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Scientific International Events

Summer Schools and Masterclasses

TiME 2025 : “Invariant Theory: from classics to modern developments"

co-organised with Kathlén Kohn, Pierpaola Santarsiero, Ettore Turatti
26-30 May 2025 @ Lie-Strømer Center, Tromsø, Norway

The school will provide a multifaceted viewpoint on the theory of invariants, tracing its origin to the pioneering works of Cayley and Sylvester, connecting the theory of XIX century and its development through computational algebra, modern algebraic geometry, and applications to other applied sciences. The four mini-courses will be given by: Harm Derkse, Kristin deVleming, Giorgio Ottaviani, Michael Walter.

Masterclass: Tensor Decompositions and...

co-organised within the TensorDec Laboratory

Within the TensorDec Laboratory of the U. of Trento we organize every year a Masterclass to offer our students a short and intense introduction on state-of-the-art topics within the area of applications of algebra and geometry. The lectures are given by an international expert invited by the lab.
2025, Tensors and their applications: foundations and recent advances, by Jeroen Zuiddam (U. Amsterdam)2024, Tensor Decompositions and applications in multi-omics data analysis, by Neriman Tokcan (U. Massachusetts Boston)2023, Algebraic Vision and Multifocal Tensors, by Kathlen Kohn (KTH Stockholm)2022, Algebraic Statistics and related topics, by Kaie Kubias (Aalto U.)2021, Tensor Decomposition and their applications, by Nick Vannieuwenhoven (KU Leuven)

EMS Summer School

TiME 2019 : "Curves and Surfaces: a history of shapes"

co-organised with Matteo Gallet, Kathlén Kohn, Marta Panizzut, Emanuele Ventura
2 September - 6 September 2019 @ Hotel Bellavista, Levico, Italy

The aim of the summer schools "TiME - Treasures in Mathematical Encounters" is to study mathematical results and methods from the 19th century and the beginning of the 20th century which have been partly forgotten. We want to explore the huge heritage of the mathematicians of the past and connect it to contemporary mathematical research. This first edition in 2019 is inspired to the work of G. Castelnuovo and F. Enriques, two of the main representatives of the classical Italian School of Algebraic Geometry. The three mini-courses were given by: Laurent Busé, Fabrizio Catanese, and Elisa Postinghel.

Conferences and Workshops

INABAG Conference 2025
with a day in honour of Alessandro Gimigliano

co-organised with Elena Guardo, Elisa Postinghel, Pierpaola Santarsiero
30 June - 2 July, 2025 @ Trento

The conference will be the second event of the Italian Network for Applied and Birational Algebraic Geometry (INABAG), a group of geometers and algebraists based in Italy, whose common research interests lie within the theory of tensors from the commutative algebraic, the birational algebro-geometric, and the applied viewpoints.The INABAG Conference 2025 wants to gather international experts to present recent achievements as well as discuss future lines of research.The conference will also be an occasion to celebrate the remarkable career and contributions of Sandro Gimigliano, a crucial member and guiding figure of the Network, honouring his 70th birthday. The special session will highlight Sandro Gimigliano’s work, innovative ideas, and lasting impact on the field of tensor decomposition and secant varieties through some of his collaborators and former students.

TENSORS

co-organised with Ada Boralevi, Enrico Carlini, Letterio Gatto, Francesco Vaccarino
10 September - 14 September, 2018 @ Politecnico di Torino, Turin, Italy

Tensors are attracting a huge amount of research activity. Some of the hottest topics are: tensor decompositions, tensor ranks, tensor trains, low-rank approximations, tensor completions, identifiability, sensitivity, signature tensors of paths. Such a fervent and vigorous activity can be easily explained: tensors are ubiquitous in describing physical quantities and laws, in modelling systems, and in representing constraints. Thus, more and more often so, even theoretical results about tensors can have significant practical consequences. One of the aims of this workshop is to bring together experts from different branches of mathematics and engineering in which tensors play a crucial role. One other significant aim is to introduce young researchers to the art of building bridges between different research fields using tensors as the leading example. Main speakers were: Luca Chiantini, Wolfgang Hackbush, Bernard Mourrain, Giorgio Ottaviani and Bernd Sturmfels.

IPPI Workshop

co-organised with Enrico Carlini, Gianfranco Casnati, Elena Guardo, Alfio Ragusa
22 March - 24 March, 2018 @ Politecnico di Torino, Turin, Italy

In the PRAGMATIC2017 research school young researchers coming from international institutions have been introduced to actual and relevant research topics in Commutative Algebra and Algebraic Geometry by the lectures of Enrico Carlini (Politecnico di Torino), Tai Hà (Tulane U.), Brian Harbourne (U. Nebraska-Lincoln) and Adam Van Tuyl (McMaster U.). Working groups have been formed to focus on some specific research problems.The main aim of this workshop is to help the young researchers to keep working on their research topics from PRAGMATIC2017 giving them feedback from senior researchers and offering them the opportunity to present their work.The senior lectures were given by Cristiano Bocci and Jürgen Herzog.

Stockholm-Uppsala Mini-Conference for PhD students in Mathematics

co-organised with O. Bergvall, A. Serio, and G. Sædén Ståhl
12 May - 13 May, 2016 @ Stockholm University, Stockholm, Sweden

The idea behind this mini-conference is to create an opportunity for PhD-students of mathematics in the Stockholm-Uppsala area to come together and discuss mathematics and get the chance to give talks about their research.

Sessions and MiniSymposia

Tensors in Algebraic Geometry
mini-symposium at SIAM Conference in Applied Geometry 2023

co-organised with F. Gesmundo, L. Sodomaco, N. Tokcan
10 July - 14 July, 2023 @ Eindhoven U. (The Netherlands)

Over the last 60 years, multilinear algebra made its way into the applied sciences. Just as matrices play a central role in linear algebra, tensors are the main actors of multilinear algebra. From mathematics to computer science, from engineering to physics, the reason for their success is that they provide a natural and compact way to store information. A standard way to extract information from tensors is to consider structured decompositions, with respect to some notion of rank which typically has a natural geometric interpretation. Algebraic geometry provides the right tools to study these structured decompositions. Geometry plays a major role in two areas of the study of tensors: the theory of secant varieties and the spectral theory of tensors. The first one is an object of a long line of research, starting from classical work from the XIX and early XX century to state-of-the-art pure and applied mathematics. The second one is a young subject, which has strong connections to optimization and witnessed promising developments in the last few years. This minisymposium brings together experts in the field as well as young researchers with the purpose of providing an overview on recent developments in the role of algebraic geometry in the study of tensor decomposition. In this way, the minisymposium offers a theoretical perspective which is complementary to the minisymposium “Tensors in Applications”.

The algebra and geometry of tensors 1: general tensors
mini-symposium at SIAM Conference in Applied Geometry 2021

co-organised with N. Vannieuwenhoven
16 August - 20 August, 2021 @ Texas A&M U., College Station, USA (online)

Tensors are ubiquitous in mathematics and science. Tensor decompositions and approximations are an important tool in artificial intelligence, chemometrics, complexity theory, signal processing, statistics, and quantum information theory. These topics raise challenging computational problems, but also the theory behind them is far from fully understood. Algebraic geometry has already played an important role in the study of tensors. It has shed light on: the ill-posedness of tensor approximation problems, the generic number of decompositions of a rank-r tensor, the number and structure of tensor eigen- and singular tuples, the number and structure of the critical points of tensor approximation problems, and on the sensitivity of tensor decompositions among many others. This minisymposium focuses on recent developments on the geometry of tensors and their decompositions, their applications, and mathematical tools for studying them, and is a sister minisymposium to "The algebra and geometry of tensors 2: structured tensors" organized by A. Bik, J. Draisma and E. Ventura.

The algebra and geometry of tensors 2: structured tensors
mini-symposium at SIAM Conference in Applied Geometry 2019

co-organised with E. Angelini, E. Carlini
9 July - 13 July, 2019 @ Universität Bern, Bern, Switzerland

Tensors are ubiquitous in mathematics and science. Tensor decompositions and approximations are an important tool in artificial intelligence, chemometrics, complexity theory, signal processing, statistics, and quantum information theory. Often, due to the nature of the problem under investigation, it might be natural to consider tensors equipped with additional structures or might be useful to consider tensor decompositions which respect particular structures. Among many interesting constructions, we might think of: symmetric, partially-symmetric and skew-symmetric tensors; tensor networks; Hadamard products of tensors or non-negative ranks. This minisymposium focuses on how exploiting these additional structures from algebraic and geometric perspectives recently gave new tools to study these special classes of tensors and decompositions. This is a sister minisymposium to "The algebra and geometry of tensors 1: general tensors" organized by Y. Qi and N. Vannieuwenhoven.

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