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UID:0-1790@hmc.edu
DTSTART;TZID=America/Los_Angeles:20260423T161500
DTEND;TZID=America/Los_Angeles:20260423T173000
DTSTAMP:20260417T222614Z
URL:https://www.hmc.edu/calendar/events/mathematical-connections-seminar-a
 ndres-vindas-melendez/
SUMMARY:Mathematical Connections Seminar: Andrés Vindas Meléndez
DESCRIPTION:“Coloring Graphs with a q-Twist: From Chromatic Polynomials t
 o Polyhedral Geometry”\nAbstract\nHow many ways can you color the vertic
 es of a graph so that no two connected vertices share the same color? This
  classic question is answered by the chromatic polynomial\, a fundamental 
 tool in combinatorics that counts "proper colorings." Meléndez introduces
  a new "weighted" version of this concept: the q-chromatic polynomial. Ins
 tead of simply counting colorings\, this invariant assigns weights to them
 \, producing a richer algebraic/combinatorial object that recovers the cla
 ssical chromatic polynomial when q=1.\n\nA key theme of the talk is the co
 nnection between graph coloring and polyhedral geometry. Meléndez will ex
 plain how proper colorings can be interpreted as lattice points inside geo
 metric objects called polytopes\, and how tools from polyhedral geometry (
 such as Ehrhart theory) help us understand these polynomials. This perspec
 tive leads to new formulas\, structural insights\, and a concrete bridge b
 etween combinatorics and geometry.\n\nNo background necessay\, just a will
 ingness to stare at graphs and polytopes.
CATEGORIES:Faculty,Staff,Students
LOCATION:Shanahan Center\, 320 E. Foothill Blvd.\, Claremont\, CA\, 91711\,
  United States
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