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UID:20250803T020959EDT-4062e5xLZB@132.216.98.100
DTSTAMP:20250803T060959Z
DESCRIPTION:Title: Triangle Presentations in ~A_2 Bruhat-Tits Buildings\n\n
 Abstract: The 1-skeleton of an ~A_2 Bruhat-Tits building is isomorphic to 
 the Cayley graph of an abstract group with relations coming from ”triangle
  presentations.” This abstract group either embeds into PGL(3\, Fq((x))) o
 r PGL(3\, Qq)\, or else is exotic. Currently\, the complete list of triang
 le presentations is only known for projective planes of orders q=2 or 3. H
 owever\, one abstract group that embeds into PGL(3\,Fq((x))) for any prime
  power q is known via the trace function corresponding to the finite field
  of order q^3. I have found a different method to derive this group as wel
 l as others via perfect difference sets. This new method demonstrates a pr
 eviously unknown connection between difference sets and ~A_2 buildings. Mo
 reover\, this new method makes the final computation of triangle presentat
 ions easier\, which is computationally valuable for large q.\n\nAs usual\,
  we will gather for seminar teatime in BURN 1024 at 5pm after Amy's talk.
 \n
DTSTART:20241023T200000Z
DTEND:20241023T210000Z
LOCATION:Room 920\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue 
 Sherbrooke Ouest
SUMMARY:Amy Herron (University at Buffalo)
URL:/mathstat/channels/event/amy-herron-university-buf
 falo-360577
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