## Barcelona Graduate School of Mathematics (BGSMath)

### 2023

### 2021

**Graduate Course:**

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)

**Colloquium:**

**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.

**Graduate Course:**

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

**Graduate Course:**

Fragments of algebraic graph theory

January 13 to March 25, 2021

This course will cover a variety of largely independent parts of algebraic graph theory. It is an intent to promote graphs to algebraists and algebraic tools to graph theorists. There will be classic results, famous open problems, and recent developments mostly from three big areas. The order is not precisely as below, but topics will also be mixed a bit. The sessions will be often independent, so selective presence is possible.

### 2019

**Graduate Course:**

**Starting day:** October 7, 2019.

**Last day**: January 23, 2020.

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

**Course Description:**

This is a basic and rather standard course on singular integrals -a topic of central importance in the areas of analysis and PDE’s. The course might be useful specially for analysts and PDE people, and also for probabilists.

**Graduate Course:**

**October 4th to November 29th, 2019**

**Lecturer**: Martí Lahoz and Joan Carles Naranjo, University of Barcelona

The main goal of this 20 hours course is to give an introduction to the theory of K3 surfaces, which is a rich and fundamental topic in algebraic geometry touching many other areas as arithmetic, complex and differential geometry, homological algebra, and even mathematical physics. Surfaces with trivial canonical bundle occupy a special place in the classification of 2-dimensional varieties. There are two types of such surfaces: Abelian surfaces and K3 surfaces. On the one hand, Abelian surfaces may be viewed as a straightforward two dimensional analogue of elliptic curves. In particular, Abelian surfaces have a commutative nontrivial fundamental group, while K3 surfaces arise as a new class of simply connected algebraic varieties. Namely, from the complex geometry point of view, they are the lowest dimensional examples of either hyperkähler manifolds or strict Calabi-Yau manifolds.

The course is organized as follows: in the first block we will provide some basics which are universal tools in many geometric theories: Kähler manifolds, sheaves and Hodge theory. In the second part we will focus in the classical theory of K3 surfaces which culminates in the famous Torelli theorem. Finally, depending of the interest of the audience, we will move to some more recent aspects, showing that the study of K3 surfaces has motivated the development of many powerful tools in each field.

**Graduate Course:**

**Date**: September 17th – December 18th, 2019

**Lecturer**: Martin Ziegler, Visiting Research Professor, University of Barcelona

**Course Description: **

This course is planned as a concise introduction to the classical theory of quadratic forms q over a field F of characteristic different from 2. We start with a detailed discussion of the fundamental theorems of Witt (1937). Then the main methods for the understanding of the Witt ring of a field will be discussed, as Pfister forms, Clifford algebras, the Brauer group, and Milnor’s K-theory. At the end, we will try to give an account of the Milnor conjecture, proved by Voevodsky in 1996.

There will be ten two-hour sessions during ten consecutive weeks. On the 17th of September, in a meeting with the registered people, a suitable schedule for the course will be agreed.

**Organizer**: Enrique Casanovas (Universitat de Barcelona)

**Junior Meeting:**

**BMS – BGSMath Junior Meeting 2019**

**Date**: 26 – 28 June 2019

**Location**: Zuse Institute Berlin (ZIB) (Berlin, Germany)

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.

In 2016, a memorandum of understanding was signed by both graduate schools in order to boost collaborative work between young researchers from both institutions. The schools declared their intention to cooperate together in initiatives aimed at promoting the mobility of and exchange between students and faculty members by way of events such as the Junior Meeting; joint summer schools; mutual visits by advanced students and postdocs of each institution; and other scientific activities.

The ultimate goal is to create strong scientific exchange, strengthen research collaboration between the respective math communities, and enhance the multicultural environment of both graduate schools. The First BMS – BGSMath Junior Meeting was held in Barcelona on 9 and 10 October 2017. The second Junior Meeting aims to intensify current collaborations and create new links between the two schools.

**Events:**

**Barcelona Analysis Conference 2019**

**Dates**: 25 – 28 June 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.

**Graduate Course:**

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.

**Graduate Course:**

**Sun Tzu approach to the Riemann Hypothesis**

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

**Organiser**: Eva Miranda (UPC-BGSMath)

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

**Events:**

**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.

**Graduate Course:**

**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)

**Graduate Course:**

**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.

**Graduate Course:**

**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

**Graduate Course:**

**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)

**Graduate Course:**

**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.

**Graduate Course:**

**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.

**Graduate Course:**

**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.

**Graduate Course:**

**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)

**Workshop:**

Frobenius Action in Commutative Algebra: Recent Developments.

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

IMUB, Barcelona, 16 – 18 January 2019

### 2017

**GRADUATE COURSES: ****Category Theory **

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

**MONTHLY PROGRAMS: ****Number Theory**

**January 23 to March 5, 2017**

*This intensive program on number theory 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.*

**GRADUATE COURSES: P-Adic Methods for Galois Representations and Modular Forms**

**January 30, 2017**

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

**GRADUATE COURSES: Arithmetic Properties of Curves of Small Genus**

**February 14, 2017**

*The course is an introduction to theoretical and computational aspects of curves of small genus as well as their Jacobians. One of the main goals is to discuss the algorithmic characterization for the decision problem on when two small genus curves are isomorphic, or when two Abelian varieties of small dimension are isomorphic or isogenous.*

**MENTORING SESSION: Dr. Joan Bruna**

*This is the first of a series of meetings addressed to BGSMath master and Ph.D. students and young researchers in order to be able to meet mathematicians who have delevoped a successful carrer and learn from their experience.*

**WORKSHOP: 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, as well as those working in related fields and/or other local organizations, to discuss ongoing research and strengthen the links of a growing network.*

**OTHER ACTIVITIES: What does a Quant do? BGSMath Seminar at UB**

*In this talk you will get information about this career path from an interest rate quant. We will talk about possible tasks and responsibilities, the skills you need for these jobs and myths about them.*

**COMPLEMENTARY TRAINING: Fundraising Module (Session 1)**

*BGSMath is starting a series of training modules addressed to the young researchers in the community, trying to help you develop complementary and transferable skills. This will include Communication/Presentation to diverse audiences, Fundraising and Proposal writing, and Knowledge Transfer Basics. *

**GRADUATE COURSES: Interactions of Harmonic Analysis, Combinatorics and Number Theory**

**April 25 to May 19, 2017**

*The main purpose of this course is to explore several applications of Fourier analytic techniques in number theory and combinatorics, as well as their interactions.*

**OTHER ACTIVITIES: Barcelona Mathematical Days. Congrés de la Societat Catalana de Matemàtiques**

*The Catalan Mathematical Society (SCM) invites participants to the second edition of the Barcelona Mathematical Days. This triennial Conference focusses on current research topics across several areas of Mathematics.*

**COMPLEMENTARY TRAINING: Fundraising Module (Session 2)**

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

**MONTHLY PROGRAMS: ****Random Discrete Structures and Beyond**

**May 22 to June 16, 2017**

*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, as well as early stage researchers on this active area.*

**GRADUATE COURSES: Algebraic and Combinatorial Phylogenetics**

**June 19 to July 3, 2017**

*The course will go from the basics of stochastic processes and combinatorial objects related to phylogenetics to the deep understanding of the reconstruction methods used nowadays and the new algebraic and combinatorial tools that are emerging in the field.*

**OTHER ACTIVITIES: Algebraic and Combinatorial Phylogenetics**

**June 26 to June 30, 2017**

*The course will go from the basics of stochastic processes and combinatorial objects related to phylogenetics to the deep understanding of the reconstruction methods used nowadays and the new algebraic and combinatorial tools that are emerging in the field.*

**COLLOQUIUM: Algebraic Geometry of Gaussian Mixtures/Instability Phenomena in the Restricted three body problem**

*Fifth BGSMath colloquium.*

**OTHER ACTIVITIES: Foundations of Computational Mathematics (FoCM)**

*Foundations of Computational Mathematics (FoCM) is an international nonprofit organization that supports and promotes research at the interface of mathematics and computation. It fosters interaction among mathematics, computer science, and other areas of computational science through conferences, events and publications.*

**OTHER ACTIVITIES: 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.*

**MONTHLY PROGRAMS: ** Algebraic and Combinatorial Phylogenetics

**June 19 to July 7, 2017**

*This BGSMath monthly program is the chance to make this interplay visible even from what is usually known as “pure mathematics” point of view and to benefit from the top level bioinformatics community in Barcelona. *

**COMPLEMENTARY TRAINING: How to talk Mathematics: Oral Communication Skills Masterclass**

*Inspired by Halmos’s advice, BGSMath organizes this session addressed to all young researchers in mathematics willing to improve their oral communication skills.*

**OTHER ACTIVITIES: Topics in Complex Dynamics 2017**

*This is the seventh edition of the school “Topics in complex dynamics” at Universitat de Barcelona organized by the group of holomorphic dynamics (HoloDyn).*

**COMPLEMENTARY TRAINING: Introduction to Responsible Research and Innovation (RRI)**

*The talk will provide us with ideas to plan and execute scientific research taking into account aspects such as accountability and transparence, through the application of open science/open software/open data approaches, think of more and better interaction with society at large, and manage diversity in research teams and organizations.*

**JUNIOR MEETINGS: BMS – BGSMath Junior Meeting**

*The Berlin Mathematical School and the Barcelona Graduate School of Mathematics both share the goal of striving for excellence in their doctoral and postdoctoral training. In order to further the collaboration between these two graduate schools, their first joint meeting of the junior researchers will be held in Barcelona in October of 2017.*

**COLLOQUIUM: Hyper-Kähler Geometry**

*UPC-BGSMath Colloquium.*

### 2015

**GRADUATE COURSES: ****Information Theory**

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

**COLLOQUIUM: Good Characterisations, Duality Theory and Computational Complexity**

**May 19, 2015**

*The second BGSMath colloquium was the starting point of the new BGSMath, after obtaining the excellence award Maria de Maeztu. From now BGSMath will have one colloquium per semester. On this occasion we had the pleasure to listen to Albert Atserias, form UPC.*

**GRADUATE COURSES: 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]. The non-commutative variety of this had already been anticipated in linguistics thirty years earlier [Lambek 1958]. Recently this convergence of mathematical logic and linguistics has consolidated in a particular categorial logic for syntax and semantics, which it is the objective of this course to present.*

**GRADUATE COURSES: Algorithmic Group Theory**

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

**COLLOQUIUM: Rational Points on Ellipctic Curves**

*Third BGSMath colloquium. After presenting the current news about BGSMath, there was a lecture given by Henri Darmon (McGill University), entitled Rational points on elliptic curves.*

**JUNIOR MEETINGS: 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.*

### 2013

**COLLOQUIUM: Cédric Villani: Of triangles, gases, prices and men**

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

**GRADUATE COURSES: A course on Dynamical Systems**

**September 26, 2013**

*The lectures will be chosen among the following list of topics, according to the interests and backgrounds of the students and adapting them to the list of short courses on nearby topics given in the Math centers of the Barcelona area.*

**GRADUATE COURSES: ****Random Structures and the probabilistic method**

**September 29 to December 19, 2013**

*The course provides an introduction to these methods, whose common theme is the use of the language of probability and the analysis of random structures and processes to derive results about deterministic structures.*

### 2022

**Graduate Course:**

BMS-BGSMath Junior Meeting 2022

**Date**: 5-7 September, 2022

**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.

**Summer School:**

BARCELONA INTRODUCTION TO MATHEMATICAL RESEARCH: 2022 SUMMER PROGRAM

FROM JULY 04, 2022 TO JULY 29, 2022

This will be the first ‘Barcelona Introduction to Mathematical Research’ Summer Program organized by CRM-UB with professors from UB-UAB-UPC-CRM, which aims to attract students in Mathematics (mainly in their 3rd or 4th year) from any university (in Barcelona or elsewhere).The program will consist of a research project, four minicourses and other activities.

**Graduate Course:**

An Invitation to p-adic Methods in Number Theory

**Dates**: From March 22nd (9 lectures)

Location: Facultat de Matemàtiques i Informàtica. Universitat de Barcelona

**Lecturers:**

Xavier Guitart (Universitat de Barcelona)

Marc Masdeu (Universitat Autònoma de Barcelona)

Santiago Molina (Universitat Politècnica de Catalunya)

**Graduate Course:**

Introduction to Fluid Mechanics

**Dates:** Feb 14, 2022

Monday and Wednesday

From February 14th (about 15 weeks)

**Location: **Aula T1, Edifici històric, Universitat de Barcelona

**Speakers:**

Claudia García (UB), Eduardo García-Juarez (UB), Javier Gómez-Serrano (UB) and Jaemin Park (UB)

**Graduate Course:**

Chaotic behavior, Invariant Manifolds and Exponentially Small Phenomena in Dynamical Systems

**Dates**:

Tuesdays and Thursdays

From February 1st (6 weeks)

**Location**

Aula 103, Facultat de Matemàtiques i Estadística, Universitat Politècnica de Catalunya,

**Lecturers**

Marcel Guardia (UPC) and Tere Seara (UPC)

### 2020

**Colloquium:**

**BGSMath – BCAM Colloquium 2020**

**Title**: Mean estimation: statistical and algorithmic problems –

by Gábor Lugosi (UPF)

**Abstract**:

We discuss the perhaps most basic problem of statistics: how can one estimate the expected value of a random variable from a sample of independent copies? We argue that the usual empirical mean is far from being optimal and we survey various alternatives and their performance guarantees. The multivariate case presents interesting challenges, both statistical and algorithmic. The talk is based on joint work with Shahar Mendelson.

**Title**: An introduction to time series mining –

by José Antonio Lozano (BCAM)

**Abstract**:

In this talk we will give an overview on time series mining. Particularly we will concentrate on classical problems in data mining such as clustering, supervised classification and outlier (anomaly) detection. For these problems we will emphasise the differences between working with time series or regular vectors. In addition to that we will present new problems that appear in the area of data mining when working with time series and also point out to the complexity of working with time series streams.

**Graduate Course:**

**Quantum Error-Correcting Codes**

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

**Course Description**

### 2018

**OTHER ACTIVITIES: **** International Day of Women and Girls in Science 2018**

*BGSMath and the Societat Catalana de Matemàtiques have jointly decided to organise a special event at the Institut d’Estudis Catalans in Barcelona to visualise successful female mathematicians and their research that has an impact on our everyday’s lives.*

**GRADUATE CURSES: ****Maths for insdustry 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, such as industrial doctoral theses, as well as the range of expertise you could benefit from.*

**GRADUATE CURSES: **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. *

**OTHER ACTIVITIES: **Intensive Research rogramme: Recent Progress in Mathematical Biology

*The aim of this programme is to bring together experts from different areas of Mathematical Biology (neuroscience, tumour modelling, population dynamics,…) which have developed different methods trying to address the new challenges in their associated areas of biological and biomedical research.*

**COLLOQUIUM: **UAB-BGSMath Colloquium: Topological vistas in Neuroscience

*The talk will include an overview of the Blue Brain Project and a brief introduction to the topological tools used.*

**GRADUATE COURSES: **An Introduction to Parameterized Complexity ntensive research programme: Recent Progress in Mathematical Biology

*The key idea is to study the different ways key secondary parameters may be interleaved with input size in the computational complexity of algorithms.*

**OTHER ACTIVITIES: **Intensive research programme: Discrete, Combinatorial and Computational Geometry

*This intensive research program will consist of8 weeks of activities focused on hot topics in discrete, combinatorial and computational geometry and their intricate relationships. The program will bring together leading researchers from all over the world to work on open problems, and to analyze its present state and perspectives.*

**COMPLEMENTARY TRAINING: **Applying for Postdoctoral Positions. Writing your First Research Proposal

*During this seminar, we will start by reviewing the academic career path from your PhD thesis until tenure, and what being a “postdoc” actually means. *

**MONTHLY PROGRAMS: **Geometric Function Theory in Fluid Mechanics

We are holding a research program on “Geometric function theory in fluid mechanics”. Our objective is to put together two communities apparently disconnected, and settle common interests and goals.

**OTHER ACTIVITIES: **XXIX International Biometric Conference

*The International Biometric Society’s (IBS) International Biometric Conference (IBC) offers a very robust scientific programme for anyone with an interest in biometry.*

**COMPLEMENTARY TRAINING: **Fundraising and Writing Research Proposals: The IF MSCA Example

*These 2 two-hour sessions aim to showing you to identify funding opportunities suitable for mathematics-related projects (“Where to find the money”), and give you tools to formulate winning proposals in competition with other people who want them (“How to get it”).*

**GRADUATE COURSES: **4th Barcelona Summer School on Stochastic Analysis: A 2018 EMS Summer School

*The Barcelona Summer School on Stochastic Analysis is a one-week scientific activity consisting mainly of courses addressed to PhD students and young researchers on current research topics in Stochastic Analysis.*

**COLLOQUIUM: **BGSMath Summer Colloquium 2018

*BGSMath Summer Colloquium 2018.*

**COMPLEMENTARY TRAINING: **Fundraising and Writing Research Proposals: The IF MSCA Example (II Session)

*These 2 two-hour sessions aim to showing you to identify funding opportunities suitable for mathematics-related projects (“Where to find the money”), and give you tools to formulate winning proposals in competition with other people who want them (“How to get it”).*

**GRADUATE COURSES: **Complex Dynamics and Applications

*An introduction to complex dynamics, aimed to survey its recent applications to statistical mechanics and the related open problems. A good portion of this course will be dedicated to review the classical theory of dynamics in one complex variables, initiated by Fatou and Julia.*

**COMPLEMENTARY TRAINING: **Innovation Inspirational Talk: BGSMath and the Collider

*The program is structured in two phases, an initial opportunity identification and validation phase and a venture building second phase. *

**OTHER ACTIVITIES: **Formae Mathematicae – Les Formes de les Matemàtiques – Shapes of Mathematics

*BGSMath participates in the European Researchers’ Night 2018 with an initiative designed by Marina Garrote and Alessandro Oneto. They will guide us in a mathematical tour in the evocative location of the Dipòsit del Rei Martí, in Barcelona, just next to the Bellesguard Tower, designed by the renowned architect Antoni Gaudí.*

**OTHER ACTIVITIES: **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.*

**JUNIOR MEETINGS: BGSMath Junior Meeting**

*The Barcelona Graduate School of Mathematics is organizing its fourth BGSMath Junior Meeting. 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.*

**OTHER ACTIVITIES: Barcelona Weekend on Operator Algebras**

**OTHER ACTIVITIES: A Theory of Spectral Clustering**

**COLLOQUIUM: **BGSMath Autumn Colloquium 2018: Chasing Finite Shadows of Infinite Groups

*An introduction to complex dynamics, aimed to survey its recent applications to statistical mechanics and the related open problems. A good portion of this course will be dedicated to review the classical theory of dynamics in one complex variables, initiated by Fatou and Julia.*

**COMPLEMENTARY TRAINING: **Training Session on Open Science and Open Acces

*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.*

### 2016

**GRADUATE COURSES: ****Symplectic Techniques in Dynamical Systems and Mathematical Physics**

*This is a course on Symplectic Geometry and Topology with an eye towards applications in Hamiltonian Dynamics. *

**GRADUATE COURSES: ****A Primer on K-Theory and its Applications**

**February 22, 2016**

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

**JUNIOR MEETINGS: II 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.*

**SCIENTIFIC DAY: Jornada Científica BGSMath**

*Annual BGSMath Scientific Meeting.*

**GRADUATE COURSES: ****2016 IEEE Internatial Symposium on Information Theory**

**July 10-15, 2016**

**WORKSHOP: Interactions Between Dynamical Systems and Partial Differential Equations (JISD 2016)**

*This meeting is organized every year and provides a working enviroment for the interaction between researchers in the areas of dynamical systems and PDEs. There will be four main courses of six hours each, some seminars, communications, and posters.*

**CONFERENCE: Barcelona Analysis Conference 2016 (BAC16)**

*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.*

**OTHER ACTIVITIES: Fourth Heidelberg Laureate Forum**

*Young computer scientists and mathematicians from all over the world can apply for one of the 200 coveted spots to participate in Heidelberg Laureate Forum (HLF), an annual networking event.*

**COLLOQUIUM: How does the Heat Equation Explore Geometric and Functional Inequalities?**

*Fourth BGSMath colloquium.*

### 2014

**GRADUATE COURSES: ****Partial Differential Equations**

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

**GRADUATE COURSES: Homology in Algebra and Geometry**

**Spring 2014**

*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.*

**GRADUATE COURSES: Lie groups and bundles**

**September 22, 2014**

*Both Lie groups and line bundles are transversal tools that are used in many mathematical fields. We start from a geometrical point view, but the course provides basic tools for students interested in algebraic and differential topology, algebraic geometry and mathematical physics.*

**GRADUATE COURSES: Computational tools for Number Theory and Algebra**

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

**GRADUATE COURSES: Interactions of Harmonic Analysis, Combinatorics and Number Theory**

*The 3rd Barcelona Summer School on Stochastic Analysis is a biennial one-week activity that started in the year 2012. The core programme consists of two courses, 10 hours each, addressed mainly to PhD students and young researchers, on topics in Stochastic Analysis at the forefront of current research. A selected group of participants are given the opportunity to deliver short talks or to display posters as a complement of the daily morning training programme.*