# Research Areas

**Algebra, Geometry, and Number Theory**

The research in this area involves algebraic geometry, arithmetic geometry, differential geometry, differential topology, global analysis, analysis on manifolds, algebraic topology, number theory, commutative algebra. The researchers in this area co-organize weekly seminars on number theory and algebraic geometry (jointly with Universitat de Barcelona and Universitat Autònoma de Barcelona), and Poisson geometry (jointly with University of Geneva).

**Analysis, Dynamical Systems, and Partial Differential Equations**

IMTech includes here Reaction-diffusion equations, integro-differential equations, Mathematical modeling, Hamiltonian systems, Astrodynamics, and Mathematical neuroscience. Talks are regularly held within the Dynamical systems seminar (jointly with Universitat de Barcelona) and the PDEs and applications seminar (jointly with Universitat Autònoma de Barcelona and Universitat de Girona).

**Discrete Mathematics, and Foundations of Computer Science**

The research in this area covers Combinatorics, Graph theory, Discrete random structures, Coding theory, Models for large networks, Complexity and logic, Algorithmic game theory, and Computational Geometry, among others. The research groups in this area run a joint seminar at UPC on combinatorics, graph theory, and theoretical computer science.

**Mathematical Modeling, and Numerical Analysis**

In this area, IMTech researchers develop mathematical and computational models to understand, quantify and control a variety of physical and biological systems. This involves new theoretical frameworks for coupled multiphysics systems, an in-depth study of existing models, new algorithms for high-performance or data-driven computing, or systematic ways to integrate mathematical modeling and experimental observations. This area is very much application-driven with contributions to high-fidelity simulations for industrial problems, the conception and design of new multifunctional materials, biological problems from sub-cellular to tissue scales, or the study of species evolution.

**Statistics, Optimization, and Operations Research**

This area covers research on biostatistics, multivariate data analysis, Bayesian data analysis, functional data analysis, continuous optimization, linear and integer optimization, large-scale computational optimization, stochastic optimization, and applications (to data science and machine learning, among others). Talks on these topics are organized in a seminar series.

The main research areas above are complemented with a transversal area on

**Interdisciplinary Mathematics**

This area promotes transversal and interdisciplinary research with an applied component towards industry and knowledge transfer, such as biomedical sciences and engineering.