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DTSTART;TZID=America/Toronto:20250731T133000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/algebraic-an
 d-enumerative-combinatorics-seminar-ura-day-kai
SUMMARY:Algebraic and enumerative combinatorics seminar-URA day! Kai Choi\,
 \nPeiran Tao\, Stephanie Penner
CLASS:PUBLIC
DESCRIPTION:Speaker\n\nURA day!  Kai Choi\, Peiran Tao\, Stephanie Penner\
 n\nAffiliation\n University of Waterloo\n\nLocation\n MC 5479\n\nKai Choi\
 n\nTITLE:Alice in Quadraticspanningforestidentityspace\n\nABSTRACT: Quant
 um field theorists study Feynman periods\, which are\nobtained by integrat
 ing expressions related to the spanning tree\npolynomials of graphs known 
 as Feynman diagrams. But if you are like\nme and know nothing about physic
 s\, the good news is that doing quantum\nfield theory often leads one to p
 lay with combinatorial objects. In\nparticular\, if one wishes to efficien
 tly compute Feynman periods\, they\nwould likely be faced with unanswered 
 questions about set partitions\,\ndeterminantal identities\, spaces of pol
 ynomials\, and the all-minors\nmatrix-tree theorem\, many of which are qui
 te accessible. I will\npresent these questions and their relevant backgrou
 nd in the context\nof my work on spaces of quadratic spanning forest ident
 ities\,\nsupervised by Dr. Karen Yeats.\n\nPeiran Tao\n\nTITLE:Alice in Qu
 adraticspanningforestidentityspace\n\nABSTRACT: It is a classical theorem
  that the diagonal of any\nbivariate rational power series is algebraic\; 
 that is\, it satisfies a\npolynomial equation. We will discuss an algorith
 m that efficiently\ncomputes this polynomial.\n\nGiven a rational generati
 ng function F(z_1\,...\,z_d) we are interested\nin the asymptotic behaviou
 r of its coefficient sequence in a specified\ndirection (r_1\,...\,r_d). A
 lthough this problem is difficult in\ngeneral\, when d=2 and when some con
 ditions are satisfied\, there is a\nknown algorithm that resolves it. We w
 ill explain the basics of\nanalytic combinatorics in several variables and
  show how this\nalgorithm operates.\n\nStephanie Penner\n\nTITLE: Combinat
 orial Exploration: Counting Chord Diagrams\n\nABSTRACT: It can often be tr
 icky to find a combinatorial specification\nof a counting sequence for a g
 iven set of objects. A recently\ndeveloped framework called \"Combinatoria
 l Exploration\" aims to\nautomate the process of finding combinatorial spe
 cifications. It has\nsuccessfully been used to find specifications for sev
 eral new\npermutation classes and looks promising for several other object
 s. In\nthis talk\, I will briefly explain how Combinatorial Exploration wo
 rks\,\nand how I am using it to automate finding specifications for famili
 es\nchord diagrams.
DTSTAMP:20260403T080508Z
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