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:20260422T185046Z 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 BIRS wor kshop: Algebraic Dynamics and its Connections to Difference and Differenti al Equations\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/20w5206/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Curtis McMullen (Harvard University) DTSTART:20201109T193000Z DTEND:20201109T202000Z DTSTAMP:20260422T185046Z UID:20w5206/2 DESCRIPTION:Title: Billiards and the arithmetic of non-arithmetic groups\nby Curtis McMul len (Harvard University) as part of BIRS workshop: Algebraic Dynamics and its Connections to Difference and Differential Equations\n\nAbstract: TBA\ n LOCATION:https://researchseminars.org/talk/20w5206/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Junyi Xie (Universite de Rennes I) DTSTART:20201110T160000Z DTEND:20201110T165000Z DTSTAMP:20260422T185046Z UID:20w5206/3 DESCRIPTION:Title: On the Zariski dense orbit conjecture\nby Junyi Xie (Universite de Ren nes I) as part of BIRS workshop: Algebraic Dynamics and its Connections to Difference and Differential Equations\n\n\nAbstract\nWe prove the followi ng theorem. Let f be a dominant endomorphism of a projective surface over an algebraically closed field of characteristic 0. If there is no nonconst ant invariant rational function under f\, then there exists a closed point whose orbit under f is Zariski dense. This result gives us a positive ans wer to the Zariski dense orbit conjecture for endomorphisms of projective surfaces.\n\nWe define a new canonical topology on varieties over an algeb raically closed field which has finite transcendence degree over Q. We ca ll it the adelic topology. This topology is stronger than the Zariski topo logy and an irreducible variety is still irreducible in this topology.\nUs ing the adelic topology\, we propose an adelic version of the Zariski dens e orbit conjecture\, which is stronger than the original one and quantifie s how many such orbits there are. We also prove this adelic version for en domorphisms of projective surfaces\, for endomorphisms of abelian varietie s\, and split polynomial maps. This yields new proofs of the original conj ecture in the latter two cases.\n LOCATION:https://researchseminars.org/talk/20w5206/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Joel Nagloo (City University of New York) DTSTART:20201110T170000Z DTEND:20201110T175000Z DTSTAMP:20260422T185046Z UID:20w5206/4 DESCRIPTION:Title: Schwarzian equation\, automorphic functions and functional transcendence\nby Joel Nagloo (City University of New York) as part of BIRS workshop: Algebraic Dynamics and its Connections to Difference and Differential Equ ations\n\n\nAbstract\nBy a Schwarzian differential equation\, we mean an e quation of the form $S_{\\frac{d}{dt}}(y) +(y')^2 R(y) =0\,$ where $S_{\\f rac{d}{dt}}(y)$ denotes the Schwarzian derivative and $R$ is a rational fu nction with complex coefficients. The equation naturally appears in the st udy 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 equation .\n\nIn this talk\, we discuss recent work towards the proof of a conjectu re/claim of P. Painlev\\’e (1895) about the irreducibility of the Schwar zian equations. We also explain how\, using the model theory of differenti ally closed fields\, this work on irreducibility can be used to tackle que stions related to the study of algebraic relations between the solutions o f a Schwarzian equation. This includes\, for example\, obtaining the Ax-Li ndemann-Weierstrass Theorem with derivatives for all Fuchsian automorphic functions.\n LOCATION:https://researchseminars.org/talk/20w5206/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Laura DeMarco (Harvard University) DTSTART:20201110T193000Z DTEND:20201110T202000Z DTSTAMP:20260422T185046Z UID:20w5206/5 DESCRIPTION:Title: Equidistribution for R-divisors and geometry of elliptic surfaces\nby Laura DeMarco (Harvard University) as part of BIRS workshop: Algebraic Dyn amics and its Connections to Difference and Differential Equations\n\nAbst ract: TBA\n LOCATION:https://researchseminars.org/talk/20w5206/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Ehud Deshalit (Hebrew University of Jerusalem) DTSTART:20201109T170000Z DTEND:20201109T175000Z DTSTAMP:20260422T185046Z UID:20w5206/6 DESCRIPTION:Title: Difference equations over fields of elliptic functions\nby Ehud Deshal it (Hebrew University of Jerusalem) as part of BIRS workshop: Algebraic Dy namics and its Connections to Difference and Differential Equations\n\n\nA bstract\nAdamczewski and Bell proved in 2017 a 30-year old conjecture of L oxton\nand van der Poorten\, asserting that a Laurent power series\, which simultaneously\nsatisfies a p-Mahler equation and a q-Mahler equation for multiplicatively independent\nintegers p and q\, is a rational function. Similar looking theorems have been proved by\nBezivin-Boutabaa and Ramis f or pairs of difference\, or difference-differential equations.\nRecently\, 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 equatio ns over fields of\nelliptic functions. Despite having the same flavor\, th ere are substantial differences\, having\nto do with issues of periodicity \, and with the existence of non-trivial (p\,q)-invariant vector\nbundles on the elliptic curve.\n LOCATION:https://researchseminars.org/talk/20w5206/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Dragos Ghioca (University of British Columbia) DTSTART:20201111T190000Z DTEND:20201111T195000Z DTSTAMP:20260422T185046Z UID:20w5206/7 DESCRIPTION:Title: A couple of conjectures in arithmetic dynamics over fields of positive cha racteristic\nby Dragos Ghioca (University of British Columbia) as part of BIRS workshop: Algebraic Dynamics and its Connections to Difference an d Differential Equations\n\n\nAbstract\nThe Dynamical Mordell-Lang Conject ure predicts the structure of the intersection between a subvariety $V$ of a variety $X$ defined over a field $K$ of characteristic $0$ with the orb it of a point in $X(K)$ under an endomorphism $\\Phi$ of $X$. The Zariski dense conjecture provides a dichotomy for any rational self-map $\\Phi$ of a variety $X$ defined over an algebraically closed field $K$ of character istic $0$: either there exists a point in $X(K)$ with a well-defined Zaris ki dense orbit\, or $\\Phi$ leaves invariant some non-constant rational fu nction $f$. For each one of these two conjectures we formulate an analogue in characteristic $p$\; in both cases\, the presence of the Frobenius end omorphism in the case $X$ is isotrivial creates significant complications which we will explain in the case of algebraic tori.\n LOCATION:https://researchseminars.org/talk/20w5206/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Piotr Kowalski (Uniwersytet Wrocławski) DTSTART:20201112T160000Z DTEND:20201112T165000Z DTSTAMP:20260422T185046Z UID:20w5206/8 DESCRIPTION:Title: Model theory of group actions on fields\nby Piotr Kowalski (Uniwersyte t Wrocławski) as part of BIRS workshop: Algebraic Dynamics and its Connec tions to Difference and Differential Equations\n\n\nAbstract\nFor a fixed group G\, we study the model theory of actions of G by field automorphisms . The main question here is to characterize the class of groups G for whic h the theory of such actions has a model companion (a first-order theory o f "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 Daniel Ho ffmann ("Existentially closed fields with finite group actions"\, Journal of Mathematical Logic\, (1) 18 (2018)\, 1850003).\nThe case of finitely ge nerated virtually free groups is joint work with Özlem Beyarslan ("Model theory of fields with virtually free group actions"\, Proc. London Math. S oc.\, (2) 118 (2019)\, 221-256).\nThe case of commutative torsion groups i s joint work with Özlem Beyarslan ("Model theory of Galois actions of tor sion Abelian groups"\, arXiv:2003.02329).\n LOCATION:https://researchseminars.org/talk/20w5206/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Anand Pillay (University of Notre Dame) DTSTART:20201112T170000Z DTEND:20201112T175000Z DTSTAMP:20260422T185046Z UID:20w5206/9 DESCRIPTION:Title: Definable Galois theory and holomorphic vector bundles\nby Anand Pilla y (University of Notre Dame) as part of BIRS workshop: Algebraic Dynamics and its Connections to Difference and Differential Equations\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/20w5206/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Vesselin Dimitrov (University of Toronto) DTSTART:20201112T193000Z DTEND:20201112T202000Z DTSTAMP:20260422T185046Z 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://researchseminars.org/talk/20w5206/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Charlotte Hardouin (Institut de mathematiques de Toulouse) DTSTART:20201113T170000Z DTEND:20201113T175000Z DTSTAMP:20260422T185046Z UID:20w5206/11 DESCRIPTION:Title: Algebraic independence of solutions of linear difference equations\nb y Charlotte Hardouin (Institut de mathematiques de Toulouse) as part of BI RS workshop: Algebraic Dynamics and its Connections to Difference and Diff erential Equations\n\n\nAbstract\nThis work is a collaboration with B. Ada mczewski (ICJ\, France)\, T. Dreyfus (IRMA\, France) and M. Wibmer (Graz U niversity of Technology\, Austria). \n\nIn this talk\, we will consider pa irs of automorphisms $(\\phi\,\\sigma)$ acting on fields of Laurent or Pui seux series: pairs of shift operators\, of $q$-difference operators and of Mahler operators. Assuming that the operators $\\phi$ and $\\sigma$ ar e "independent"\, we show that their solutions are also "independent" in t he sense that a solution $f$ to a linear $\\phi$-equation and a solution $ g$ to a linear $\\sigma$-equation are algebraically independent over the f ield of rational functions unless one of them is a rational function. As a consequence\, we settle a conjecture about Mahler functions put forward by Loxton and van der Poorten in 1987. We also give an application to the algebraic independence of $q$-hypergeometric functions. \n Our approach 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://researchseminars.org/talk/20w5206/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Serge Cantat (CNRS -- Université de Rennes) DTSTART:20201113T193000Z DTEND:20201113T202000Z DTSTAMP:20260422T185046Z UID:20w5206/12 DESCRIPTION:Title: Finite orbits and canonical heights for large groups of automorphisms.\nby Serge Cantat (CNRS -- Université de Rennes) as part of BIRS worksho p: Algebraic Dynamics and its Connections to Difference and Differential E quations\n\n\nAbstract\nConsider a complex projective surface $X$\, with a non-abelian free group $G$ acting \nfaithfully and regularly on $X$. It m ay happen that $G$ has infinitely many periodic orbits: \nthis is the case when $X$ is an abelian surface and all torsion points are $G$-periodic. \ nIn this talk\, I will describe recent results obtained with Romain Dujard in aiming at a\ncomplete classification of all such examples. The main pla yers will be canonical heights\, \narithmetic equidistribution\, and rigid ity results in ergodic theory.\n LOCATION:https://researchseminars.org/talk/20w5206/12/ END:VEVENT END:VCALENDAR