Keynote Speakers

Title of the talk: Slice regular functions on alternative *-algebras: prescribing zeroes and values on discrete sets and related extension problems

Abstract: Slice regular functions are a generalization of holomorphic functions where alternative real∗-algebras are considered instead of the field of complex numbers. For such functions we show that zero sets and function values on suitable subsets may be prescribed. As a consequence, we show that for any axially symmetric domain there exist slice regular functions which (due to the nature of its zero set) can not be extended to a larger such domain.

Short Bio, including current research interests

I'm currently Full Professor at the University of Ferrara. 

I obtained my Ph.D. degree at Florence University. Then I was Post-Doc in Paris .

My first permanent position as a researcher  was at the University of Calabria, before moving to Ferrara University where I became firstly associate and then full professor.

I'm currently Director of the "Consorzio Interuniversitario di Alta Formazione Matematica" which organizes each year  together with "Scuola Matematica Universitaria" high level international summer courses in all subjects of Mathematics in Perugia and Cortona.

My research interests are : Clifford and octonionic analysis and geometry, hypercomplex analysis and geometry with applications.

Title of the talk: TBA

Abstract: TBA

Short Bio, including current research interests

Giulia Sarfatti is an Associate Professor at the Department of Industrial Engineering and Mathematical Sciences of the Università Politecnica delle Marche. She received her PhD in Mathematics from the University of Florence, with a thesis on function theory in the unit ball of quaternions and has held research positions at the University of Bologna, the University of Florence, and the Institut de Mathématiques de Jussieu in Paris. She has been awarded fellowships including a Marie Curie INdAM Cofund Fellowship and a UMI grant for a visiting period at MIT. Her research focuses on complex and hypercomplex analysis and geometry, with particular interest in quaternionic function theory, and slice regular functions. Her recent works concern slice regular quaternionic polynomials, Nullstellensatz-type theorems, slice regular algebraic sets, and Carleson measures.

Title of the talk:  Quaternionic Convolutional Neural Networks with Trainable Bessel-Type Activation Functions 

Abstract:  This talk addresses quaternionic convolutional neural networks (QCNNs) equipped with trainable Bessel-type activation functions, constructed as particular instances of a broader multi-parametric hypergeometric activation framework. The starting point is a general class of activation functions defined via generalised hypergeometric series, from which many standard real-valued activations arise by suitable specialisation of parameters. A specific choice of these parameters yields one-parameter Bessel-type activations based on the Bessel function of the first kind $J_\nu$ with half-integer order $\nu$, which can be represented in closed form using combinations of polynomials and elementary trigonometric functions. These activations are embedded into quaternionic convolutional layers, leveraging the ability of QCNNs to encode both local spatial structure and inter-channel dependencies, as well as to represent three-dimensional rotations in a compact quaternionic form. The presentation outlines the mathematical construction of the activation functions, the resulting QCNN architecture, and numerical experiments on a colour image classification task (Colored FashionMNIST). The results indicate that QCNNs with Bessel-type trainable activations can achieve higher accuracy and faster convergence than analogous architectures using the ReLU activation, suggesting the potential of trainable special-function-based activations in quaternionic deep learning. 

Short Bio, including current research interests

Nelson Felipe Loureiro Vieira is an Assistant Professor in the Department of Mathematics at the University of Aveiro and a researcher at CIDMA – Center for Research and Development in Mathematics and Applications. He received his PhD in Mathematics from the University of Aveiro in 2009. His research centers on Clifford and hypercomplex analysis, fractional calculus, special functions, and their applications to differential equations, signal processing, and machine learning. He has published extensively in these fields and holds competitive FCT research positions (CEECIND 2018, Investigador FCT 2014). He participates in funded projects and serves on editorial boards while reviewing for international journals.