Hitzaldi Nagusiak

RSMEren Ikertzaile Gazteen VII. Kongresuan, zazpi hitzaldi nagusiak nazio eta nazioarteko izen handiko matematikariek emango dituzte. Hitzaldi nagusiak ingelesez izango dira. Hitzaldi nagusi bakoitzak Bilboko Alde Zaharreko zazpi kaleen izena du.

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“Goienkale” Hitzaldi Nagusia

Astelehena 13, 11:30
[Bizkaia Aretoaren Mitxelena Entzunaretoa]

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Topologia sinplektioa, dinamika, eta fluido idealak

Originating in the works of Poincaré at the end of the XIX century, dynamical systems and symplectic (and contact) topology are two disciplines of mathematics that first developed in a rather independent way. In the last two decades, "Symplectic dynamics" has become a flourishing new field on its own that integrates ideas of these two classical disciplines. In this talk, we first give an accessible overview of some ideas and recent developments in this theory. We will explore its connections to hydrodynamics, and propose a new framework that links contact topology and symplectic dynamics to the study of the time-dependent Euler equations for ideal fluid motion on three-manifolds. The latter is based on joint work with Francisco Torres de Lizaur.

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MSC Kodigoak: 57K43; 57K33; 37J06; 35Q31

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“Artekale” Hitzaldi Nagusia

Asteartea 14, 9:30
[UPV/EHUren Areto Nagusia]

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Optimizazio matematikoa gainbegiratu gabeko ikaskuntzarako, datuz beteriko mundu batean

Decision-making is present in many areas such as location, planning, network design, finance, transport, and more. Making good decisions (ideally, the best ones) is crucial in these fields. In decision processes, Operations Research (OR) offers the theories and tools needed to make better decisions. Among all the theories in OR, Mathematical Optimization leads to optimal choices. Since we live in a data-driven world, many decisions today involve the use of data. Clustering is a data analysis technique used to identify groups or clusters within a dataset, serving as a key tool to facilitate the decision-making process in various areas. Hierarchical clustering is a clustering method that builds a hierarchy of groups. It groups data points into a nested tree of clusters, which is visualized as a dendrogram. Different definitions of the distance between two clusters (known as linkages) lead to different dendrograms. Dendrograms are constructed by running iterative greedy algorithms.

In this talk, three optimization models for hierarchical clustering will be considered. First, the problem of Feature Selection in Single-Linkage Clustering is addressed via Mixed Integer Linear Programming (MILP) formulations. Second, MILP approaches will be developed for computing the purity of a dendrogram. Purity is a measure of the quality of clustering that can be calculated when observations in the data are labeled; it allows for comparing dendrograms. Finally, we will present a formulation for Complete-Linkage clustering.

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MSC Kodigoak: 90C05; 90C11; 90C46

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“Dendarikale” Hitzaldi Nagusia

Asteazkena 15, 9:00
[Bizkaia Aretoaren Mitxelena Entzunaretoa]

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Alborapen, falazia eta beste hainbat izaki estatistiko

Statistics play a much greater role in our lives than we often realize, especially in the functioning of a democracy. Why are most political leaders born in the early months of the year? What do political campaigns have in common with World War II and traffic accidents? How can a lottery decide your fate in a war? Why was counting taxis crucial for political parties before modern technology? What are the most common errors in conducting phone surveys? How do chance and uncertainty shape our lives? This plenary talk will explore some of the most frequent statistical biases and fallacies that affect us daily.

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MSC Kodigoak: 62-07

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“Belostikale” Hitzaldi Nagusia

Asteazkena 15, 10:30
[Bizkaia Aretoaren Mitxelena Entzunaretoa]

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Beroaren ekuazioaren kontrolagarritasuna Lipschitz domeinuetan

Beroaren ekuazioa ekuazio parabolikorik oinarrizkoena da. Ekuazio horren zeroranzko kontrolabilitatea edozein domeinu $C^2$ frogatu zuten 90ko hamarkadan Fursikov eta Imanuvilov. Halere, problema berbera edozein domeinu Lipschitziarrentzat oraindik dago irekita. Hitzaldi honetan, hasteko, kontrolabilitate eta obserbabilitate nozioak aurkeztuko ditugu, eta nozio dualak direla erakutsiko dugu. Ostean, $C^2$ eremuetarako kontrolabilitate emaitzak frogatzeko ezagutzen diren teknikak azalduko ditugu. Azkenik, eztabaidatuko da eremua $C^2$ klasekoa ez denean beroaren ekuazioa kontrolagarria dela frogatzeko dauden tekniken inguruan. Hau guztia nahiko era elemental batean egingo dugu, Matematika Graduko Analisi Matematikoko nozioa soilik behar izanik.

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MSC Kodigoak: 93-02; 93C20; 35K05

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“Harategi Zahar Kalea” Hitzaldi Nagusia

Osteguna 16, 9:00
[UPV/EHUren Areto Nagusia]

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Trentzak, kurbak eta azpitalde parabolikoak

Hitzaldi honen helburua nire ikerketaren objektu nagusiak azaltzea eta horiei buruzko motibazioa ematea da: azpitalde parabolikoak. Txirikordak oso objektu moldagarriak dira, ikuspegi topologiko eta erabat algebraikoan oinarritutako deskribapenak baitituzte. Definizio topologikoarekin, mapping class groups bezalako orokorpenak aurkitzen ditugu, eta definizio aljebraikoarekin, orokorpen garrantzitsuena Artin taldeak dira. Oso gutxi dakigu Artin taldeen inguruan (Dehnen arazo klasikoak oraindik ere irekiak dira oro har). Gehiago jakiteko, estrategia bat da talde topologikoek txirikorda taldearen ekintza azaleran kurben konplexuan nola erabiltzen duten aztertzea, eta hori testuinguru aljebraikora itzultzea. Testuinguru honetan, kurben baliokide aljebraikoak, hain zuzen ere, azpitalde parabolikoak dira. Hitzaldi honetan, azpitalde horiei buruzko galdera irekirik nagusienak eta horiek lantzeko dauden estrategia ezberdinak aztertuko ditugu.

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MSC Kodigoak: 20F36; 20F65

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“Barrenkale” Hitzaldi Nagusia

Osteguna 16, 15:00
[UPV/EHUren Areto Nagusia]

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Zenbaki teoriaren formalizazioa Lean-en

Mathematical formalization consists of digitizing mathematical definitions and results using a "proof assistant", a computer program capable of checking whether a proposition can be deduced from a set of inference rules and a collection of basic axioms. In recent years, the community of mathematicians working on formalization has grown rapidly and has reached milestones that demonstrate the ability to formalize results at the frontier of knowledge. Proof assistants have applications to mathematics research, teaching, and communication.

After a brief introduction to formalization, I will present several of my number theory formalization results in the Lean interactive proof assistant, from sub-areas that include class field theory, p-adic Hodge theory, and the theory of Drinfeld modules.

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MSC Kodigoak: 68V20; 68V15; 11-XX

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“Barrenkale Barrena” Hitzaldi Nagusia

Ostirala 17, 11:30
[UPV/EHUren Areto Nagusia]

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Gorputz anitzetako sistema kuantiko irekien termalizazioa

A dissipative evolution of an open quantum many-body system weakly coupled to a thermal bath can be modelled by a quantum Markov semigroup, and its mixing time can be bounded using optimal constants of certain quantum functional inequalities, such as the modified logarithmic Sobolev constant. In this talk, we will review the mathematical formalism of dissipative evolutions governed by Lindbladians, and we will summarize the current state of the art on mixing times when the system has an associated commuting Hamiltonian.

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MSC Kodigoak: 47N50; 39B62; 15A90

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