# 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

# PREVIOUS GRADUATE COURSES

## Algorithmic Learning and Deep Neural Networks

The main purpose of the course is to describe the nature of algorithmic learning (AL), of its most relevant modalities and most successful applications, together with a presentation of the main mathematical ingredients that provide the basis for both the definition and study of models and for the analysis of the algorithms. Along the way, open questions and problems will be highlighted.

ONLINE (October 5th – November 18th)

## (POSTPONED) BMS-BGSMath Junior Meeting 2021

Date

1-3 September, 2021

Location

The event will be held at the historical building of the University

of Barcelona (Gran Via, 585, 08007 Barcelona)

The Berlin Mathematical School (BMS) and the Barcelona Graduate School of Mathematics (BGSMath) share the common goal of striving for excellence in their doctoral and postdoctoral training programs.

## BGSMath Colloquium 2021

Speakers

Robert Ghrist (University of Pennsylvania)

This colloquium will be held online via ZOOM. The relevant link will be provided to all registered participants in the days leading up to the colloquium.

## 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.

April 19 – May 7, 2021

ONLINE

## Fragments of algebraic graph theory

Date:

From January 13 to March 25, Wednesdays and Thursdays 17h-19h (Barcelona time)

Location:

The course will be entirely accessible through the web.

## BGSMath – BCAM Colloquium 2020

Online

Speakers:

José Antonio Lozano (BCAM)

Gábor Lugosi (UPF)

## Career Management beyond PhD in Math

Date: Wednesday, February 26th, 2020

Time: 15:30 – 17:30

Location: Room Pol-2, Centre de Recerca Matemàtica

## 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

## BMS – BGSMath Junior Meeting 2019

The Second BMS – BGSMath Junior Meeting will take place from Wednesday 26 to Friday 28 June 2019 at Zuse Institute Berlin (ZIB).

## Barcelona Analysis Conference 2019

The BAC19 conference is a continuation of the BAC06 and BAC16 conferences, both held also in Barcelona in September 2006 and September 2016. As in 2006 and 2016, the main objective of the conference is to gather leading researchers in Mathematical Analysis and close areas to present the latest developments and discuss future lines of research. Participation of young researchers, to whom the conference is especially addressed, is encouraged.

25 – 28 June 2019, Aula Magna Historical Building UB.

## Coding Theory and Rings

The foundations of classical coding theory are described with specific attention to the MacWilliams relations and the Singleton bound. The transfer of these fundamental ideas to coding theory over more general alphabets is described. The use of rings in coding theory is also highlighted. We end with a discussion of the major open problems in coding theory.

Speaker: Steven T. Dougherty (University of Scranton, Pennsylvania (USA))

Escola d’Enginyeria. Universitat Autònoma de Barcelona.

## 17th School on Interaction between Dynamical Systems, and Partial Differential Equations (JISD19)

The “School on Interactions between Dynamical Systems and Partial Differential Equations” is an international summer school. It is an annual meeting between scientists dedicated to Dynamical Systems and/or to PDEs to exchange knowledge and methods which may help to study new leading border problems in these two fields of mathematics.

CRM, 17 – 21 June 2019

## 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)

## BGSMath María de Maeztu Unit of Excellence 2015-2019: Closing Workshop

The BGSMath/MdM excellence program finishes this year. To celebrate this success story we organize in June 6, 2019 a workshop highlighting the most relevant scientific results obtained within the program in the main research areas of BGSMath. We invite all BGSMAth faculty, students and friends to participate in this event.

## 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)

## Pricing valuation adjustments by correlation expansion

We consider firstly the problem of computing the Credit Value Adjustment (CVA) of a European option in a default intensity setting and in presence of the so-called Wrong Way Risk (WWR). Under appropriate conditions, the method can be extended to include several XVA’s, such as bilateral CVA, DVA (Debt Value Adjustment), FVA (Funding Value Adjustment) and LVA (Liquidity Value Adjustment) due to collateralization.

Speaker: Alessandro Ramponi (University of Roma Tor Vergata (Italy))

Aula S5, Soterrani, Faculty of Mathematics and Computer Science, UB. 23 May 2019.

## VIII Complexitat Day

Complexitat.cat organizes an annual meeting, in which its members gather for a day to display their work, discuss and exchange ideas, or as an opportunity to meet future students. This year, the VIII Jornada de la Complexitat: “Interdisciplinary Research on Complexity” will be held at Institut d’Estudis Catalans (IEC), Universitat Oberta de Catalunya, on May 21, organized by the Complex Systems Group at CRM.

Keynote speaker: Iain Couzin (Max Planck Institute of Ornithology)

## An introduction to derivators with applications to the study of t-structures

The theory of stable derivators can be thought of as a minimal enhancement of triangulated categories that allows for a good theory of homotopy co/limits. The idea of a derivator has been introduced independently by several authors in different areas of Pure Mathematics: Heller (in Algebraic Topology), Grothendieck (in Algebraic Geometry), Franke, Keller (in Representation Theory), and possibly others. This theory has recently found several applications to classical problems that had remained open for a long time in the setting of triangulated categories.

Speakers: Manuel Saorín (Universidad Murcia) y Simone Virili (Universidad de Murcia)

CRM, 2 – 6 May 2019

## 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)

## Topics in Complex Dynamics 2019

This conference aims to bring together (experienced and junior) researchers in holomorphic dynamics from several different perspectives.

Barcelona, 25 -29 March 2019.

## Fourteenth Barcelona Weekend in Group Theory

This is a meeting specialized in Theory of Groups, organized for the benefit of local specialists in Theory of Groups and in Geometry and Topology, and which contributes to the dissemination of the latest results obtained in our field, with the participation of international experts in the area.

15 – 16 March 2019, UPC.

## 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.

## INPhINIT doctoral fellowship call 2019

The doctoral fellowship programme INPhINIT “la Caixa” is devoted to attracting talented Early-Stage Researchers who wish to pursue doctoral studies in Spanish or Portuguese territory. Deadline: 6 February 2019 (Incoming modality); 27 February 2019 (Retaining modality).

## 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)

## Dia internacional de la dona i de la nena en la ciència 2019

Join us for an event organised jointly by BGSMath & Societat Catalana de Matemàtiques for the International Day of Women and Girls in Science 2019: “Matemàtiques, substantiu femení i plural”.

## Maria de Maeztu Master Internships Programme 2019

The Barcelona Graduate School of Mathematics (BGSMath), Unit of Excellence Maria de Maeztu (MdM), launches a Call for 4 Master Internship Grants, aiming to attracting master students to carry out his/her Master thesis Project in a BGSMath group.

## FACARD 2019 workshop

Frobenius Action in Commutative Algebra: Recent Developments.

Speakers: Linquan Ma (Purdue University) & Holger Brenner (Universität Osnabrück)

IMUB, Barcelona, 16 – 18 January 2019

## Training Session on Open Science and Open Access

This training session aims to provide an introduction to the concepts and historical background into Open Science, as well as the diverse routes to guarantee Open Access and contribute to research open Data. We will finish by presenting the CRM Repository.

## Chasing finite shadows of infinite groups

BGSMath Autumn Colloquium 2018

Speakers: Martin R. Bridson FRS (University of Oxford)

## A Theory of Spectral Clustering

Title: A Theory of Spectral Clustering

Speaker: Luca Trevisan, University California Berkeley

## Barcelona weekend on Operator Algebras

This workshop aims to become the annual meeting of the Operator Algebras community in Barcelona. We would like to bring together leading experts and active researchers in the field to disseminate results as well as to set out perspectives for the future. We also plan to foster interactions between Algebra, Geometry and Topology.

## BGSMath 2018 Junior Meeting

The fourth BGSMath Junior Meeting is upcoming! This is an excellent opportunity for young researchers of the BGSMath community to meet senior researchers and colleagues from various universities and share their knowledge and skills. Don’t forget to present your poster!

## Open call for PhD positions (Ministry of Science) 2018

Open PhD positions: two associated to the “María de Maeztu Unit of Excellence” (MDM-2014-0445) and eight to other BGSMath projects.

Deadline: 29 Oct 2018 (15.00h CET). English help guide available.

## Open call for PhD positions (AGAUR) 2018

The Catalan Government has opened a call for PhD positions. Application on the AGAUR page.

Deadline: 25 Oct 2018.

## Barcelona-Toulouse Probability Days

The Barcelona-Toulose Probability Days is a two-day scientific activity whose main objective consists in gathering researchers on probability theory, and particularly on stochastic analysis, from different institutions of Barcelona and Toulouse.

## BGSMath–BANCO DE SANTANDER POSTDOCTORAL CALL 2018

The Barcelona Graduate School of Mathematics opens a call for a “Banco de Santander – María de Maetzu” postdoctoral positions, to work in any of its seven research strategic areas. PhD must have been obtained between 1 January 2013 and 31 December 2015.

## Formae mathematicae – Les formes de les matemàtiques – Shapes of mathematics

European Researchers’ Night Event – Shapes of mathematics

29.09.2018

Dipòsit Rei Martí, Barcelona

## Innovation inspirational talk: BGSMath and the Collider

“At The Collider we bring together the best scientists, engineers and entrepreneurs to help them create the disruptive startups that will shape the future”

Speaker: Manuel Palacín

## ”la Caixa” Postdoctoral Fellowships Programme

The “la Caixa” Foundation’s Junior Leader postdoctoral fellowships programme has the goal to attract international Early-Stage Researchers to the top Spanish research centres. Deadline: 26 Sep 2018

## BGSMath POSTDOCTORAL CALL 2018

The Barcelona Graduate School of Mathematics opens a call for 1 junior postdoctoral positions in any area of mathematics. The fellowships will be funded through the Maria de Maeztu Unit of Excellence Award (2015-2019). Deadline for submission: 14/9/2018.

## Fundraising and Writing research proposals: The IF MSCA example (II session)

Where’s the money? How do I get it? These 2 sessions will show you how to identify funding opportunities suitable for mathematics-related projects and will give you tools to formulate winning proposals.

Please note date change!

## 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

## BGSMath Summer Colloquium 2018

BGSMath Summer Colloquium 2018

Speakers: Diego Córdoba (ICMAT) and Anna Cima (UAB/BGSMath)

## 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.

## XXIX INTERNATIONAL BIOMETRIC CONFERENCE

The International Biometric Society organises the XXIX International Biometric Conference (IBC2018) to be held July 8–13, 2018 at the Barcelona International Conference Centre, Barcelona.

## Fundraising and Writing research proposals: The IF MSCA example

Where’s the money? How do I get it? These 2 sessions will show you how to identify funding opportunities suitable for mathematics-related projects and will give you tools to formulate winning proposals.

Please note date change!

## Geometric function theory in fluid mechanics

Our objective is to put together two communities apparently disconnected, and settle common interests and goals.

## Introduction to Functional Data Analysis with R

This course offers an introduction to FDA and presents some of the R libraries oriented to this type of data. Course organized by Servei d’Estadística Aplicada with the support of the BGSMath, through the ”María de Maeztu” Programme for Units of Excellence in R&D”.

## Summer internships 2018

The BGSMath launches a first Summer Internship Program to provide undergraduate students in Mathematics and close-by disciplines the opportunity to conduct summer research projects. The goal of the Program is to encourage students, from any nationality, in the pursuit of a scientific career and provide them with a first experience as researchers.

## Writing your first research proposal

Tips with do’s and don’ts for Maths PhD students looking to move on with their careers

## Discrete, Combinatorial and Computational Geometry

This intensive research program will consist of 8 weeks of activities focused on hot topics in discrete, combinatorial and computational geometry and their intricate relationships.

## 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.

## Topological vistas in neuroscience

What does topology have to do the Blue Brain Project? Professor Kathryn Hess Bellwald will explain the results obtained in this collaboration

## Intensive research programme: recent progress in Mathematical Biology

The aim of this IRP is to bring together experts from different areas of Mathematical Biology (neuroscience, tumour modelling, population dynamics, …).

## 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!***

## Maths for Industry 4.0

Maths for Industry 4.0 will showcase how academic excellence at BGSMath is helping companies becoming digital. Join us to learn about successful collaborative initiatives.

## Matemàtiques com tu

Join us for an event organised jointly by BGSMath & Societat Catalana de Matemàtiques for the International Day of Women and Girls in Science 2018.

## INPhINIT doctoral fellowship call

INPhINIT is a doctoral fellowship programme devoted to attracting international Early-Stage Researchers to the top Spanish research centres. Deadline: 1 February 2018

## BGSMath–BANCO DE SANTANDER POSTDOCTORAL CALL 2017

The BGSMath opens a call for two “Banco de Santander – María de Maetzu” postdoctoral positions, one on Dynamical Systems, and one on Probability, Statistics and/or Computer Science.

## Hyper-Kähler geometry

UPC-BGSMath Colloquium.

Speaker: Claire Voisin, Còllege de France

Registration required

## Welcome to new UPC Maths Department staff & Congratulations to awardees

Welcome to new UPC Maths Department staff & Congratulations to awardees

## Open call for Ph.D. Positions (Mineco) 2017

The Spanish MINECO opens 2 PhD positions positions associated to BGSMath groups.

## Introduction to Responsible Research and Innovation (RRI)

How to plan and execute scientific research taking into account aspects such as accountability and transparence…

## BMS – BGSMath Junior Meeting

The first Junior Meeting organized jointly between the Berlin Mathematical School and BGSMath….

## Topics in Complex Dynamics 2017

This is the seventh edition of the school “Topics in complex dynamics” at Universitat de Barcelona

## How to talk Mathematics: Oral Communication Skills Masterclass

With this same title, Paul Halmos published an article more than 40 years ago in the Notices of the AMS, which is still worth reading today.

## Algebraic and Combinatorial Phylogenetics

Statistics, probability, computation, differential equations, algorithmics, combinatorics, geometry and algebra all play an important role in biology, biostatistics and bioinformatics. Algebra and geometry have showed up in phylogenetics via the new discipline “algebraic statistics”.

## Foundations of Computational Mathematics (FoCM)

Foundations of Computational Mathematics (FoCM) is an international nonprofit organization that supports and promotes research …

## RET Summer School on h-Principles

h-Principles are a powerful tool that lie on the interface between the geometry of manifolds and algebraic topology.

## Algebraic Geometry of Gaussian Mixtures / Instability phenomena in the restricted three body problem

BGSMath Summer Colloquium 2017

Speakers: Bernd Sturmfels (University of California at Berkeley / Max Planck Institute) and Marcel Guardia (BGSMath / UPC)

## Algebraic and combinatorial phylogenetics

Registration:

The deadline for applying for financial support was February 20th 2017.

## 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, …

## Random Discrete Structures and Beyond

The BGSMath Monthly Program Random Discrete Structures and Beyond aims to bring together top leader researchers in combinatorics, probability theory and computer science in the area of random discrete structures.

## Fundraising module (session 2)

This is the second module on Fundraising: “Writing Proposals: the IF example”.

## Random discrete structures and beyond

With the support of the Spanish Ministry of Economy and Competitiveness, through the ”María de Maeztu” Programme for Units of Excellence in R&D” (MDM‐2014‐0445).

## 3 BGSMath SENIOR postdoctoral positions 2017-2019

BGSMath opens a call for 3 SENIOR postdoctoral positions in all areas of mathematics. Deadline May 3rd, 2017.

## 3 BGSMath JUNIOR postdoctoral positions 2017-2019

BGSMath opens a call for 3 JUNIOR postdoctoral positions in all areas of mathematics. Deadline May 3rd, 2017.

## BARCELONA MATHEMATICAL DAYS

Congrés de la Societat Catalana de Matemàtiques

## 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, …

## Fundraising module (Session 1)

The first of a series of training modules addressed to the young researchers, to develop complementary and transferable skills.

## BGSMath doctoral call 2017-2020

Applications welcome for 4 Ph.D. positions in all areas of mathematics. Deadline March 23rd. Incorporation before September 2017.

## What does a quant do? BGSMath seminar at UB

Quants, short for quantitative analysts, are persons who apply and develop mathematical or statistical methods in the context of problems in finance or risk…

## 1st BGSMath Data Science Workshop.

The 1st BGSMath Data Science Workshop aims to bring together the internal practitioners in the area across the Barcelona Graduate School of Mathematics…

## Dr. Joan Bruna

This is the first of a series of meetings addressed to BGSMath master and Ph.D. students and young researchers…

## 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.

## Number Theory

It seems the right time for the STNB to organize a six-week intensive program on number theory. It will contribute to maintain the level of exceptional research that is being done in Barcelona in the field. In addition, it will be a great opportunity to train a new generation of graduate students and to introduce them to this active, exciting, and fruitful area of research.

## Category theory

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

## BGSMath Postdoctoral Call 2017-2019

BGSMath opens two postdoctoral positions financed through the María de Maeztu Excellence project.

## Postdoctoral call Banco de Santander – María de Maeztu

Banco de Santander, within the framework of the agreement between the consortium Centre de Recerca Matemàtica (CRM) and Banco Santander…

## Postdoctoral fellowships 2016 from the EU P-SPHERE project

The European P-SPHERE project offers a 3 year postdoctoral fellowship on

“Geometrical Analysis and Partial Differential Equations…

## How does the heat equation explore geometric and functional inequalities?

The BGSMath Colloquium – Fall 2016 presents Michel Ledoux’s (Université de Toulouse) research: As is classical, the heat equation is a parabolic partial differential equation that describes the distribution of heat (or variation in temperature) in a given region over time.

## Open call for Ph.D. Positions (Mineco) 2016

7 PhD positions associated to BGSMath research projects are opened by the Spanish Ministry of Economy and Competitiveness.

## Heidelberg Laureate Forum

Young computer scientists and mathematicians from all over the world can apply for one of the 200 coveted spots to participate…

## Barcelona Analysis Conference 2016 (BAC16)

The BAC16 conference, from September 5 – 9, 2016, is a continuation of the BAC06 conference, held also in Barcelona in September 2006…

## 14th Workshop on Interactions between Dynamical Systems and Partial Differential Equations (JISD2016)

## 2016 IEEE International Symposium on Information Theory

The 2016 IEEE International Symposium on Information Theory will be held in Barcelona…

## Jornada Científica BGSMath

In June 8 took place the annual BGSMath Scientific Meeting. The external members of the Advisory Scientific Committee will be present at the meeting.

## II BGSMath Junior Meeting

BGSMath is a thriving community with many researchers from diverse areas of Mathematics. One of its most dynamic sections is that of Junior Researchers, …

## BGSMath doctoral call 2016-2019

BGSMath opens a call for 4 Ph.D. three-year positions in all areas of mathematics and its applications. Applications till May 13th, 2016.

## Call for BGSMath Monthly Programs

Convocatòria BGSMath d’ajuts per a Programes Mensuals de Recerca

## 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.

## BGSMath postdoctoral call 2016-2018

The Barcelona Graduate School of Mathematics opens a call for postdoctoral positions.

## I BGSMath Junior Meeting

The purpose of this workshop is to give the opportunity to young researchers and PhD students to present their current research in a friendly and collaborative environment.

## Rational points on elliptic curves

BGSMATH COLLOQUIUM – FALL 2015. After presenting the current news about BGSMath, a lecture given by Henri Darmon (McGill University).

## 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].

## MINECO doctoral call 2015

The aim of the contracts is to develop a doctoral training project in one of the research groups of the Barcelona Graduate School of Mathematics (BGSMath).

## Good Characterisations, Duality Theory, and Computational Complexity

The second BGSMath Colloquium was the starting point of the new BGSMath, after obtaining the excellence award Maria de Maeztu.

Speaker: Albert Atserias – UPC

Good Characterisations, Duality Theory, and Computational Complexity

## 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.

## Interactions of Harmonic Analysis, Combinatorics and Number Theory

The 3rd Barcelona Summer School on Stochastic Analysis will be held at the Centre de Recerca Matemàtica (Bellaterra, Barcelona)

## 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…

## Cédric Villani: Of triangles, gases, prices and men

The first BGSMath Colloquium presents a talk by Fields Medallist Cedric Villani (IHP, Paris)