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SUMMARY:Angus McAndrew (BU)
DTSTART:20201009T140000Z
DTEND:20201009T143000Z
DTSTAMP:20260404T094534Z
UID:BUcomm/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/BUcom
 m/1/">How to prove the Hodge conjecture</a>\nby Angus McAndrew (BU) as par
 t of BU Community Seminar\n\n\nAbstract\nFor a complex manifold or algebra
 ic variety\, there are many different invariants one can study. One of the
  premier options are certain vector spaces called the cohomology of the sp
 ace. There are many different approaches to cohomology\, specialised to di
 fferent context/purposes: singular\, etale\, de Rham\, crystalline\, flat\
 , etc.\n\nThere are often ways to take subspaces (called "cycles"\, in ref
 erence to classical homology) and map them into the cohomology groups. In 
 the complex case the ability to integrate over a subspace gives a pairing 
 between the cycles and de Rham cohomology. The Hodge Conjecture states tha
 t cohomology classes of a certain kind always arise from cycles. This is c
 losely related to the Tate conjecture\, which makes a similar claim for et
 ale cohomology\, and more generally to the (conjectural) theory of motives
 .\n\nIn this talk we'll introduce the above ideas in more detail\, show ho
 w to interpret it in the case of a product of complex elliptic curves\, an
 d in fact prove it by explicit computation. This case is actually more gen
 erally covered theoretically by the Lefschetz (1\,1) theorem\, which time 
 permitting we may also discuss.\n
LOCATION:https://stable.researchseminars.org/talk/BUcomm/1/
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BEGIN:VEVENT
SUMMARY:Ben Draves (BU)
DTSTART:20201022T140000Z
DTEND:20201022T143000Z
DTSTAMP:20260404T094534Z
UID:BUcomm/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/BUcom
 m/2/">Common Principal Component Analysis</a>\nby Ben Draves (BU) as part 
 of BU Community Seminar\n\n\nAbstract\nDimensionality reduction attempts t
 o transform often high dimensional data into a lower dimensional represent
 ation while maintaining the data's intrinsic properties. Several methods h
 ave been developed to accomplish this task\, but perhaps the most widely u
 sed is Principal Component Analysis (PCA). While PCA is well known\, its e
 xtension to multiple populations\, Common Principle Component Analysis (CP
 CA)\, is much lesser known. In this talk we introduce CPCA and discuss its
  efficacy for completing dimensionality reduction across multiple populati
 ons. In addition\, we discuss spectral approaches for fitting CPCA in prac
 tice\, including randomized algorithms for truncated singular value decomp
 ositions. Finally\, we employ CPCA for simultaneous dimensionality reducti
 on across penguin species in the Palmer Penguin dataset.\n
LOCATION:https://stable.researchseminars.org/talk/BUcomm/2/
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