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DTSTART:20230101T000000
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BEGIN:VEVENT
DTSTART;VALUE=DATE:20241108
DTEND;VALUE=DATE:20241114
DTSTAMP:20260415T221327
CREATED:20240930T083348Z
LAST-MODIFIED:20240930T084043Z
UID:3366-1731024000-1731542399@ccg.ibs.re.kr
SUMMARY:Giancarlo Urzua (Pontificia Universidad Catolica de Chile)
DESCRIPTION:Giancarlo Urzua \nVisitor (2024.11.8-2024.11.13) from Pontificia Universidad Catolica de Chile \nOffice: –
URL:https://ccg.ibs.re.kr/event/giancarlo-urzua-241108-241113/
CATEGORIES:Visitors
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20241112T160000
DTEND;TZID=Asia/Seoul:20241112T170000
DTSTAMP:20260415T221327
CREATED:20240930T082034Z
LAST-MODIFIED:20241111T063450Z
UID:3357-1731427200-1731430800@ccg.ibs.re.kr
SUMMARY:Giancarlo Urzua\, The Birational Geometry of Markov Numbers
DESCRIPTION:    Speaker\n\n\nGiancarlo Urzua\nPontificia Universidad Catolica de Chile\n\n\n\n\n\n\nThe projective plane is rigid. However\, it may degenerate to surfaces with quotient singularities. After the work of Bădescu and Manetti\, Hacking and Prokhorov 2010 classified these degenerations completely. They are Q-Gorenstein partial smoothings of P(a2\, b2\, c2)\, where a\, b\, c satisfy the Markov equation x2+y2+z2=3xyz. Let us call the corresponding degenerations Markovian planes. They are part of a bigger picture of degenerations with Wahl singularities\, where there is an explicit MMP whose final results are either K nef\, smooth deformations of ruled surfaces\, or Markovian planes. Although it is a final result of MMP\, we can nevertheless run MMP on small modifications of Markovian planes to obtain new numerical/combinatorial data for Markov numbers via birational geometry. New connections with Markov conjecture (i.e. Frobenius Uniqueness Conjecture) are byproducts. This is joint work with Juan Pablo Zúñiga (Ph.D. student at UC Chile)\, the pre-print can be found here https://arxiv.org/abs/2310.17957.
URL:https://ccg.ibs.re.kr/event/2024-1112/
LOCATION:B236-1\, IBS\, Korea\, Republic of
CATEGORIES:Algebraic Geometry Seminar
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