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DTSTART:20240310T070000
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DTSTART:20231105T060000
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DTSTART;TZID=America/Toronto:20240328T140000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/algebraic-an
 d-enumerative-combinatorics-harper-niergarth
SUMMARY:Algebraic and Enumerative Combinatorics - Harper Niergarth
CLASS:PUBLIC
DESCRIPTION:TITLE: On the faces of the Kunz cone and the numerical semigrou
 ps\nwithin them\n\nSPEAKER:\n Harper Niergarth\n\nAFFILIATION:\n Universit
 y of Waterloo\n\nLOCATION:\n MC 5479\n\nThere will be a pre-seminar presen
 ting relevant background at the\nbeginning graduate level starting at 1pm.
 \n\nABSTRACT: A numerical semigroup is a subset of the natural numbers\nt
 hat is closed under addition\, contains 0\, and has finite complement.\nEa
 ch numerical semigroup $S$ with fixed smallest positive element $m$\ncorre
 sponds to an integer point in a polyhedral cone $C_m \\subset\n\\mathbb{R}
 ^{m-1}$ called the Kunz cone. Moreover\, numerical semigroups\ncorrespondi
 ng to points on the same face $F$ of $C_m$ are known to\nshare many proper
 ties\, such as the number of minimal generators. But\nnot all faces of the
  Kunz cone contain integer points corresponding to\nnumerical semigroups. 
 In this talk\, we will classify all the faces\nthat do contain such points
 . Additionally\, we will present sharp\nbounds on the number of minimal ge
 nerators of $S$ in terms of the\ndimension of the face of $C_m$ containing
  the point corresponding to\n$S$.\n\nThis is joint work with Levi Borevitz
 \, Tara Gomes\, Jiajie Ma\,\nChristopher O'Neill\, Daniel Pocklington\, R
 osa Stolk\, Jessica Wang\, and\nShuhang Xue.
DTSTAMP:20260404T085231Z
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