Roger Casals, University of California

19 / 12 / 2024 - 12:15

Location: T1

Títol: Topologia simplèctica i de contacte

Abstract: La topologia simplèctica i de contacte neix de l’estudi de diversos fenòmens físics, incloent-hi l’evolució dels fronts d’ones, les lleis de la termodinàmica i l’estudi d’òrbites periòdiques en sistemes dinàmics. En aquesta xerrada, motivarem i discutirem la classificació de varietats Lagrangianes, un dels problemes oberts més centrals de l’àrea. Mitjançant exemples il·lustratius i intuïcions geomètriques, explicarem els desenvolupaments més recents en aquesta classificació. En aquest trajecte, veurem com la topologia simplèctica i de contacte connecta amb altres àrees de les matemàtiques i es pot emprar per resoldre conjectures que semblen ser llunyanes. En particular, presentarem la resolució recent d’una conjectura important dins àlgebra commutativa i com aquesta nova connexió també ha donat lloc a noves preguntes i conjectures dins de geometria i topologia.

Short Bio: Roger Casals és un matemàtic especializat en geometria i topologia. Llicenciat en matemàtiques per la Universitat Politècnica de Catalunya, obtingué el seu màster de matemàtiques a la Universidad Complutense de Madrid i el seu doctorat a la Universidad Autónoma de Madrid i l’Instituto de Ciencias Matemáticas (ICMAT-CSIC). Actualment és catedràtic a la facultat de matemàtiques de la Universitat de Califòrnia Davis. Les seves contribucions a la topologia simplèctica i de contacte han estat reconegudes amb diversos premis, incloent el Premi José Luis Rubio de Francia, el Premi Vicent Caselles, la Sloan Fellowship i un NSF Career award.

Francisco Santos, Universidad de Cantabria

16 / 10 / 2024 - 12:15

Location: T1

Title: The space of Delzant polytopes

Abstract: A Delzant polytope is a simple polytope with rational edge directions and such that all its vertex cones are unimodular. Equivalently, it is a polytope with a rational, simplicial, unimodular normal fan. Their name comes from a theorem of Delzant, stating that these polytopes are precisely the momentum polytopes of symplectic toric manifolds. Delzant polytopes are also important in toric algebraic geometry, since their normal fans are the fans of smooth projective toric varieties.

We explore the space of Delzant polytopes of a given dimension $n$ from both a discrete and a continuous perspective:

– In the first one we look only at their fans and connect them via «blow-ups/blow downs», that is, via unimodular stellar refinements/coarsenings.

– In the continuous perspective we consider Delzant polytopes as a subspace of the metric space of full-dimensional $n$-polytopes, with respect to either the Hausdorff distance or the symmetric-difference distance. These distances are not metrically equivalent (e.g., they produce two different completions) but they are topologically equivalent.

In both perspectives we show drastic differences between the cases $n=2$ and $n=3$.

The talk is based in joint work with Álvaro Pelayo.

Matthew Dean Foreman, University of California

06 / 06 / 2024 - 12:15

Location: Aula Magna

Títol: Impossibility results in Mathematics

Abstract: Impossibility results have played an important role in mathematics, from questions like solutions of polynomials, the word problem in group theory to non-measurable subsets of [0,1]. This talk will present new impossibility results about classical problems in dynamical systems and ergodic theory. They answer questions dating to Poincaré and others asked by von Neumann and Smale.

Biography: Matthew Foreman was born in Los Alamos, New Mexico, got his undergraduate degree from University of Colorado and his Ph.D. at Berkeley in 1980. His thesis supervisor was Robert Solovay. He is currently a Distinguished Professor of Mathematics at the University of California, Irvine.
His main work is in two areas: Set Theory and Ergodic Theory. In Set Theory his interests lie in generic versions of large cardinals and other axioms that settle classical questions such as the continuum hypothesis. He was a pioneer in applying descriptive set theory to classical problems in ergodic theory, settling several questions asked by Halmos and von Neumann. This has led to a growing subject and has spread to work in smooth dynamical systems.
Foreman is also an avid sailor, having sailed across both the Atlantic and Pacific and on a chartered boat around Cape Horn.

Kristian Seip Norwegian University of Science and Technology – NTNU

17 / 04 / 2024 - 12:15

Location: T1

Títol: Fourier interpolation and the uncertainty principle

Abstract: A new direction of research in analysis, known as Fourier interpolation, has emerged from a celebrated 2019 paper of Radchenko and Viazovska which was an outgrowth of the solution to the sphere packing problem in dimension 8. I will give an overview of this and subsequent developments, with emphasis on a connection with the zeros of the Riemann zeta function. I will comment briefly on Freeman Dyson’s idea to approach the Riemann hypothesis by describing all one-dimensional quasicrystals.

Biography: Kristian Seip (1962) obtained his doctor’s degree at the Norwegian Institute of Technology in 1988, and became a professor in 1994. He was an invited speaker at the International Congress of Mathematicians in Berlin in 1998.
Seip chaired the Norwegian Mathematical Society from 2003 to 2007 and the committee that awards the Abel Prize from 2007 to 2010. He is a member of the Norwegian Academy of Science and Letters and the Royal Norwegian Society of Science. In 2012 he became a fellow of the American Mathematical Society.
His research areas are currently operator related function theory and analytic number theory.

Colloquium to celebrate the 100th anniversary of Albert Einstein’s visit to Catalonia.

20 / 12 / 2023 - 12:15

Contact: Xavier Jarque | Location: T1

On December 20th, 2023, we will have an (extraordinary) colloquium to celebrate the 100th anniversary of Albert Einstein’s visit to Catalonia.

The event will consist of two talks on Einsteien’s work and his historical visit to Barcelona and Catalonia. The talks will be in Catalan.

12.15 – 12.55 Emili Elizalde (CSIC), «Una visió contemporània i actual de les teories de la relativitat i la visita d’Einstein a la Catalunya de 1923»

13.00 – 13.40 Ignasi Mundet (Universitat de Barcelona), «Relativitat general: de l’equació del camp gravitatori a la conjectura de Poincaré i més enllà»

Lorenzo Zambotti, Laboratoire des Probabilités, Statistique et Modélisation. Sorbonne Université

22 / 05 / 2024 - 12:15

Location: T1

Title: The revolution of patwhise stochastic analysis

Abstract.

Stochastic analysis was created by Itô in the 40s and this approach dominated the theory of stochastic processes until the end of the 20th century. In the last 25 years a series of new ideas has enriched this theory and allowed spectacular progresses, notably in the study of stochastic partial differential equations. The main techniques in this new wave of research are rough paths, the sewing lemma, regularity structures, paracontrolled distributions. Among others, the people who have driven this activity are Terry Lyons, Massimiliano Gubinelli and Martin Hairer.
In this talk I want to explain the main ideas of this line of research, in particular the new notion of pathwise stochastic integration and the crucial definition of a product between a Schwartz distribution and a function.

Biography. Lorenzo Zambotti has graduated at the Scuola Normale Superiore (SNS, Pisa) under the supervision of Giuseppe Da Prato, and has held positions in SNS, in Politecnico di Milano and in Université Pierre et Marie Curie (now Sorbonne Université) in Paris, since 2006. He studies stochastic partial differential equations (SPDEs), in particular in connection with fine properties of Brownian motion and Bessel processes, and more recently he has contributed to the general theory of regularity structures and the renormalisation of singular SPDEs.

Javier Fresán, Institut de Mathématiques de Jussieu-Paris Rive Gauche. Sorbonne Université

21 / 02 / 2024 - 12:15

Location: T1

Gabor Lugosi (Universitat Pompeu Fabra, Barcelona)

25 / 10 / 2023 - 12:15

Location: T1

Title: Mathematical models of network archaeology

Abstract: Large networks that change dynamically over time are ubiquitous in
various areas such as social networks,
and epidemiology. These networks are often modeled by random dynamics
which, despite being relatively simple,
give a quite accurate macroscopic description of real networks. In
«network archaeology» one studies statistical
problems of inferring the past properties of such growing networks,
given the current state of the network. In this
talk we discuss some simple network models and review recent results
on revealing the past of the networks.

Brief Bio: Gabor Lugosi is an ICREA research professor at the Department of Economics of the
Pompeu Fabra University in Barcelona. His main research interests
include statistical, learning theory, sequential prediction, nonparametric classification
and regression, random graphs, and concentration inequalities.
He has published four research monographs and over 120 papers on these topics.

In 2021, Lugosi delivered the “Breiman lecture» at NeurIPS, the prime conference on Machine Learning,
and was an invited speaker in the newly created Statistics section at the 2022 International Congress of Mathematicians.

He has also been “Medallion Lecturer” and “Blackwell lecturer” in conferences organized by the Institute of Mathematical Statistics.

Alberto Enciso (ICEMAT-CSIC)

22 / 03 / 2023 - 12:00

Contact: http://www.imub.ub.edu/next-colloquium/ | Location: Room T1

Speaker: Alberto Enciso

Affiliation: ICEMAT-CSIC

Title: Water under a bridge: the interplay between analysis and geometry in the study of incompressible fluids

Abstract: It is well known that many high profile problems in the theory of partial differential equations in general, and in fluid mechanics in particular, are of a strongly geometric nature. Our goal is to discuss some problems of this kind. As we will see, their dual character makes them particularly attractive, and their solution frequently involves a rich (and at times surprising) interaction between various areas of mathematics.

Brief Bio: 

Étienne Ghys (École Normale Supérieure de Lyon)

03 / 05 / 2023 - 12:10

Contact: http://www.imub.ub.edu/next-colloquium/ | Location: T1

Speaker: Étienne Ghys

Affiliation: École Normale Supérieure de Lyon

Title: The group of homeomorphisms of the sphere

Abstract: In 1935 Ulam conjectured that the component of the identity in the group of homeomorphisms of the sphere is a simple group (no non-trivial normal subgroup). Today we know that this is indeed the case but since that time many similar problems have been solved. But the question concerning area respecting homeomorphisms has resisted for forty years. To my great surprise, D. Cristofaro-Gardiner, V. Humilière and S. Seyfaddini have shown recently that the corresponding group is not simple. I would like to tell the story of this mathematical adventure, from 1935 to 2023.

Brief Bio: