BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:André Oliveira (CMUP & UTAD\, Portugal) DTSTART:20210519T150000Z DTEND:20210519T160000Z DTSTAMP:20260404T111445Z UID:What_is_seminars_at_CMA-UBI/1 DESCRIPTION:Title: What is… a moduli space?\nby André Olive ira (CMUP & UTAD\, Portugal) as part of What is...? [CMA-UBI seminar]\n\ n\nAbstract\nMathematicians like to classify and organize mathematical obj ects\, up to some fixed equivalence relation. Sometimes the objects in que stion do not admit continuous variations and so the classification is give n by discrete invariants. But many other times\, especially for objects co ming from algebraic geometry\, the objects admit such variations. Then the y are classified by what is known as a moduli space. It turns out that man y moduli spaces are usually themselves algebraic varieties with a very ric h geometry and topology\, under current intensive research. Moduli space t heory is indeed a vast and intricate topic\, whose origins go back to Riem ann and which has been behind several Fields Medals (like Mumford\, Donald son or Mirzakhani\, just to name a few). Even their rigorous definition is not a trivial matter and\, somehow contradicting the title\, it will not be given in this talk. The aim is just to provide a general idea of what a moduli space is supposed to be and mainly focus on basic examples.\n LOCATION:https://stable.researchseminars.org/talk/What_is_seminars_at_CMA- UBI/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuri Lima (Universidade Federal do Ceará\, Brazil) DTSTART:20210317T150000Z DTEND:20210317T160000Z DTSTAMP:20260404T111445Z UID:What_is_seminars_at_CMA-UBI/2 DESCRIPTION:Title: What is...Symbolic Dynamics?\nby Yuri Lima (Universidade Federal do Ceará\, Brazil) as part of What is...? [CMA-UB I seminar]\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/What_is_seminars_at_CMA- UBI/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Manuel Silva (Universidade Nova de Lisboa\, Portugal) DTSTART:20210623T150000Z DTEND:20210623T160000Z DTSTAMP:20260404T111445Z UID:What_is_seminars_at_CMA-UBI/3 DESCRIPTION:Title: What is... Ramsey theory?\nby Manuel Silva (Universidade Nova de Lisboa\, Portugal) as part of What is...? [CMA-UBI seminar]\n\n\nAbstract\nIn 1928 Frank P. Ramsey\, motivated by philosophi cal considerations\, proved a theorem in his paper “On a problem of form al logic”. This result can be viewed as a powerful generalization of the pigeonhole principle and implies that every large combinatorial structure contains some regular substructure. Since then\, Ramsey Theory has become an important area of combinatorics with connections to other fields of ma thematics such as number theory\, ergodic theory\, mathematical logic\, an d graph theory. In the same spirit\, Van der Waerden proved in 1927 a regu larity result about partitions of the natural numbers. We will see several examples of Ramsey-type results\, trying in each case to find some order in a large combinatorial system.\n LOCATION:https://stable.researchseminars.org/talk/What_is_seminars_at_CMA- UBI/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Sérgio Mendes (ISCTE – IUL & CMA-UBI\, Portugal) DTSTART:20210721T150000Z DTEND:20210721T160000Z DTSTAMP:20260404T111445Z UID:What_is_seminars_at_CMA-UBI/4 DESCRIPTION:Title: What is… the Langlands Program?\nby Sér gio Mendes (ISCTE – IUL & CMA-UBI\, Portugal) as part of What is...? [ CMA-UBI seminar]\n\n\nAbstract\nLet f ∈ Z[x] be an irreducible monic pol ynomial of degree n > 0 with integer coecients. Given a prime p\, reducing the coecients of f modulo p\, gives a new polynomial which can be reducib le. A reciprocity law is the law governing the primes modulo which f facto rs completely. The celebrated quadratic reciprocity law\, introduced by Le gendre and completely solved by Gauss\, is the case when f has degree two. Many other reciprocity laws due to Eisenstein\, Kummer\, Hilbert and othe rs lead to the general Artin’s reciprocity law and (abelian) class eld t heory in the early 20th century.\n\nIn 1967\, in a letter to André Weil\, Robert Langlands paved the way for what is known today as the Langlands P rogram: a set of far reaching conjec tures\, connecting number theory\, re presentation theory (harmonic analysis) and algebraic geometry. It contain s all the abelian class eld theory as a particular case\, and another spec ial case plays a crucial role in Wile’s proof of Fermat’s Last Theorem .\n\nThere is a vast amount of number theory problems than can be studied in the framework of the Langlands Program\, namely: (i) non-abelian class eld theory\; (ii) several conjectures regarding zeta-functions and L-funct ions\; (iii) and an arithmetic parametrization of smooth irreducible repre sentations of reductive groups.\n\nIn this talk we will give an elementary introduction to the Langlands Program\, dedicating special attention to t he local Langlands correspondence and explain how it can be seen as a gene ral non-abelian class eld theory. We\nshall concentrate more on examples\, avoiding general and long denitions.\n\nIf time permits\, an application to noncommutative geometry will also be presented.\n LOCATION:https://stable.researchseminars.org/talk/What_is_seminars_at_CMA- UBI/4/ END:VEVENT END:VCALENDAR