### 2023

**Summer Programme**

Barcelona Introduction to Mathematical Research (BIMR 2023)

July 3-28, 2023

**BGSMath Training for PhD Candidates:**

**Organizing and Structuring a Science Article**

March 21st, 2023

**BGSMath Training for PhD Candidates:**

**Latex: Tips and Tricks**

March 16th, 2023

**BGSMath Training for PhD Candidates:**

**DOs and DON’Ts about Giving Math Talks**

March 16th, 2023

**Masterclass Outreach BGSMath:**

**How to Speak about Mathematics to Broad Audiences**

March 6th, 2023

**Graduate Course:**

Stallings Automata and Applications

**Date**: January 17 – February 16, 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

**COLLOQUIUM**

**Hyper-Kähler Geometry**

November 29, 2017

**JUNIOR MEETINGS:**

**BMS – BGSMath Junior Meeting**

October 9 to October 10, 2017

**COMPLEMENTARY TRAINING:**

**Introduction to Responsible Research and Innovation (RRI)**

September 28, 2017

**OTHER ACTIVITIES:**

**Topics in Complex Dynamics 2017**

October 2 to October 6, 2017

##### GRADUATE COURSES

##### Category Theory

January 10, 2017

##### MONTHLY PROGRAMS

##### Number Theory

January 23 to March 5, 2017

##### GRADUATE COURSES

##### P-Adic Methods for Galois Representations and Modular Forms

January 30, 2017

##### GRADUATE COURSES

##### Arithmetic Properties of Curves of Small Genus

February 14, 2017

##### MENTORING SESSION:

##### Dr. Joan Bruna

February 21, 2017

##### WORKSHOP:

##### 1st BGSMath Data Science Workshop

February 22, 2017

##### OTHER ACTIVITIES:

##### What does a Quant do? BGSMath Seminar at UB

March 22, 2017

##### COMPLEMENTARY TRAINING:

##### Fundraising Module (Session 1)

April 4, 2017

##### GRADUATE COURSES:

##### Interactions of Harmonic Analysis, Combinatorics and Number Theory

April 25 to May 19, 2017

##### OTHER ACTIVITIES:

##### Barcelona Mathematical Days. Congrés de la Societat Catalana de Matemàtiques

April 27 to April 28, 2017

##### COMPLEMENTARY TRAINING:

##### Fundraising Module (Session 2)

May 12, 2017

##### MONTHLY PROGRAMS:

##### Random Discrete Structures and Beyond

May 22 to June 16, 2017

##### GRADUATE COURSES:

##### Algebraic and Combinatorial Phylogenetics

June 19 to July 3, 2017

##### OTHER ACTIVITIES:

##### Algebraic and Combinatorial Phylogenetics

June 26 to June 30, 2017

##### COLLOQUIUM:

##### Algebraic Geometry of Gaussian Mixtures/Instability Phenomena in the Restricted three body problem

June 29, 2017

##### OTHER ACTIVITIES:

##### Foundations of Computational Mathematics (FoCM)

July 10 to July 19, 2017

##### OTHER ACTIVITIES:

##### RET Summer School on h-Principles

July 10 to July 19, 2017

##### MONTHLY PROGRAMS:

##### Algebraic and Combinatorial Phylogenetics

June 19 to July 7, 2017

##### COMPLEMENTARY TRAINING:

##### How to talk Mathematics: Oral Communication Skills Masterclass

September 28, 2017

### 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

**Junior Meeting:**

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

**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

**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!

**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

**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.

**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.

**Writing your first research proposal**

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

**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.

**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.

### 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.*