BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Simion Filip (University of Chicago) DTSTART:20201111T163000Z DTEND:20201111T172000Z DTSTAMP:20260404T040244Z UID:20w5206/1 DESCRIPTION:Title: Equivariant currents and heights on the boundary of the ample cone of a K3 surface.\nby Simion Filip (University of Chicago) as part of B IRS workshop: Algebraic Dynamics and its Connections to Difference and Dif ferential Equations\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/20w5206/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Curtis McMullen (Harvard University) DTSTART:20201109T193000Z DTEND:20201109T202000Z DTSTAMP:20260404T040244Z UID:20w5206/2 DESCRIPTION:Title: Billiards and the arithmetic of non-arithmetic groups\nby Curti s McMullen (Harvard University) as part of BIRS workshop: Algebraic Dynami cs and its Connections to Difference and Differential Equations\n\nAbstrac t: TBA\n LOCATION:https://stable.researchseminars.org/talk/20w5206/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Junyi Xie (Universite de Rennes I) DTSTART:20201110T160000Z DTEND:20201110T165000Z DTSTAMP:20260404T040244Z UID:20w5206/3 DESCRIPTION:Title: On the Zariski dense orbit conjecture\nby Junyi Xie (Universite de Rennes I) as part of BIRS workshop: Algebraic Dynamics and its Connect ions to Difference and Differential Equations\n\n\nAbstract\nWe prove the following theorem. Let f be a dominant endomorphism of a projective surfac e over an algebraically closed field of characteristic 0. If there is no n onconstant invariant rational function under f\, then there exists a close d point whose orbit under f is Zariski dense. This result gives us a posit ive answer to the Zariski dense orbit conjecture for endomorphisms of proj ective surfaces.\n\nWe define a new canonical topology on varieties over a n algebraically closed field which has finite transcendence degree over Q. We call it the adelic topology. This topology is stronger than the Zaris ki topology and an irreducible variety is still irreducible in this topolo gy.\nUsing the adelic topology\, we propose an adelic version of the Zaris ki dense orbit conjecture\, which is stronger than the original one and qu antifies how many such orbits there are. We also prove this adelic version for endomorphisms of projective surfaces\, for endomorphisms of abelian v arieties\, and split polynomial maps. This yields new proofs of the origin al conjecture in the latter two cases.\n LOCATION:https://stable.researchseminars.org/talk/20w5206/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Joel Nagloo (City University of New York) DTSTART:20201110T170000Z DTEND:20201110T175000Z DTSTAMP:20260404T040244Z UID:20w5206/4 DESCRIPTION:Title: Schwarzian equation\, automorphic functions and functional transcen dence\nby Joel Nagloo (City University of New York) as part of BIRS wo rkshop: Algebraic Dynamics and its Connections to Difference and Different ial Equations\n\n\nAbstract\nBy a Schwarzian differential equation\, we me an an equation of the form $S_{\\frac{d}{dt}}(y) +(y')^2 R(y) =0\,$ where $S_{\\frac{d}{dt}}(y)$ denotes the Schwarzian derivative and $R$ is a rati onal function with complex coefficients. The equation naturally appears in the study of automorphic functions (such as the modular $j$-function): if $j_{\\Gamma}$ is the uniformizing function of a genus zero Fuchsian group of the first kind\, then $j_{\\Gamma}$ is a solution of some Schwarzian e quation.\n\nIn this talk\, we discuss recent work towards the proof of a c onjecture/claim of P. Painlev\\’e (1895) about the irreducibility of the Schwarzian equations. We also explain how\, using the model theory of dif ferentially closed fields\, this work on irreducibility can be used to tac kle questions related to the study of algebraic relations between the solu tions of a Schwarzian equation. This includes\, for example\, obtaining th e Ax-Lindemann-Weierstrass Theorem with derivatives for all Fuchsian autom orphic functions.\n LOCATION:https://stable.researchseminars.org/talk/20w5206/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Laura DeMarco (Harvard University) DTSTART:20201110T193000Z DTEND:20201110T202000Z DTSTAMP:20260404T040244Z UID:20w5206/5 DESCRIPTION:Title: Equidistribution for R-divisors and geometry of elliptic surfaces\nby Laura DeMarco (Harvard University) as part of BIRS workshop: Algebr aic Dynamics and its Connections to Difference and Differential Equations\ n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/20w5206/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Ehud Deshalit (Hebrew University of Jerusalem) DTSTART:20201109T170000Z DTEND:20201109T175000Z DTSTAMP:20260404T040244Z UID:20w5206/6 DESCRIPTION:Title: Difference equations over fields of elliptic functions\nby Ehud Deshalit (Hebrew University of Jerusalem) as part of BIRS workshop: Algeb raic Dynamics and its Connections to Difference and Differential Equations \n\n\nAbstract\nAdamczewski and Bell proved in 2017 a 30-year old conjectu re of Loxton\nand van der Poorten\, asserting that a Laurent power series\ , which simultaneously\nsatisfies a p-Mahler equation and a q-Mahler equat ion for multiplicatively independent\nintegers p and q\, is a rational fun ction. Similar looking theorems have been proved by\nBezivin-Boutabaa and Ramis for pairs of difference\, or difference-differential equations.\nRec ently\, Schafke and Singer gave a unified treatment of all these theorems. \n\nIn this talk we shall discuss a similar theorem for (p\,q)-difference equations over fields of\nelliptic functions. Despite having the same flav or\, there are substantial differences\, having\nto do with issues of peri odicity\, and with the existence of non-trivial (p\,q)-invariant vector\nb undles on the elliptic curve.\n LOCATION:https://stable.researchseminars.org/talk/20w5206/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Dragos Ghioca (University of British Columbia) DTSTART:20201111T190000Z DTEND:20201111T195000Z DTSTAMP:20260404T040244Z UID:20w5206/7 DESCRIPTION:Title: A couple of conjectures in arithmetic dynamics over fields of posit ive characteristic\nby Dragos Ghioca (University of British Columbia) as part of BIRS workshop: Algebraic Dynamics and its Connections to Differ ence and Differential Equations\n\n\nAbstract\nThe Dynamical Mordell-Lang Conjecture predicts the structure of the intersection between a subvariety $V$ of a variety $X$ defined over a field $K$ of characteristic $0$ with the orbit of a point in $X(K)$ under an endomorphism $\\Phi$ of $X$. The Z ariski dense conjecture provides a dichotomy for any rational self-map $\\ Phi$ of a variety $X$ defined over an algebraically closed field $K$ of ch aracteristic $0$: either there exists a point in $X(K)$ with a well-define d Zariski dense orbit\, or $\\Phi$ leaves invariant some non-constant rati onal function $f$. For each one of these two conjectures we formulate an a nalogue in characteristic $p$\; in both cases\, the presence of the Froben ius endomorphism in the case $X$ is isotrivial creates significant complic ations which we will explain in the case of algebraic tori.\n LOCATION:https://stable.researchseminars.org/talk/20w5206/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Piotr Kowalski (Uniwersytet Wrocławski) DTSTART:20201112T160000Z DTEND:20201112T165000Z DTSTAMP:20260404T040244Z UID:20w5206/8 DESCRIPTION:Title: Model theory of group actions on fields\nby Piotr Kowalski (Uni wersytet Wrocławski) as part of BIRS workshop: Algebraic Dynamics and its Connections to Difference and Differential Equations\n\n\nAbstract\nFor a fixed group G\, we study the model theory of actions of G by field automo rphisms. The main question here is to characterize the class of groups G f or which the theory of such actions has a model companion (a first-order t heory of "large" actions). In my talk\, I will discuss several classes of groups G in this context.\nThe case of finite groups is joint work with Da niel Hoffmann ("Existentially closed fields with finite group actions"\, J ournal of Mathematical Logic\, (1) 18 (2018)\, 1850003).\nThe case of fini tely generated virtually free groups is joint work with Özlem Beyarslan ( "Model theory of fields with virtually free group actions"\, Proc. London Math. Soc.\, (2) 118 (2019)\, 221-256).\nThe case of commutative torsion g roups is joint work with Özlem Beyarslan ("Model theory of Galois actions of torsion Abelian groups"\, arXiv:2003.02329).\n LOCATION:https://stable.researchseminars.org/talk/20w5206/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Anand Pillay (University of Notre Dame) DTSTART:20201112T170000Z DTEND:20201112T175000Z DTSTAMP:20260404T040244Z UID:20w5206/9 DESCRIPTION:Title: Definable Galois theory and holomorphic vector bundles\nby Anan d Pillay (University of Notre Dame) as part of BIRS workshop: Algebraic Dy namics and its Connections to Difference and Differential Equations\n\nAbs tract: TBA\n LOCATION:https://stable.researchseminars.org/talk/20w5206/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Vesselin Dimitrov (University of Toronto) DTSTART:20201112T193000Z DTEND:20201112T202000Z DTSTAMP:20260404T040244Z UID:20w5206/10 DESCRIPTION:by Vesselin Dimitrov (University of Toronto) as part of BIRS w orkshop: Algebraic Dynamics and its Connections to Difference and Differen tial Equations\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/20w5206/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Charlotte Hardouin (Institut de mathematiques de Toulouse) DTSTART:20201113T170000Z DTEND:20201113T175000Z DTSTAMP:20260404T040244Z UID:20w5206/11 DESCRIPTION:Title: Algebraic independence of solutions of linear difference equations \nby Charlotte Hardouin (Institut de mathematiques de Toulouse) as par t of BIRS workshop: Algebraic Dynamics and its Connections to Difference a nd Differential Equations\n\n\nAbstract\nThis work is a collaboration with B. Adamczewski (ICJ\, France)\, T. Dreyfus (IRMA\, France) and M. Wibmer (Graz University of Technology\, Austria). \n\nIn this talk\, we will cons ider pairs of automorphisms $(\\phi\,\\sigma)$ acting on fields of Laurent or Puiseux series: pairs of shift operators\, of $q$-difference operator s and of Mahler operators. Assuming that the operators $\\phi$ and $\\si gma$ are "independent"\, we show that their solutions are also "independen t" in the sense that a solution $f$ to a linear $\\phi$-equation and a sol ution $g$ to a linear $\\sigma$-equation are algebraically independent ove r the field of rational functions unless one of them is a rational functio n. As a consequence\, we settle a conjecture about Mahler functions put f orward by Loxton and van der Poorten in 1987. We also give an application to the algebraic independence of $q$-hypergeometric functions. \n Our a pproach provides a general strategy to study this kind of questions and is based on a suitable Galois theory: the $\\sigma$-Galois theory of linear $\\phi$-equations developed by Ovchinnikov and Wibmer.\n LOCATION:https://stable.researchseminars.org/talk/20w5206/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Serge Cantat (CNRS -- Université de Rennes) DTSTART:20201113T193000Z DTEND:20201113T202000Z DTSTAMP:20260404T040244Z UID:20w5206/12 DESCRIPTION:Title: Finite orbits and canonical heights for large groups of automorphi sms.\nby Serge Cantat (CNRS -- Université de Rennes) as part of BIRS workshop: Algebraic Dynamics and its Connections to Difference and Differe ntial Equations\n\n\nAbstract\nConsider a complex projective surface $X$\, with a non-abelian free group $G$ acting \nfaithfully and regularly on $X $. It may happen that $G$ has infinitely many periodic orbits: \nthis is t he case when $X$ is an abelian surface and all torsion points are $G$-peri odic. \nIn this talk\, I will describe recent results obtained with Romain Dujardin aiming at a\ncomplete classification of all such examples. The m ain players will be canonical heights\, \narithmetic equidistribution\, an d rigidity results in ergodic theory.\n LOCATION:https://stable.researchseminars.org/talk/20w5206/12/ END:VEVENT END:VCALENDAR