# 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

## An Invitation to p-adic Methods in Number Theory

Since their introduction by Kurt Hensel in 1897, p-adic numbers have become ubiquitous in number theory, as they provide a way to use analytic techniques in arithmetic problems. These play a key role in most of modern results in number theory, such as Fermat’s Last Theorem, the known cases of the Birch and Swinnerton-Dyer conjecture, or the proof of the Sato-Tate conjecture. These lectures, aimed at a broad audience, aim to introduce several techniques that illustrate their power.

Dates: starting the week of the 23rd of March, 2020.

## Poisson processes: Stochastic Analysis, Malliavin-Stein Method, and Stochastic Geometry

Poisson processes are an important class of stochastic processes featuring in many branches of probability theory. They play a central role in stochastic geometry, where one is often interested in random geometric structures constructed from underlying Poisson processes. Examples include random tessellations, geometric random graphs, Boolean models, and random polytopes.

Days: 15, 20, 23, 27, 30 april from 10h-12h aula de seminaris, IMUB

# PREVIOUS GRADUATE COURSES

## Quantum Error-Correcting Codes

We will focus for a large part of the course on stabiliser codes which have an analogue in classical error-correcting codes. This will give us an opportunity to delve into classical error-correction too and it will turn out that some constructions of quantum codes can be lifted from the classical case.

Lecturers: Simeon Ball (UPC) and Felix Huber (ICFO)

January 21st and 23rd, 2020. Two sessions of two hours each day of the course (morning/afternoon).

UPC

## Singular Integrals

Starting day: October 7, 2019. Last day: January 23, 2020

Organiser: Xavier Tolsa, ICREA-UAB

Speakers: Xavier Tolsa, ICREA-UAB (theory), Yorgos Sakellaris, UAB (problem sessions)

## Course on K3 Surfaces

Fridays from 10:30 to 13:00 (October 4th to November 29th, 2019)

Organiser: Joan Carles Naranjo (Universitat de Barcelona)

Speakers: Martí Lahoz and Joan Carles Naranjo, University of Barcelona

## Lectures on Quadratic Forms

September 17th, 2019. Organiser: Enrique Casanovas (Universitat de Barcelona)

Speakers: Martin Ziegler, Visiting Research Professor, University of Barcelona

## Sun Tzu approach to the Riemann Hypothesis

An introduction to the Riemann Hypothesis and a panoramic overview of the conjecture.

11 – 14 June 2019. Organiser: Eva Miranda (UPC-BGSMath)

Speakers: Vicente Muñoz (University of Málaga), Ricardo Pérez Marco (CNRS & University of Paris Diderot)

## An Introduction to Equilibrium Problems and their applications

The goal of this course is to provide a comprehensive overview of the main theoretical results and solution algorithms for Ky Fan inequalities, together with a wealth of applications.

Lecturer: Mauro Passacantando (University of Pisa)

## An introduction to wavelets and their applications

This BGSMath Graduate Course will consist of six two-hours sessions devoted to wavelets and their applications.

New room! Aula T1, Faculty of Mathematics and Computer Science, Univ. of Barcelona

Speakers: Joaquim Bruna (UAB & BGSMath), Josep Maria Mondelo (UAB & BGSMath)

## Introduction to statistical learning theory

The goal of this 10-hour course is to lay out some of the basic principles and introduce mathematical tools that help understand and analyze machine learning algorithms.

Speaker: Gábor Lugosi, ICREA Research Professor, BGSMath – Universitat Pompeu Fabra.

## An introduction to Malliavin calculus and its applications

This BGSMath Graduate Course will consist of five two-hours sessions devoted to Malliavin calculus and its applications.

Speaker: David Nualart, University of Kansas (USA)

## Complex Dynamics and Applications

This BGSMath Graduate Course will take place on the week of 16 July.

Speaker: Juan Rivera-Letelier (University of Rochester)

Topic: Complex Dynamics and Applications

## 4th Barcelona Summer School on Stochastic Analysis: a 2018 EMS Summer School

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

## An introduction to Parameterized Complexity

The course (9-12 Apr 2018) covers the concept of problem parameterization, explains why and how this induced the definition of the parameterized complexity hierarchy, and provides some links of this theory to the classical complexity theory.

## 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…