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\textsc{Combinatorics}
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\textsc{Seminar}
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\textit{Codegree problems for projective geometries}
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Yi Zhao\par
Georgia State University
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The codegree density (F) of an r-graph F is the largest number such that there are 
F-free r-graphs G on n vertices such that every set of r - 1 vertices is contained 
  in at least (\gamma - o(1))n edges. For the Fano plane PG(2, 2), Mubayi showed   
that \gamma(PG(2, 2)) = 1/2. For general projective geometries we obtain the upper 
  bound \gamma(PG(m, q)) 1/m. We show that equality holds whenever m = 2 and q is  
  odd, and whenever m = 3 and q is 2 or 3. We also give examples of r-graphs with  
                codegree densities equal to 1-1/k for all r and k.                 
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Monday, March 26, 2007, 4:00 pm\par
Mathematics and Science Center, W301
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\textsc{Mathematics and Computer Science}\par
\textsc{Emory University}
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