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SUMMARY:Hailong Dao (University of Kansas)
DTSTART:20200625T203000Z
DTEND:20200625T220000Z
DTSTAMP:20260423T021432Z
UID:FOTR/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FOTR/10/">A 
 truly mutually beneficial friendship: how Stanley-Reisner theory enhanced 
 both combinatorics and algebra</a>\nby Hailong Dao (University of Kansas) 
 as part of Fellowship of the Ring\n\n\nAbstract\nGiven a simplicial comple
 x on n vertices\, one can associate to it a quotient of the polynomial rin
 g in n variables\, called the Stanley-Reisner ring. Starting with the proo
 f of the Upper Bound Conjecture for spheres\, this approach has been spect
 acularly useful in bringing tools from commutative algebra to the study of
  simplicial complexes. In the first part of the talk I will sketch some re
 levant parts of this story. In the second\, I will describe how modern too
 ls\, including cohomological vanishing results and characteristic p method
 s\, have inspired new developments. At the same time\, results obtained on
  the combinatorics side now can be brought back to induce interesting new 
 questions and theorems on the algebra side. One thing I really like about 
 this topic is that it can be used to generate good problems at all levels\
 , including for high school students.\n
LOCATION:https://researchseminars.org/talk/FOTR/10/
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