Keynote Speakers

Anna Gori

University of Milan

Italy

Cinzia Bisi

Università degli Studi di Ferrara

Italy

Cristina Flaut

Ovidius University of Constanta

Romania

Giulia Sarfatti

Polytechnic University of Marche

Italy

Jasna Prezelj

University of Ljubljana

Slovenia

Nelson Vieira

Universidade de Aveiro

Portugal

Abstracts

Anna Gori

University of Milan

Italy

Title of the talk: On the Irreducibility of Slice Algebraic Sets

Abstract: A quaternionic version of the classical Hilbert Nullstellensatz has recently been established in its strong form within the framework of slice regular polynomials. This result naturally led to the introduction of the notion of a quaternionic slice algebraic set, endowing (\mathbb{H}^n) with a Zariski-type topology. In this seminar, after a brief overview of the subject, we will discuss a characterization of the irreducibility of slice algebraic sets in terms of algebraic properties of the associated ideals of slice regular polynomials. The results presented are based on joint works with Giulia Sarfatti and Fabio Vlacci.

Short Bio, including current research interests

Anna Gori is an Associate Professor of Geometry and Algebra at the University of Milan. Her early research background is in differential and symplectic geometry, with contributions to Kähler and quaternionic geometry, Hamiltonian group actions, Lagrangian submanifolds. In recent years, her research has progressively shifted toward quaternionic analysis and noncommutative algebraic geometry, with particular emphasis on slice regular functions, generalized quaternionic manifolds, and Hilbert Nullstellensatz-type theorems in the quaternionic setting. Her current work focuses on the structure and irreducibility of slice algebraic sets and on developing geometric foundations for quaternionic algebraic geometry.

Cinzia Bisi

Università degli Studi di Ferrara

Italy

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.

Cristina Flaut

Ovidius University of Constanta

Romania

Title of the talk: Remarks regarding algebras obtained by the Cayley-Dickson process

Abstract: In October 1843, William Rowan Hamilton discovered the quaternions, H, a 4-dimensional algebra over R, which is an associative and noncommutative algebra. In December 1843, John Graves discovered the octonions, O, an 8-dimensional algebra over R which is a nonassociative and noncommutative algebra. This algebra was rediscovered by Arthur Cayley in 1845, octonions being also known Cayley numbers. This process, of passing from R to C, from C to H and from H to O has been generalized to algebras over fields and over rings. It is called the Cayley-Dickson doubling process or the Cayley–Dickson process. Even if are old, quaternions and octonions have at present many applications, as for example in physics, coding theory, computer vision, etc. In this talk, we review some aspects regarding properties and some applications of these algebras.

Short Bio, including current research interests

I got my PhD in 2002 with a thesis on nonassociative algebras. Since 1991, I have been working at Ovidius University of Constanta, Romania. Since 2016, I have advised two PhD students. In the present I am professor in the Department of Mathematics and Computer Science, Faculty of Mathematics and Computer Science at the Ovidius University of Constanţa, România. I am the author and the co-author of more than 60 monographs, chapters of books, and papers in important journals (as for example books in Taylor & Francis and Springer or papers in the journals: Ann. Mat. Pura Appl., Adv. Appl. Clifford Algebras, Bull. Korean Math. Soc., Results Math., Chaos, Solitons & Fractals, Soft Computing, Algebr. Represent. Theor., J. Differ. Equ. Appl., etc.).

I am Editor-in-Chief of the journal Analele Ştiinţifice ale Universităţii Ovidius Constanţa-Seria Matematica, an ISI journal. In 2016, I was considered the best researcher of the Ovidius University of Constanţa.

Areas of interest: algebra (nonassociative algebras, logical algebras), coding theory and cryptography.

Giulia Sarfatti

Polytechnic University of Marche

Italy

Title of the talk: Quaternionic Carleson measures

Abstract: Carleson measures are a central object in complex analysis, introduced by Carleson to solve the well-known Corona Problem. They have applications in several areas of complex analysis and operator theory. For instance, they can be used to characterize the continuity of Toeplitz, Hankel, and composition operators, and they appear in the study of interpolation problems. Moreover, using the special class of vanishing Carleson measures, one can determine when the previously mentioned operators are compact.

Slice regularity is a notion of holomorphicity in the quaternionic setting, introduced in 2006 by Gentili and Struppa, which gave rise to a rich theory, still in rapid development. Function spaces in this setting have been extensively studied from various perspectives by several authors in the recent years.

In this talk I will discuss a general construction of a quaternionic Banach space of slice regular functions from a given Banach space of holomorphic functions, called its quaternionic lift, which encompasses many relevant examples of quaternionic Banach spaces of slice regular functions in the literature.

I will then give a characterization of Carleson and vanishing Carleson measures for such quaternionic Banach spaces in terms of the corresponding Carleson measures of the underlying holomorphic function space. This offers a unified approach to a problem that so far has been treated on a case-by-case basis.

This talk is based on a joint work with Nikolaos Chalmoukis.

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.

Jasna Prezelj

University of Ljubljana

Slovenia

Title of the talk: Quaternionic Cartan covers

Abstract: We present the topological foundations for the solvability of multiplicative Cousin problems formulated on an axially symmetric domain $\Omega \subset \H.$ In particular, we provide a geometric construction of quaternionic Cartan coverings, which are generalizations of (complex) Cartan coverings. Because of the requirements of symmetry inherent to the domains of definition of quaternionic regular functions, the existence of quaternionic Cartan coverings of $\Omega$ is not a consequence of the existence of complex Cartan coverings; for the latter, there are no requirements for the symmetries with respect to the real axis. Due to the real axis's special role, the covering restricted to $\Omega \cap \R$ must have additional properties. All these required properties were achieved by starting from a particular symmetric tiling of the symmetric set $\Omega \cap (\R + i\R)$. Finally, we apply these results to prove the vanishing of 'antisymmetric' cohomology groups of planar symmetric domains for $n \geq 2$.

Short Bio, including current research interests

Jasna Prezelj is an associate professor at the Faculty of Mathematics and Physics at the University of Ljubljana, where she obtained a PhD in 2000, at the Faculty of Mathematics, Natural Sciences and Information Technologies of the University of Primorska, Koper, and a researcher at the Institute of Mathematics, Physics and Mechanics in Ljubljana. She is also the president of the Committee of Mathematics at The Society of Mathematicians, Physicists, and Astronomers of Slovenia (DMFA Slovenije) and a former coordinator of EWM for Slovenia. Her research interests vary from Oka theory to function theory in quaternionic and octonionic settings and in the combination of complex analytic methods with the theory of slice-regular functions.

Nelson Loureiro

Universidade de Aveiro

Portugal

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.

Page updated

Google Sites

Report abuse