BIMR 2024 - Barcelona Introduction to Mathematical Research

This new edition of the ‘Barcelona Introduction to Mathematical Research’ Summer School, now under the BGSMath aims to attract students in Mathematics (mainly in their 3rd or 4th year), from any University (in Barcelona or elsewhere).

The students will participate in the following activities:

• Working on a research project in Mathematics during the month of July. This will be done under the supervision of an Advisor/Tutor, and may consist of reading one or a few research papers (or book chapters), or working on a small open problem.
• Attendance to the Minicourses (4 short courses of 4 or 5 hours long) that will take place during the weeks of July 1-4 and 8-11. The courses are given by professors from catalan universities research centers covering a wide range of areas in mathematics. Still to be decided by the organization committee.
• Attendance to the Round Table: ‘Academic career in mathematical research: what to do and when’ and a General Public talk, that will take place during the afternoon in mid-July.
• Participation in weekly social events (coffee breaks during the minicourses, and one social pizza evening for each week of July).

This will be done under the supervision of a senior Advisor, and will consist of reading one or a few research papers (or book chapters) and/or working on a small open problem.

A committee will assign the students to their senior Advisors based on the preferences of both.

Each of these courses will be 4h or 5h long, and will take place at Facultat de Matemàtiques i Estadística de la Universitat Politècnica de Catalunya (FME).

Gissell Estrada | Universitat Politècnica de Catalunya

Title: From particle systems to collisional kinetic equations: An introduction

Núria Fagella | Universitat de Barcelona

Title: Exotic topology in complex dynamics.

Abstract: In this course we will discover exotic topological objects that appear naturally as invariant sets of holomorphic dynamical systems, like for example Cantor sets, Sierpinski carpets, indecomposable continua or Cantor bouquets among many others. To find them, we will introduce the basics of iteration of holomorphic maps on the complex plane and the surprising properties of its invariant fractals. 

Joaquim Ortega | Universitat de Barcelona

Title: Roots of random polynomials and random analytic functions.

Abstract: Motivated by the need to understand particles with a local repulsion, the following model has been proposed: Consider a polynomial with independent random coefficients and let us compute its zeros in the complex plane. This is easily simulated numerically.  The careful choice of random coefficients allows us to obtain a random distribution of zeros which are invariant under translations in the plane or Möbius transforms in the unit disk. We will study the interplay between complex analysis, probability, and potential theory.

Francesc Perera | Universitat Autònoma de Barcelona

Title: What is classification good for?

Abstract: We spend a lot of time trying to classify different objects, both in our life as well as when doing maths. In this minicourse, I intend to convey the basic idea at the core of classification theory. For example, what is a classifying category? What is a classifying functor? I will particularize these notions for a class of objects with a strong presence in both functional analysis and modern algebra. For said class, a program towards classification which began in earnest in the early 90s culminated recently with results that open up new avenues of research. I will explain the original invariant and variations of it that are currently being used.

• Round Table: ‘Academic career in mathematical research: what to do and when’.
• Weekly social events: coffee breaks during the minicourses, and a social pizza evening each week of July.

The CRM offers accommodation fellowships for the month of July for students who live outside the Barcelona metropolitan area.

The selection of applicants will be done based on:

• • CV.
  • Academic transcript.
  • Expression of interest letter.
  • Two recommendation letters. Professors can send Recomendation Letters to crmactivitats@crm.cat with the subject: BIMR recommendation letter for “name of student”

Applications will open: January/February 2024.
Application deadline: March 21st 2024.
Resolutions: April 15th 2024.
Summer Program: July 1st – July 26th 2024.

Olli Saari

Universitat Politècnica de Catalunya

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