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SUMMARY:Angus McAndrew (BU)
DTSTART:20201009T140000Z
DTEND:20201009T143000Z
DTSTAMP:20260422T212610Z
UID:BUcomm/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BUcomm/1/">H
 ow to prove the Hodge conjecture</a>\nby Angus McAndrew (BU) as part of BU
  Community Seminar\n\n\nAbstract\nFor a complex manifold or algebraic vari
 ety\, there are many different invariants one can study. One of the premie
 r options are certain vector spaces called the cohomology of the space. Th
 ere are many different approaches to cohomology\, specialised to different
  context/purposes: singular\, etale\, de Rham\, crystalline\, flat\, etc.\
 n\nThere are often ways to take subspaces (called "cycles"\, in reference 
 to classical homology) and map them into the cohomology groups. In the com
 plex case the ability to integrate over a subspace gives a pairing between
  the cycles and de Rham cohomology. The Hodge Conjecture states that cohom
 ology classes of a certain kind always arise from cycles. This is closely 
 related to the Tate conjecture\, which makes a similar claim for etale coh
 omology\, and more generally to the (conjectural) theory of motives.\n\nIn
  this talk we'll introduce the above ideas in more detail\, show how to in
 terpret it in the case of a product of complex elliptic curves\, and in fa
 ct prove it by explicit computation. This case is actually more generally 
 covered theoretically by the Lefschetz (1\,1) theorem\, which time permitt
 ing we may also discuss.\n
LOCATION:https://researchseminars.org/talk/BUcomm/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Draves (BU)
DTSTART:20201022T140000Z
DTEND:20201022T143000Z
DTSTAMP:20260422T212610Z
UID:BUcomm/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BUcomm/2/">C
 ommon Principal Component Analysis</a>\nby Ben Draves (BU) as part of BU C
 ommunity Seminar\n\n\nAbstract\nDimensionality reduction attempts to trans
 form often high dimensional data into a lower dimensional representation w
 hile maintaining the data's intrinsic properties. Several methods have bee
 n developed to accomplish this task\, but perhaps the most widely used is 
 Principal Component Analysis (PCA). While PCA is well known\, its extensio
 n to multiple populations\, Common Principle Component Analysis (CPCA)\, i
 s much lesser known. In this talk we introduce CPCA and discuss its effica
 cy for completing dimensionality reduction across multiple populations. In
  addition\, we discuss spectral approaches for fitting CPCA in practice\, 
 including randomized algorithms for truncated singular value decomposition
 s. Finally\, we employ CPCA for simultaneous dimensionality reduction acro
 ss penguin species in the Palmer Penguin dataset.\n
LOCATION:https://researchseminars.org/talk/BUcomm/2/
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