This is the second volume of the proceedings of the third European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners as well as papers by plenary and parallel speakers. The second volume collects articles by prize winners and speakers of the mini-symposia.
This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician.

Autorentext
Rubén Ballester is a PhD student in Topological Machine Learning at the Department of Mathematics and Computer Science of the University of Barcelona (UB). He received his bachelor s degrees in Mathematics and Computer Science from UB in 2021 and completed the Advanced Mathematics and Mathematical Engineering MSc at Universitat Politècnica de Catalunya (UPC) in 2022, achieving the highest master s degree GPA recognition. He has published articles on the connection between generalizations of neural networks and persistent homology and on the design of neural networks for topological domains. He won the Topological Deep Learning Challenge in the modality of combinatorial complexes, organized within the 2nd Annual Workshop on Topology, Algebra, and Geometry in Machine Learning at ICML 2023. In addition, he has actively contributed to the TopoX software suite for topological neural networks.Carles Casacuberta is Full Professor of Geometry and Topology at the University of Barcelona (UB) since 2001. He earned his doctoral degree in 1988, specializing in algebraic topology. He has edited ten books and authored 55 research articles in areas such as homotopy theory, category theory, homological algebra, and more recently, topological data analysis. He serves on the editorial board of the Springer Universitext series and two research journals. Currently, he coordinates the Topological Machine Learning Seminar at UB and participates in several Horizon Europe projects focused on applications of artificial intelligence in biomedicine.Sergio Escalera is Full Professor at the Department of Mathematics and Computer Science of the University of Barcelona. He is action editor of the Journal of Data-centric Machine Learning Research and IEEE Transactions on Pattern Analysis and Machine Intelligence. He is vice-president of ChaLearn Challenges in Machine Learning, leading ChaLearn Looking at People events. He is co-creator of the Codalab open source platform for challenge organization and co-founder of the NeurIPS competition and Datasets and Benchmarks tracks. He has published more than 400 research papers and participated in the organization of scientific events. His research interests include machine learning fundamentals, and inclusive and transparent analysis of humans from visual and multi-modal data by means of deep learning mechanisms.

Inhalt
Table of Contents of Volume II.- Articles by Prize Winners.- Classification Results on Valuations on Convex Sets.- Towards a Microscopic Theory of Phase Coexistence.- Constructing Compact 8-Manifolds with Holonomy Spin(7) from Calabi-Yau Orbifolds.- Banach KK-Theory and the Baum-Connes Conjecture.- An Introduction to Non-Commutative Mori Theory.- Geometric Methods in Complex Analysis.- Vanishing Cycles and Mutation.- Critical Exponents, Conformal Invariance and Planar Brownian Motion.- Mini-Symposium on Computer Algebra.- Computer Algebra Algorithms for Linear Ordinary Differential and Difference Equations.- Some Introductory Remarks on Computer Algebra.- A Study of Iteration Formulas for Root Finding, Where Mathematics, Computer Algebra and Software Engineering Meet.- Industrial Applications of Computer Algebra: Climbing Up a Mountain, Going Down a Hill.- Applications of Computer Algebra to Algebraic Geometry, Singularity Theory and Symbolic-Numerical Solving.- Mini-Symposium on Curves over Finite Fields and Codes.- Explicit Towers of Drinfeld Modular Curves.- Curves over Finite Fields Attaining the Hasse-Weil Upper Bound.- Asymptotically Good Towers of Global Fields.- Explicit Constructions of Towers of Function Fields with Many Rational Places.- Curves over Finite Fields and Codes.- Authentication Codes and Algebraic Curves.- Mini-Symposium on Free Boundary Problems.- Some Aspects of Mean Curvature Flow in Presence of Nonsmooth Anisotropies.- A Phase-Field Model for Diffusion-Induced Grain Boundary Motion.- Evolution of a Closed Interface between Two Liquids of Different Types.- Applications of a Local Energy Method to Systems of PDE's Involving Free Boundaries.- Phase Boundaries in Alloys with Elastic Misfit.- Some Aspects of the Thin Film Equation.- A BriefOverview on the Obstacle Problem.- The Impact of Monotonicity Formulas in Regularity of Free Boundaries.- A Free Boundary Problem: Contributions from Modern Analysis.- Mini-Symposium on Mathematical Finance- Theory and Practice.- Risk Sensitive Control with Applications to Fixed Income Portfolio Management.- Wavelet Based PDE Valuation of Derivatives.- Some Analytic Facts on the Generalized Hyperbolic Model.- Functionals of Brownian Motion in Path-Dependent Option Valuation.- Optimal Portfolios under a Value at Risk Constraint.- Mini-Symposium on Quantum Chaology.- Trace Formulas and Spectral Statistics of Diffractive Systems.- Semiclassical Results in the Linear Response Theory.- The Berry- Tabor Conjecture.- On Quantum Unique Ergodicity for Linear Maps of the Torus.- Mini-Symposium on Quantum Computing.- Bound Information: The Classical Analog to Bound Quantum Entanglement.- Mini-Symposium on String Theory and M-Theory.- D-Branes on Calabi-Yau Manifolds.- Knot Invariants and Chern-Simons Theory.- Topological Quantum Field Theory and Four-Manifolds.- D-Brane Conformal Field Theory and Bundles of Conformal Blocks.- From Quiver Diagrams to Particle Physics.- Mini-Symposium on Symplectic and Contact Geometry and Hamiltonian Dynamics.- From Symplectic Packing to Algebraic Geometry and Back.- New Invariants of Legendrian Knots.- Contact Topology in Dimension Greater than Three.- The Hamiltonian Seifert Conjecture: Examples and Open Problems.- The Fine Geometry of the Cantor Families of Invariant Tori in Hamiltonian Systems.- Symplectic and Contact Geometry and Hamiltonian Dynamics.- Simple Coisotropic Projections and Caustics.- Mini-Symposium on Wavelet Applications in Signal Processing.- Reassigned Scalograms and Singularities.- The Impact of Wavelet Coefficient Correlations on Fractionally Differenced Process Estimation.- Wavelet-Based Modelling of Persistent Periodicities.- Network Traffic Modeling Using a Multifractal Wavelet Model.- Denoising Via Block Wiener Filtering in Wavelet Domain.- Wavelet Analysis of Discrete Time Series.