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ORGANIZER;CN=Kushnerchuk Nataliia:mailto:nataliia.kushnerchuk@aalto.fi
ATTENDEE;ROLE=REQ-PARTICIPANT;PARTSTAT=NEEDS-ACTION;RSVP=FALSE;CN=agc-math-
 aalto@list.aalto.fi:mailto:agc-math-aalto@list.aalto.fi
ATTENDEE;ROLE=REQ-PARTICIPANT;PARTSTAT=NEEDS-ACTION;RSVP=FALSE;CN=matlait-h
 enkilosto@helsinki.fi:mailto:matlait-henkilosto@helsinki.fi
DESCRIPTION;LANGUAGE=en-GB:We would like to invite you to the next talk of 
 autumn in the Aalto AGC (Algebra\, Geometry and Combinatorics) Seminar!\n\
 nThe talk is on\nMon 07.9. at 14:15-15:00\nin\nM3 (M234)\, Otakaari 1.\n\n
 The speaker is\nNataliia Kushnerchuk (Aalto)\ngiving the talk\nPosets of t
 rek polynomials for directed graphical models\n\nAbstract:\nWhen a variety
  V𝜑 equals the image of a polynomial map 𝜑 whose coordinate\nfunctio
 ns are combinatorial generating polynomials (i.e. polynomials enumerating 
 combinatorial\nobjects)\, the geometry of V𝜑 reflects identities satisf
 ied by the generating polynomials. The\nresulting interplay between combin
 atorics and algebraic geometry can be used to answer questions about V𝜑
  . A recent technique proposes to do so using a partially ordered set (pos
 et) 𝑃𝜑 defined via the coefficient vectors of the polynomials defini
 ng 𝜑.\nIn this talk I am going to talk about a subfamily of Gaussian di
 rected graphical models that we have studied with this new technique. For 
 this family\, the generating polynomials of 𝜑 defining a graphical mode
 l enumerate certain subgraphs known as treks. We characterized the poset 
 𝑃𝜑\, and used the characterization to compute the linear span of V
 𝜑 \, prove it is toric and deduce\na basis for its vanishing ideal. As 
 an additional consequence\, it is shown that the varieties for two distinc
 t directed trees intersect in a strictly lower-dimensional variety. This s
 olves an instance of the structural identifiability problem in the graphic
 al models program from statistics.\nBased on https://arxiv.org/abs/2608.08
 325\n\nThe webpage of the seminar is at\nmath.aalto.fi/en/research/discret
 e/seminars/agc/<https://math.aalto.fi/en/research/discrete/seminars/agc/>\
 nand we have a mailing list at\nhttps://list.aalto.fi/mailman/listinfo/agc
 -math-aalto\n\n\n\n
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 010000000D2BF55041D3C0346AF94B80061F8C1F4
SUMMARY;LANGUAGE=en-GB:[Aalto AGC Seminar] Nataliia Kushnerchuk | Posets of
  trek polynomials for directed graphical models | Mon 07.09. at 14:15
DTSTART;TZID=FLE Standard Time:20260907T141500
DTEND;TZID=FLE Standard Time:20260907T150000
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DTSTAMP:20260902T133832Z
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