Singular cohomology of a space carries a natural CDGA structure induced by cup product at the level of cochains. While cup product is a well-defined operation on singular cochains, commutativity only holds after passing to cohomology, due to the presence of non-trivial Steenrod operations. This fact will be the motivating example for introducing E_∞-algebras and to explain how the E_∞-structure on cochains encodes this phenomenon in a precise way. Since the theory of E_∞-algebras needs the notion of operad, general recollections on the basics of operad theory will be provided.
  N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)

  Shifted quantum affine algebras are quantum groups parameterized by a coweight of the underlying Lie algebra. In 2022, Hernandez introduced a category O of representations of these algebras, and in 2024, Geiss–Hernandez–Leclerc proved that the Grothendieck ring of this category O admits a cluster algebra structure. In this talk, after introducing the necessary background, I will explain how to construct a quantization of this cluster algebra, leading to a definition of the quantum Grothendieck ring for category O.
  If time permits, I will also discuss some applications and directions for future research.
  N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)

In this talk, we will demonstrate how the celebrated connection between Ricci curvature, optimal transport, and geometric inequalities such as the Brunn-Minkowski inequality, extends to the setting of general Lagrangians on weighted manifolds. As applications, we will state a generalization of the horocyclic Brunn-Minkowski inequality to complex hyperbolic space of arbitrary dimension, and a new Brunn-Minkowski inequality for contact magnetic geodesics on odd-dimensional spheres. The main technical tool is a generalization of Klartag's needle decomposition technique to the Lagrangian setting.

Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023–2027).

Recent interest in vertex operator algebra theory has focused on examples whose representation theory describes conformal field theories with logarithmic divergences in their correlation functions (logCFTs). These VOAs admit non-semisimple representations that play a key role in the CFT, and additionally often feature infinitely many simple representations. A large class of examples of such VOAs are W-algebras associated to affine VOAs at fractional admissible level. However, representations for these VOAs are notoriously difficult to construct in a general way. One approach to solving this problem is known as inverse quantum hamiltonian reduction (IQHR). The aim of this talk will be to introduce the ideas behind IQHR in some accessible examples, and then discuss generalisations.

TBA

An important problem in enumerative geometry is counting rational curves that interpolate a configuration of points on an algebraic surface. Over the complex numbers, the answer does not depend on the configuration of points and is called the Gromov-Witten invariant. In contrast, over the real numbers, this invariance fails. To recover it, Welschinger invented an “sign” rule that gives rise to Welschinger invariants. Recently, Kass, Levine, Solomon, and Wickelgren constructed an invariant over an (almost) arbitrary field. The small “inconvenience” is that these latter invariants are no longer numbers, but quadratic forms. In a current work with Erwan Brugallé and Kirsten Wickelgren, we establish direct relationships between these different types of invariants. In my talk, I want to give an introduction to this topic.
Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027) and the PRIN 2022 Moduli Spaces and Birational Geometry and Prin PNRR 2022 Mathematical Primitives for Post Quantum Digital Signatures

In Classical Probability, a sequence of random variables is said to be exchangeable if its joint distributions are invariant under all finite permutations. Ryll-Nardzeski’s Theorem establishes that exchangeability is the same as spreadability, the a priori weaker symmetry where all subsequences of the given sequence have the same joint distributions. In the non-commutative setting, it is known that the two symmetries no longer coincide for general quantum stochastic processes. We show that under very natural hypothesis there is an extension of the Ryll-Nardzewski Theorem in the noncommutative setting which covers a wide variety of models. Furthermore we obtain an extended De Finetti’s Theorem for various models including processes based on the CAR algebra and on the infinite noncommutative torus. This talk is based on joint work in progress with Valeriano Aiello and Stefano Rossi.

We consider a scalar Euclidean QFT with interaction given by a bounded, measurable function V such that V± := lim w → ±∞ V(w) exist. We find a field renormalization such that all the n-point connected Schwinger functions for n ≠ 2 exist non-perturbatively in the UV limit. They coincide with the tree-level one-particle irreducible Schwinger functions of the erf(ϕ/ √ 2) interaction with a coupling constant (V+ - V-)/2. By a slight modification of our construction we can change this coupling constant to (V+ - V-)/2., where V± := lim w → 0± V(w). Thereby, non-Gaussianity of these latter theories is governed by a discontinuity of V at zero.

Boundary integral methods represent a powerful class of numerical techniques for the solution of partial differential equations, particularly in problems involving infinite or semi-infinite domains, such as those arising in potential theory, acoustics, elasticity, and fluid dynamics. By reducing the dimensionality of the problem and focusing computations on the boundary, these methods can offer significant advantages in terms of accuracy, efficiency, and mesh simplicity. This talk will provide an overview of the numerical challenges that arise when using boundary integral methods, discuss recent advances in efficient algorithms, and present some applications in microfluidics. The talk will highlight both the theoretical elegance and the practical utility of boundary integral methods, and will provide insight into when and why these methods are especially effective.