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DESCRIPTION: The Ph.D. defense starts with a 25' lecture about     Growth o
 f polyominoes     (see below for the abstract)\, which is followed by a dis
 cussion and  a short presentation of the Ph.D. thesis with the title:     G
 rowth of bilinear maps     Abstract of the first talk: Growth of polyominoe
 s   A polyomino is an edge-connected set of cells in the square lattice. Al
 though the  notion is simple and natural\, many problems related to polyomi
 noes are open\,  namely computing efficiently the number of polyominoes A(n
 ) with n cells and  estimating its exponential growth constant λ = lim {n→∞
 }  A(n)^ (1/n) \, which is  known as Klarner's constant. The best algorithm
  for the former problem still  suffers the exponential time complexity\, wh
 ose base can be decreased usually by  using more space. It follows that the
  natural way to bound λ from below by A(n)^ (1/n)   asks for a lot of compu
 tation. The best approach for a bound so far is by  considering twisted cyl
 inders\, a model that is similar to polyominoes  but a bit simpler to compu
 te. This allows the lower bound to just exceed 4 by  Barequet\, Rote\, and 
 Shalah in 2016\, which is close to the believed value λ ≈ 4.06.  The known 
 upper bounds are however not so good: the bound 4.65 has existed since  197
 3 by Klarner and Rivest\, and only very recently got improved to 4.53 in 20
 22  by Barequet and Shalah\, which actually asks for a good deal of computa
 tion.  Related aspects and new approaches will be also discussed. 
DTEND:20231218T140000
DTSTAMP:20231212T171500
DTSTART:20231218T123000
CLASS:PUBLIC
LOCATION:Seminarraum 053\n Institut für Informatik\n Takustraße 9\n Freie U
 niversität Berlin
SEQUENCE:0
SUMMARY:Ph.D. defense of Vuong Bui: Growth of polyominoes and of bilinear m
 aps
UID:139028467@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/events/2023-12-18-PhD-Defense-Vuong-Bu
 i.html
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