BEGIN:VCALENDAR VERSION:2.0 PRODID:-// - ECPv6.16.3//NONSGML v1.0//EN CALSCALE:GREGORIAN METHOD:PUBLISH X-ORIGINAL-URL:https://aarms.math.ca X-WR-CALDESC:Events for REFRESH-INTERVAL;VALUE=DURATION:PT1H X-Robots-Tag:noindex X-PUBLISHED-TTL:PT1H BEGIN:VTIMEZONE TZID:UTC BEGIN:STANDARD TZOFFSETFROM:+0000 TZOFFSETTO:+0000 TZNAME:UTC DTSTART:20220101T000000 END:STANDARD END:VTIMEZONE BEGIN:VEVENT DTSTART;VALUE=DATE:20230313 DTEND;VALUE=DATE:20230318 DTSTAMP:20260612T171457 CREATED:20230228T164404Z LAST-MODIFIED:20230228T164444Z UID:7135-1678665600-1679097599@aarms.math.ca SUMMARY:Automorphisms And Derivations In Affine Algebraic Geometry DESCRIPTION:Mini-course by Professor Leonid Makar-Limanov\, Wayne University\,  USA \nBrief description of the mini course\nAfter this course you will know the proofs of several classical theorems of Affine Algebraic Geometry. The original proofs of these theorems were quite involved and a much longer course would be needed for their exposition. \nIn the first lecture we will discuss the theorems of Heinrich Jung and Rudolf Rentschler. The first one describes all invertible transformations of the plane by polynomials and the second all generalized shifts of the plane. Algebraically speaking\, Jung’s theorem describes all automorphisms of the ring of polynomials with two variables and Rentschler theorem describes all subgroups of this group which are isomorphic to the group of complex numbers under addition. If we have time\, we will  discuss the groups of polynomial automorphisms of several other surfaces. \nThe second lecture is devoted to the following topic: if a cylinder is given\, is it possible to recover the base of this cylinder. In general the answer is no\, but we discuss two cases when this is possible. We show that if the cylinder over a curve is given then we can recover this curve (this is the theorem of Shreeram Abhyankar\, Paul Eakin\, and William Heinzer). If the cylinder over a surface is isomorphic to a three-dimensional space then the surface is isomorphic to a plane (this is a theorem of Takao Fujita). \nHere is an algebraic translation: \nIf A is an integral domain of transcendence degree one and A[x1\, x2\,…\, xn] is given\, we can recover A up to an isomorphism. If A is an integral domain of transcendence degree two and A[x] is isomorphic to C[y1\,y2\,y3] then A is isomorphic to C[z1\,z2].  The main tool used in these two lectures is locally nilpotent derivations. \nIn the third lecture we prove one of the most famous theorems in affine algebraic geometry\, the AMS Theorem (after Abhyankar\, Tsuong-tsieng Moh\, Masakazu Suzuki): any smooth “good” embedding of a line to a plane is the image of a coordinate line under an automorphism of the plane. Algebraically\, this means the following: if two polynomials f(t)\, g(t)∈ C[t] generate C[t] then the smaller of the degrees of f(t)\, g(t) divides the larger of the degrees of f(t)\, g(t). The main tool here is a new algorithm for finding an irreducible dependence between two polynomials in one variable. \nThe lectures will be delivered during three time periods\, as shown below. They will take place at the St. John’s campus of Memorial University and will be broadcast via Webex. All the times are in Newfoundland Time (NST=UTC-3:30). \nMonday\, March 13th: TBA \nTuesday\, March 14th: TBA \nThursday\, March 16th: TBA \nThe lectures will be available online via Webex.  The details will be given later.  Contact the organizers for more information:   Mikhail Kotchetov ;  Yuri A Bakhturin URL:https://aarms.math.ca/event/automorphisms-and-derivations-in-affine-algebraic-geometry/ LOCATION:Memorial University (St. John’s Campus)\, St. John's\, Newfoundland and Labrador\, Canada CATEGORIES:AARMS schools and minicourses ORGANIZER;CN="Mikhail Kotchetov":MAILTO:Mikhail@mun.ca END:VEVENT BEGIN:VEVENT DTSTART;TZID=UTC:20230315T153000 DTEND;TZID=UTC:20230315T163000 DTSTAMP:20260612T171457 CREATED:20230315T123936Z LAST-MODIFIED:20230315T123936Z UID:7144-1678894200-1678897800@aarms.math.ca SUMMARY:Atlantic Graph Theory Seminar: Caleb Jones and Rylo Ashmore (Memorial University) DESCRIPTION:Speaker 1: Caleb Jones\, Memorial University\n \nTitle: Extending Graph Burning to Hypergraphs\n \nAbstract:\nWe introduce a round-based model much like graph burning which applies to hypergraphs. The rules for this new model are very natural\,and generalize the original model of graph burning. We also introduce a variant called lazy hypergraph burning\, along with a new parameter\, the lazy burning number. Interestingly\, lazily burning a graph is trivial\, while lazily burning a hypergraph can be quite complicated. Moreover\, the lazy burning model is a useful tool for analyzing the round-based model on hypergraphs. We obtain bounds on the burning number and lazy burning number of a hypergraph in terms of its parameters.\n \n \nSpeaker 2: Rylo Ashmore\, Memorial University\n \nTitle: Herding Cats Stuck in Trees.\n \nAbstract:\nIn the game of Cat Herding on a graph\, one player (the herder) will omnipresently delete edges\, while the other player (the cat) is on a vertex of the graph\, and will move along any path to a new vertex. Eventually\, the cat is isolated on a single vertex\, and the cat’s objective is to delay this event\, while the herder tries to hasten it. In an optimally played game\, the number of cuts the herder made to isolate the cat is the cat number of the graph. In this talk\, we will investigate this graph parameter for both dense and sparse graphs. We will see an argument that the asymptotic behaviour of the cat number of complete graphs is n^2/3. We also look at an unexpected connection between cat herding on trees and Fibonacci numbers. In particular\, we will see that trees with maximum cat number amongst graphs with n vertices have cat number asymptotically log_φ (n).\n\nZoom link: https://us02web.zoom.us/j/86415230827?pwd=QUxLUnlMdWYzL05zSUJ4bnBCOUJnZz09 \n\nMeeting ID: 864 1523 0827\nPasscode: 835547 URL:https://aarms.math.ca/event/atlantic-graph-theory-seminar-caleb-jones-and-rylo-ashmore-memorial-university/ LOCATION:Online via Zoom CATEGORIES:AARMS Atlantic Graph Theory Seminar ORGANIZER;CN="jeannette Janssen":MAILTO:jeannette.janssen@dal.ca END:VEVENT END:VCALENDAR