# GRADUATE COURSES

# GRADUATE COURSES

From the fall of 2016, BGSMath offers intensive advanced graduate courses every semester on specialized topics. The duration is 10 to 20 hours distributed along 2 to 3 weeks. Some are in connection with our monthly programs while others stand alone. The courses are organized by BGSMath members and taught by research leaders in the corresponding fields.

# FORTHCOMING GRADUATE COURSES

## 4th Barcelona Summer School on Stochastic Analysis

Two courses: Some stochastic models in eco-evolution, by S. Méléard & Topology of zero sets of smooth random Gaussian functions, by M. Sodin.

# PREVIOUS GRADUATE COURSES

## Metaheuristics Course

The first goal of this course is to give the students a general idea of the class of problems that benefit from and are amenable to be efficiently solvable by metaheuristics.

*** Please note some last-minute change!***

## Algebraic and combinatorial phylogenetics

The course will go from the basics of stochastic processes and combinatorial objects related to phylogenetics to the deep understanding of …

## Random Discrete Structures

Random methods have become one of the most active and fruitful areas of research in many areas of mathematics, science and engineering, …

## Interactions of harmonic analysis, combinatorics and number theory

The main purpose of this course is to explore several applications of Fourier analytic techniques in number theory and combinatorics, …

## Arithmetic properties of curves of small genus

The course is an introduction to theoretical and computational aspects of curves of small genus as well as their Jacobians. …

## p-adic methods for Galois representations and modular forms

We organize three advanced courses by leading experts in the subject, suitable for PhD students, postdoc researchers and senior number-theorists.

## Category theory

This course is a systematic introduction to modern Category Theory, useful to all students in Algebra, Geometry, Topology, Combinatorics, or Logic.

## A primer on K-theory and its applications

In this course we will present the basic tools of the subject, with a stress on applications in various areas by means of examples.

## Algorithmic group theory

In this course we propose a trip through modern infinite group theory with a special emphasis on algorithmic issues.

## Mathematical logic and linguistics

One of the new directions taken by mathematical logic in the late 20th century was the turn towards substructural or resource-conscious inference [Girard 1987].

## Information theory

The aims of this course are to review the fundamental principles and methods of information theory.

## Quasiconformal mappings and Complex Dynamics

This course will explore the interplay between quasiconformal geometry and holomorphic dynamics.

## Computational tools for Number Theory and Algebra

REMARK: The course will include a number of laboratory sessions to practice the main topics with SAGE and Magma.

## Lie groups and bundles

Both Lie groups and line bundles are transversal tools that are used in many mathematical fields. We start from a geometrical point view, …

## Partial differential equations

The course will start with a modern review of the key topics learnt in a first PDE course.

## Homology in Algebra and Geometry

The course will present the classical setting of homology as well as an introduction to the more recent aspects that right now are changing the subject.

## Random Structures and the probabilistic method

Probabilistic methods have a wide range of applications in several areas of mathematics, including analysis, geometry, combinatorics,…

## A course on Dynamical Systems

The lectures will be chosen among the following list of topics, according to the interests and backgrounds of the students…