BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Libby Taylor (Stanford University) DTSTART:20210129T160000Z DTEND:20210129T170000Z DTSTAMP:20260404T111000Z UID:RationalVarieties/1 DESCRIPTION:Title: Derived equivalences of gerbey curves.\nby Libby Tayl or (Stanford University) as part of Rational Varieties Seminar (Séminaire Variétés Rationnelles)\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/RationalVarieties/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Igor Rapinchuk (Michigan State University) DTSTART:20210212T150000Z DTEND:20210212T160000Z DTSTAMP:20260404T111000Z UID:RationalVarieties/2 DESCRIPTION:Title: Algebraic groups with good reduction\nby Igor Rapinch uk (Michigan State University) as part of Rational Varieties Seminar (Sém inaire Variétés Rationnelles)\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/RationalVarieties/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Vladimir Mitankin (Leibniz University Hannover) DTSTART:20210312T133000Z DTEND:20210312T143000Z DTSTAMP:20260404T111000Z UID:RationalVarieties/3 DESCRIPTION:Title: Rational points on del Pezzo surfaces of degree 4\nby Vladimir Mitankin (Leibniz University Hannover) as part of Rational Varie ties Seminar (Séminaire Variétés Rationnelles)\n\n\nAbstract\nIn this t alk I shall explain how often failures of local-to-global principles arise in a family of del Pezzo surfaces of degree four. This is addressed in te rms of the Brauer group. More precisely\, we give an explicit description of its generators modulo constants and incorporate in the Brauer-Manin obs truction the information obtained. This allows us to use tools from analyt ic number theory to get sharp upper and lower bounds for the number of sur faces in the family with a prescribed Brauer group as well as bounds for t he number of Hasse and weak approximation failures. This talk is based on a joint work with Cecília Salgado.\n LOCATION:https://stable.researchseminars.org/talk/RationalVarieties/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Anand Sawant (Tata Institute of Fundamental Research) DTSTART:20210326T123000Z DTEND:20210326T133000Z DTSTAMP:20260404T111000Z UID:RationalVarieties/4 DESCRIPTION:Title: Near-rationality properties of algebraic varieties via A^ 1-connectedness\nby Anand Sawant (Tata Institute of Fundamental Resear ch) as part of Rational Varieties Seminar (Séminaire Variétés Rationnel les)\n\n\nAbstract\nI will outline an argument proving that the standard n orm\nvariety associated with a symbol in mod-l Milnor K-theory is R-trivia l\nover an algebraically closed field of characteristic 0. Rational\nconn ectededness of such standard norm varieties was previously known. \nThis r esult is achieved by relating R-triviality and retract rationality\nproper ties of varieties with A^1-connectedness in the sense of\nMorel-Voevodsky and finding purely geometric criteria to determine\nA^1-connectedness. Th e talk is based on joint work with Chetan Balwe and\nAmit Hogadi.\n\nUnusu al time!\n LOCATION:https://stable.researchseminars.org/talk/RationalVarieties/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Vivek Sadhu (Indian Institute of Science Education and Research Bh opal) DTSTART:20210507T113000Z DTEND:20210507T123000Z DTSTAMP:20260404T111000Z UID:RationalVarieties/5 DESCRIPTION:Title: Brauer groups of valuation rings\nby Vivek Sadhu (Ind ian Institute of Science Education and Research Bhopal) as part of Rationa l Varieties Seminar (Séminaire Variétés Rationnelles)\n\n\nAbstract\nA classical result of Auslander and Goldman says that for a regular ring R\, the Brauer group of R injects into the Brauer group of the function field . In this talk\, I will discuss a proof of the above stated result in the case of arbitrary valuation rings.\n LOCATION:https://stable.researchseminars.org/talk/RationalVarieties/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Davide Lombardo (Università di Pisa) DTSTART:20210528T140000Z DTEND:20210528T150000Z DTSTAMP:20260404T111000Z UID:RationalVarieties/6 DESCRIPTION:Title: Sur la distribution des points rationnels sur les revête ments des variétés abéliennes\nby Davide Lombardo (Università di P isa) as part of Rational Varieties Seminar (Séminaire Variétés Rationne lles)\n\n\nAbstract\nSoit $A$ une variété abélienne définie sur un cor ps de nombres $K$\, avec $A(K)$ Zariski-dense dans $A$. Le but de cet expo sé est de montrer que pour tout revêtement irréductible et ramifié $\\ pi : X \\to A$ l'ensemble $A(K) \\setminus \\pi(X(K))$ est encore Zariski- dense dans $A$ (et même qu'il contient une classe latérale de $A(K)$ sou s un sous-groupe d'indice fini). Ce résultat est motivé par la conjectur e de Lang sur les points rationnels des variétés de type général et co nfirme une conjecture de Corvaja et Zannier sur la ``propriété d'Hilbert faible" dans le cas des variétés abéliennes.\n\nIl s'agit d'un travail en commun avec P. Corvaja\, J. Demeio\, A. Javanpeykar et U. Zannier.\n LOCATION:https://stable.researchseminars.org/talk/RationalVarieties/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Martir Orr (University of Manchester) DTSTART:20210625T113000Z DTEND:20210625T123000Z DTSTAMP:20260404T111000Z UID:RationalVarieties/7 DESCRIPTION:Title: The invariant Brauer group of abelian varieties\nby M artir Orr (University of Manchester) as part of Rational Varieties Seminar (Séminaire Variétés Rationnelles)\n\n\nAbstract\nCao defined the invar iant Brauer group Br_G(X) where G is a\nconnected algebraic group and X is a smooth variety on which G acts.\nThis group is useful for understanding the Brauer-Manin obstruction and\nstrong approximation. If G is a linear algebraic group over a field of\ncharacteristic 0\, then Br_G(G) is equal to the algebraic Brauer group\nBr_1(G). However\, for an abelian variety A\, the group Br_A(A) is much\nmore mysterious.\n\nIn this talk\, I will discuss examples of calculating Br_A(A) for an\nabelian variety\, over the complex numbers and over the real numbers.\nThese two base fields are alr eady sufficient for complicated behaviour\nto occur: I will present exampl es showing that neither Br_A(A) nor\nBr_1(A) needs to be contained in the other. This is joint work with A.\nSkorobogatov\, D. Valloni and Y. Zarhi n.\n LOCATION:https://stable.researchseminars.org/talk/RationalVarieties/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Florian Pop (University of Pennsylvania) DTSTART:20211029T123000Z DTEND:20211029T160000Z DTSTAMP:20260404T111000Z UID:RationalVarieties/8 DESCRIPTION:Title: Complements of line/hyperplane arrangements and absolute Galois groups\nby Florian Pop (University of Pennsylvania) as part of Rational Varieties Seminar (Séminaire Variétés Rationnelles)\n\n\nAbstr act\nOne of the main themes of Grothendieck’s "Esquisse d'un Programme" was to give a combinatorial/topological description of absolute Galois gro ups. In this talk I plan to:\nFirst briefly recall two developments concer ning the above theme from the Esquisse\, namely the Grothendieck-Teichmuel ler group (GT) and the Ihara question/Oda-Matsumoto conjecture (I/OM)\, an d explain how they fit into the bigger picture about the above theme.\nSec ond\, I plan to explain a very recent result (collaboration with Adam Topa z) concerning a line/hyperplane variant of GT which: (i) is closer in natu re to GT than I/OM is\; (ii) it gives a topological description of absolut e Galois\, e.g. of that of Q.\n LOCATION:https://stable.researchseminars.org/talk/RationalVarieties/8/ END:VEVENT END:VCALENDAR