BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Eva-Marie Hainzl (TU Wien) DTSTART:20230209T233000Z DTEND:20230210T003000Z DTSTAMP:20260422T054035Z UID:SFUQNTAG/87 DESCRIPTION:Title: Universal types of singularities of solutions to functional equation sys tems\nby Eva-Marie Hainzl (TU Wien) as part of SFU NT-AG seminar\n\nLe cture held in K-9509.\n\nAbstract\nDecompositions of combinatorial structu res translate very often to functional equations with positive coefficient s for their generating functions. A theorem by Bender says that if the gen erating function is univariate and the equation not linear\, the generatin g function always has a dominant square root singularity - which in turn m eans that the the coefficients a(n) grow asymptotically at the rate c*n^(- 3/2) R^n\, where c and R are suitable constants. The result extends to str ongly connected finite systems of equations\, but as the system becomes in finite we can observe a broader variety of singularities appearing. \nIn t his talk\, I will give an overview of functional equations systems and the ir singular behaviour in combinatorics and present some recent results on universal types of singularities of solutions to infinite systems which co llapse to a single equation by introducing a second (catalytic) variable.\ n LOCATION:https://researchseminars.org/talk/SFUQNTAG/87/ END:VEVENT END:VCALENDAR