Talks and breaks will be in the Auditorium Building on the TU/e campus.

Room: Auditorium 16

Coffee break Monday: zijbeuk on the first floor

Coffee breaks Tuesday: Section E, first floor

Travel options:

• Plane: The closest airport is Eindhoven. Amsterdam Schiphol is about 1.5 hour away, with regular train service.

• Train: Eindhoven Centraal Station is within walking distance of TU/e.

Abstract: Understanding how the shape of crystalline materials influences their physical and functional properties is critical for designing next-generation materials. For example, the pore shapes of porous materials determine their gas adsorption properties, and the shapes of potential energy landscapes in battery materials govern their ionic conductivities. Gaining insight into and utilizing shape-property relations requires mathematical modeling and quantification of relevant shape aspects.

In this talk, I will introduce three approaches that I have used to illuminate shape-property relations in crystalline materials, based on: (1) the analysis of 3-periodic nets describing bond structures, (2) persistent homology, and (3) the analysis of a filtration of sub-level sets of scalar fields. I will provide examples of how these methods have been used to gain theoretical insight and show that they offer a rich framework for developing descriptors of crystalline materials that complement existing ones for machine learning studies.

Abstract: Interpolation is a prime tool in algebraic computation while symmetry is a qualitative feature that can be more relevant to a mathematical model than the numerical accuracy of the parameters. We shall show how to exactly preserve symmetry in multivariate interpolation while exploiting it to alleviate the computational cost. We revisit minimal degree and least interpolation with symmetry adapted bases, rather than monomial bases.

An interpolation problem is defined by a set of linear forms on the polynomial ring and values to be achieved by an interpolant. For Lagrange interpolation the linear forms consist of evaluations at some nodes, while Hermite interpolation also considers the values of successive derivatives. Both are examples of ideal interpolation in that the kernels of the linear forms intersect into an ideal.

For a space of linear forms invariant under a group action, we construct bases of invariant interpolation spaces in blocks, capturing the inherent redundancy in the computations. With the so constructed symmetry adapted interpolation bases, the uniquely defined interpolant automatically preserves any equivariance the interpolation problem might have. Even with no equivariance, the computational cost to obtain the interpolant is alleviated thanks to the smaller size of the matrices to be inverted.

Joint work with Erick Rodriguez Bazan (Inria Côte d'Azur)

Journal of Symbolic Computation 107 (2021) https://doi.org/10.1016/j.jsc.2021.01.004

Journal of Symbolic Computation 115 (2023) https://doi.org/10.1016/j.jsc.2022.08.014

Abstract: Tubes are a quintessential model for a homogeneous linear–chain biopolymer. Owing to their simplicity, tubes serve as a test case for much more complex systems like that of a protein, with which one can probe big questions, like how such materials fold or change their configuration upon environmental queues. In this talk I will present work on optimal packings of tubes as inspired by the morphometric approach to solvation, a novel application of results from integral geometry to thermodynamics developed by Klaus Mecke. How do deformable materials—like tubes or filaments—occupy space? How can this be quantified?

Whilst we take tubes as our case study, the approach is broadly applicable to many systems, where shape and arrangement are the principal measurable quantities governing their properties.

Abstract: In this talk, I introduce a new normal form framework for fully inhomogeneous feedforward network dynamical systems with nilpotent linear parts. We develop a triangular sl2​-style normal form that systematically classifies such systems and extends the theory to include quadratic terms in arbitrary dimensions. Our approach integrates classical tools, such as Hermite reciprocity, transvectants, and Sylvester’s foundational results on quadratic covariants, with a modern Lie algebraic formulation. In particular, we derive an orbital normal form using outer transformations, which yields a block-triangular outer normal form. Applications in two and three dimensions demonstrate how this framework produces simplified models that are well-suited for bifurcation analysis.

Abstract: Development of a Smart User Terminal and an Advanced PNT Testbed supporting Galileo 2nd Generation, integrating: 

GNSS (e.g., Galileo)

LEO/NTN constellations (e.g., Starlink, OneWeb)

5G/6G terrestrial infrastructure

Bayesian Fusion and Trust Evaluation Models.

Abstract: The expectation maximization (EM) algorithm is a popular method of density estimation for Gaussian mixture models. Fundamental to understanding the performance of this algorithm is to understand the set of points closest to a given Gaussian, where “closest" is defined in terms of the maximum likelihood function. We call this set of points a Gaussian Voronoi cell. In this talk, I will outline new results regarding the geometry and combinatorics of Gaussian Voronoi cells. This is joint work with Joe Kileel.

Abstract: Contrary to popular belief, the global positioning problem on earth may have more than one solutions even if the user position is restricted to a sphere. In this talk, we will discuss the mathematics behind global positioning, and complications that may arise if satellites are in bad positions.

Abstract: This presentation gives a high-level overview of XR systems and how the various sub-systems interact together to deliver an immersive virtual reality experience. The problem of reprojection will be addressed, illustrating the impacts on the overall system. The impact of the display pipeline on the overall visual quality of the system is explored, highlighting opportunities to model this subsystem to determine optimizations for overall performance and user experience. 

Abstract: Join to find out!

Abstract: Besides from the well-known lithography machines, ASML produces also Scanning Electron Microscopes (SEMs). ASML customers use these machines for the inspection of electronic circuits printed on wafers with the lithography system. SEMs take images of wafers by pointing an electron beam to the object. These electrons interact with the surface and subsurface geometry, depending on their landing energy. The secondary and backscattered electrons are detected and create SEM images.

SEM images are used for the metrology of components of electronic circuits, for example the edge placement of the components. SEM images taken with high landing energies depict multiple layers of components stacked on top of each other. For many geometries, components from different layers will overlap. Identification of all separate structures in the images is a challenging task, where standard (segmentation) methods aren't able to differentiate between different structures. We propose to lift the image to the space of positions and orientations SE(2) where crossing structures are disentangled. In this higher-dimensional space, we develop algorithms to properly identify all components. In this presentation, we present some of these methods and show the corresponding results.

Abstract: Retinal images are often used to examine the vascular system in a non-invasive way. Studying the behavior of the vasculature on the retina allows for noninvasive diagnosis of several diseases as these vessels and their behavior are representative of the behavior of vessels throughout the human body. For early diagnosis and analysis of diseases, it is important to compare and analyze the complex vasculature in retinal images automatically.

During this talk, we will talk about different approaches for automatic tracking of vasculature in retinal images. We discuss a new model that is better able to handle difficult structures, like high curvature and crossings. Additionally, we discuss the influence of the image and the manifold on which the algorithm takes place. All methods take place on a lifted representation of the image: The first two on the homogeneous space of planar positions and orientations, whereas the last on the homogeneous space of spherical positions and orientations. This lifted image representation allows us to differentiate between crossings and bifurcations.

Abstract: An important task in statistics is to match a statistical model to observed data. In this talk, I will discuss a way to analyse the behaviour of this model-to-data matching for very large or very small data sizes using tools from tropical geometry. As a main result, we derive exact expressions for the asymptotics of the maximum likelihood estimate using only the asymptotics of the data, in the case of log-linear statistical models. The main mathematical ingredients are tropical affine spaces, matroid theory and regular subdivisions.

This is based on joint work with Emma Boniface and Serkan Hoşten.

Abstract: Modern cryptography relies heavily on the hardness of mathematical problems to ensure security, privacy, and trust in digital systems. Many advanced cryptographic protocols—such as Zero-Knowledge Proofs (ZK), Fully Homomorphic Encryption (FHE), Multi-Party Computation (MPC), and digital signatures—ultimately reduce their security to the difficulty of solving systems of polynomial equations that encode secret data. Understanding the complexity of solving these systems is thus critical for assessing cryptographic strength.

Gröbner basis techniques are powerful tools in computational algebraic geometry, providing a general method for solving systems of polynomial equations. In modern cryptography, they have become essential for both the analysis and, increasingly, the design of cryptographic primitives. This talk explores how Gröbner basis algorithms are applied to study the security of cryptographic systems—especially those optimized for advanced protocols like ZK, FHE, and MPC, which often rely on primitives with simple algebraic structures. We will review state-of-the-art methods for solving polynomial systems arising in cryptographic contexts and outline possible research directions in this area.

Abstract: Mathematics can be a superset of reality. Ranging from quantum physics where mathematical constructs precede understanding to Artificial Intelligence which creates a whole new reality by itself, math can be seen as the source of all innovation. But we do not live alone. After our hard work on algorithms, theorems and proofs some of our ideas creep into the real world. In my talk, I want to have a closer look on the interactions we have with other disciplines and how they see us and what they expect from us.

Abstract: Topological interlocking assemblies (TIAs) are arrangements of blocks that are kinematically constrained by a fixed frame, such that all rigid body motions of each block are prevented by the neighbouring blocks and the frame. This results in a modular construction approach that enhances recyclability and, consequently, sustainability. Using a group-theoretic approach based on wallpaper groups we can design various interlocking blocks that can be arranged symmetrically where even combinations of two different blocks within a single assembly are allowed. For evaluating and comparing different TIAs, we are using finite element simulations and already developed a fast, flow-based a priori evaluation method. We employ these tools to analyse planar TIAs as well as tubular interlockings.

Abstract: Pipelines for transport of water and other fluids are often buried underground or otherwise inaccessible. Since they usually deteriorate over time, they can start leaking and finding such leaks can be very expensive, troublesome and timeconsuming. This can be avoided through swarms of evolving sensors that float with the streaming fluid and observe the environment through sensors for detecting leaks and weak spots in the pipe walls, without taking the pipelines out of service. One especially difficult problem is determining the location where the sensor readings have been recorded. In this presentation the underlying technology and boundary conditions will be presented and the problem of finding the location, or even knowing whether the location can be found, will be discussed.

Abstract: Securing containers for sea freight transport poses a significant challenge for port operators.  As of today, this process is entirely performed manually. This talk introduces the solution provided by SEAL Robotics and the related challenges. The primary focus of this presentation lies on the optimizing of the reachability of the manipulator and on trajectory optimization using diffusion policies.

Abstract: A Chow decomposition of a symmetric tensor is a decomposition of the corresponding polynomial as a sum of products of linear forms. In this talk, I will discuss a novel algorithm for computing such decompositions. Our algorithm is based on a more general algebraic tool for tensor sparsification known as chiseling. This talk is based on joint work in progress with Daniele Taufer and Nick Vannieuwenhoven. 

Abstract: Loop invariants are properties of a program loop that hold before and after each iteration of the loop. They are often employed to verify programs and ensure that algorithms consistently produce correct results during execution. Consequently, the generation of invariants becomes a crucial task for loops. I specifically focus on polynomial loops, where both the loop conditions and assignments within the loop are expressed as polynomials. Although computing polynomial invariants for general loops is undecidable, efficient algorithms have been developed for certain classes of loops. For instance, when all assignments within a while loop involve linear polynomials, the loop becomes solvable. 

       I will talk the more general case where the polynomials exhibit arbitrary degrees. Applying tools from algebraic geometry, I present two algorithms designed to generate all polynomial invariants for a while loop, up to a specified degree. These algorithms differ based on whether the initial values of the loop variables are given or treated as parameters.

Abstract: Communication between single cells or higher organisms by means of diffusive compounds is an important phenomenon in biological systems. A straightforward model is by a diffusion equation with suitable flux boundary conditions at the cell boundaries. Such a model will become computationally inefficient and analytically complex when there are many cells, even more so when they are moving. We propose to consider also a point source model. Each cell is virtually reduced to a point and appears in the diffusion equation for the compound on the full spatial domain as a singular reaction term in the form of a Dirac delta measure located at the cell’s centre. The amplitude of the Dirac delta measure is a nonlocal term of the compound’s concentration near the virtual cell boundary so as to preserve the essential biological features. To investigate the positivity of the solution and the structure of steady states, we employ the Laplace transform. Furthermore, we incorporate techniques from the theory of elliptic curves to study the system.

There are a number of hotels at walking distance from the university. 

The closest option is The Social Hub, and we have a block reservation for a limited number of rooms at 105 euro per night (between 25-28 May; if you wish to add more dates, you will need to contact the hotel). Click here to book. Please note that this link is valid until 12/05/2025, so please make sure to book before then. We agreed with TSH to ensure anyone using this link is informed about the TSH Hotel Terms and Conditions and House Rules, found at https://www.thesocialhub.co/terms-and-conditions/, as well as about the Privacy Statement, found at https://www.thesocialhub.co/privacy-statement.

Breakfast is not included, but can be added in advance by contacting groups.eindhoven@thesocialhub.co (at 14 euro per person per morning), or added upon arrival (at 15.50 euro per person per morning).