ICMAT Newsletter #18 First semester 2019 CSIC - UAM - UC3M - UCM EDITORIAL A new year has begun, and another has come to an end, which makes us especially aware of the ICMAT as a “home for mathe- matics” that is open to the international community. This News- letter contains information about some of the most interesting results that have recently been obtained at the Institute. How- Image: ICMAT. ever, it is also worth pointing out that the influence of a centre like the ICMAT is not confined to a mere list of its publications and its members, but will always extend to cover all the results, projects and collaborations that originate in our facilities and go on to bear fruit later, very often far from where they started. The prime objective of the ICMAT is mathematical research, arising from the stimulus of that original thought which produces deci- sive advances in science, enriching our knowledge of nature and leading to applications that were frequently once unimaginable. Appointments for the next four years of new faculty members be- Antonio Córdoba. longing to the three universities of the Institute were completed in January, with the ratification of the Steering Committee for the proposal drawn up by the Joint Committee (consisting of the three universities and the CSIC), and which had already received approv- CONTENTS al from the Governing Board of the ICMAT. We welcome these new members and congratulate those renewing their membership of Editorial: Antonio Córdoba (ICMAT)........................1 the Institute. There is no doubt that their abilities, good work and Report: The Theory of Moduli Spaces: dedication will help the ICMAT continue to advance, with an excit- The Treasure Map....................................................3 ing project which this year includes the application for the third Severo Ochoa Centre of Excellence award. We are fully justified in Interview: Xenia de la Ossa and Philip Candelas feeling optimistic for its renewal, especially because of the enthu- (Oxford University)..................................................7 siastic and favourable report we have received from the external ICMAT Questionnaire: Frances Kirwan Scientific Committee appointed by the Ministry of Science, Innova- (Oxford University)..................................................9 tion and Universities. However, we take this application very seri- ously, since the Severo Ochoa funding is vital for maintaining the Scientific Review: A resolution of Guth’s conjecture activities of the Institute. regarding the Kakeya problem on algebraic varieties...............................................................11 The appointment process as set out in the statutes has revealed an ostensible lack of symmetry between the CSIC and the three Scientific Review: “Global solutions for the universities (UAM, UCM and UC3M). This is an important matter surface quasi-geostrophic equation”....................12 that should be addressed again when the statutes and the part- She Does Maths: Makrina Agaoglou (ICMAT)........13 nership agreement come up for revision. This asymmetry is also clear in the amount of red tape from the CSIC that the Institute Portrait: Diego Alonso Orán (ICMAT).....................14 has to deal with, which far exceeds the administrative formalities Interview: Ali Nelsin (Leelavati Prize 2018 for required of the other three institutions. The recent restructuring of public outreach in mathematics).........................15 the divisions in the CSIC is also a cause for concern, since there is no mathematician on the Commission that affects us directly and Tell me about your thesis: Víctor Arnaiz Solórzano is charged with decisions concerning new posts and resources. (ICMAT) ................................................................17 This has revived some ghosts from the past, when we lacked any ICMAT News.........................................................19 mathematical interlocutor on the commission. Negotiations with the CSIC Board have failed to yield a solution, a situation we made Agenda.................................................................25 clear during the visit to the Institute by the coordinators of the area and the associate vice-president of research on February 5th. 1 (Continued on the next page) (Continued from the previous page) Since its creation, the ICMAT has belonged by right to the fact that the status we enjoy imposes its own restrictions. The SOMMA (Severo Ochoa and Maria de Maeztu) network of insti- ICMAT seal requires that whoever is involved in outreach must tutions that have received funding through these two projects speak with due authority, and have a thorough knowledge of a of excellence. The network is an interesting club whose aim, subject when writing about it, while taking care to make it acces- among others, is to act as a lobby for science and as an inter- sible to the public at large and putting it across with a modicum locutor for the Ministry. It is a mouthpiece for the expression of of originality. informed opinion and for putting forward measures to improve Finally, the body: the transfer of knowledge. According to a fairly the management of these institutes, a task that is indispensa- generalized opinion, we are on the threshold of a fourth industrial ble for enabling us to compete in better conditions in the world revolution in which the word “algorithm” is the key, and in which league of science. In the hypothetical pyramid of mathematics the centaur consisting of a mathematician with his or her com- in a country, research occupies the upper vertex; the main base puter is perhaps the most highly evolved specimen of contempo- is education and the body the transfer of knowledge. The in- rary technology. This explains the demand for mathematicians terrelation and communication between these three strata are and computer scientists by industry, medical facilities, financial fundamental for the health of the system. The ICMAT finds its entities, security firms, telephone companies and large shopping natural niche on this vertex, and I believe we can say with pride centres. The change in the quality of students who reach degree that we have performed very well. We have shown ourselves level in mathematics has been both spectacular and highly pos- to be adept at resolving conjectures that have been the object itive. The same may be said of a numerous collective of math- of mathematical desire, at producing good theorems that have ematicians with a sound background in the discipline, capable been published in the best journals, and at successfully obtain- of undertaking such tasks, contributing with their knowledge to ing competitive projects from the Ministry, the ERC and the Eu- improve the running and competitiveness of business and com- ropean Commission. panies, and forming part of their necessary advisory bodies in There is no doubt that the base of education is vital: together with matters of research and development. the study of one’s own language, mathematics plays a crucial role The prosperity of the country depends on these things. So, what in general education. It is precisely through elementary arithme- part should a centre like the ICMAT play in these affairs? This tic and geometry that deductive reasoning can best be taught, is an important question about which it seems to me that our and thus install an operational system in the human brain. This faculty should pause to take stock and test its strengths. Math- is a difficult task that requires a great deal of support, both in the ematical problems stemming from the business sector pose production of appropriate texts and in raising society’s aware- real intellectual challenges; they constitute an incentive for the ness of the important role played by mathematics. The ICMAT is quality mathematical research that is our raison d’ tre and are itself committed to this valuable task. By means of our Commu- ê undoubtedly always welcome. The work of the ICMAT in all these nication Bureau, we collaborate with initiatives such as “Café y areas promises to be of great importance in the coming years. Teoremas” in the El País daily, or with the “Mi científica favorita” project, funded in part by the FECYT. We have also participated in the production of books as back-up material for Secondary Ed- Antonio Córdoba, ICMAT director and Professor in Analysis ucation, in collaboration with Spanish Federation of Societies of at Universidad Autónoma de Madrid. Teachers of Mathematics. It is important not to lose sight of the Image: ICMAT. 2 ICMAT Newsletter #18 First semester 2019 REPORT: The Theory of Moduli Spaces: The Treasure Map A thematic trimester devoted to the so-called theory of moduli spaces, organized by the ICMAT Donaldson-Hitchin Laborato- ry, was held at the Institute at the end of 2018. This field, the origins of which date from the middle of the 19th century with the work of the German mathematician, Bernard Riemann, is of great interest for solving problems in algebraic geometry, differential geometry and topology. It also has profound connections with quantum field theory and other areas of theoret- ical physics. “Moduli spaces are at the heart of classification problems in algebraic geometry. They are also related to the idea of quantization, which is a universal concept, and for that reason they are extremely useful”, says ICMAT researcher, Mario García-Fernández, who is our guide to this incursion into the world of moduli spaces. Ágata Timón García-Longoria. Classification is