TRINO

Speaker: Mark Pencovitch (University of Glasgow) 

Title: Simply Slicing Knots

When: 22nd April 2026 @ 11:00

Where: SISSA, room 132.

Abstract: A knot on the boundary of a 4-manifold X is _slice_ if it bounds a disc inside X. The study of such knots is a popular pass-time for people who want to know more about the underlying structures of 4-manifolds and their potential exotica. 

We will look into this problem topologically, focusing on a classification of which second homology classes of X can be represented by slice discs.

Speaker: Marithania Silvero Casanova (Univ. Sivilla) 

Title: Diagnosing positivity in links. Any Doctor in the room?

When: April 9 @15h45

Where: UniTS, aula seminario, third floor of  H2bis building.

Abstract: When studying knots (or, more generally, links), it is common to classify them into families according to certain properties. A common approach is to declare that a knot belongs to a given family if it admits a diagram satisfying a specific condition. This is the case for the various notions of positivity for links (positive links, braid-positive links, quasipositive links, etc.). The definitions of these families (that is, the requirements imposed on their diagrams) are motivated by the contexts in which they arise. Moreover, several invariants exhibit special properties when restricted to these families.

In this talk, we will explore the main notions of positivity for knots and links and discuss the relationships between them. We will also highlight some key properties that are reflected in several well-known link invariants. The talk will be mostly self-contained, and several examples will be shown to illustrate the definitions and results.

Speaker: Vanja Zuliani (Paris Orsay). 

Title: Toward the noncommutative minimal model program.

When: April 9 @14h30

Where: UniTS, aula seminario, third floor of  H2bis building.

Abstract: The aim of the talk is to introduce the noncommutative minimal model program (ncMMP) proposed by Halpern-Leistner and inspired by some works of Dubrovin and Kontsevich.

For a given projective variety X, the classical minimal model program asks if there is a variety Y that is birational to X but has simpler geometry, such Y is called a minimal model of X. In the noncommutative context, we consider the derived category D(X) of coherent sheaves on X, and we ask if we can decompose it canonically. The biggest factor of the decomposition is then a minimal model for D(X). In order to find such a decomposition Halpern-Leistner proposes to use the quantum cohomology of X.

We will discuss some examples where Halpern-Leistner’s proposal is satisfied: Grassmannians, quadrics, and cubics in dimensions 3 and 4.

Speaker: Giacomo Graziani (Univ. Padova). 

Title:  Algebraic Neurovarieties and Secant Varieties.

When: March 25 @14h30

Where: UniTS, aula seminario, third floor of  H2bis building.

Abstract: In recent years, the notion of algebraic neurovarieties has attracted growing interest in algebraic geometry, both because of its connections with machine learning and for its close relationship with tensor varieties and decomposition problems.

In this talk, we will show how such varieties arise naturally from the study of polynomial neural models and, in the case of a single layer, how they can be identified with classical varieties, such as Segre-Veronese secant varieties. This geometric description provides a natural framework to study global invariants of interest in applied settings using tools from projective geometry and intersection theory.