⊕, ⊙, ∨, ∧, 0, 1}?

    We explain why an equational axiomatization is not possible, and we provide a finite quasi-equational one. To obtain this axiomatization we rely on a generalization of a theorem by Mundici connecting unital Abelian lattice-ordered groups and MV-algebras.


  • Nonclassical Logic Webinar. University of Denver, Online.
    Is the category of locally finite MV‑algebras equivalent to an equational class?
    May 2021.
    Abstract

    Locally finite MV-algebras form a subclass of MV-algebras which is closed under homomorphic images, subalgebras, and finite products, but not under arbitrary ones. However, the category of locally finite MV-algebras with homomorphisms has arbitrary products in the classical categorical sense. Driven by these considerations, D. Mundici posed the following question:

    Is the category of locally finite MV-algebras equivalent to an equational class? (D. Mundici. Advanced Lukasiewicz calculus. Trends in Logic Vol. 35. Springer 2011, p. 235, problem 3.)

    We answer this question.

    Our proofs rest upon the duality between locally finite MV-algebras and multisets established by R. Cignoli, E. J. Dubuc, and D. Mundici, and categorical characterizations of varieties established by J. Duskin, F. W. Lawvere, and others.

    Slides, Recording.

  • Nonclassical Logic Seminar. University of Denver, Online.
    Equivalence à la Mundici for lattice-ordered monoids.
    May 2020.
    Abstract, Slides.

  • University of Salerno, Italy.
    Equivalence à la Mundici for lattice-ordered monoids.
    January 2020.
    Abstract, Slides.

  • Groupe de travail `Dualité de Stone, langages formels et logique'. University of Nice, France.
    On concrete dual adjunctions.
    October 2019.

  • Applied Mathematical Logic Seminar. Institute of Computer Science of the Czech Academy of Sciences, Prague, Czech Republic.
    The dual of compact ordered spaces is a variety.
    February 2019.
    Abstract, Slides.

  • University of Salerno, Italy.
    Archimedean Cauchy-complete MV-algebras form a variety.
    December 2018.
    Abstract, Slides.

  • PhD^2 - PhD days. University of Milan, Italy.
    Operations that preserve integrability: characterization and related algebraic structures.
    July 2018.
    Slides (in Italian).

Posters

  • Congresso Unione Matematica Italiana 2019. University of Pavia, Italy.
    Dualità di Stone-Gelfand per i gruppi.
    September 2019.
    Poster (in Italian).