[Turkmath:6058] Feza Gursey Merkezinde "Dual Perspectives" konusmasi (14 Nisan Cuma)

[sadik.deger at boun.edu.tr]

Sayin liste uyeleri,

Bogazici Universitesi Kandilli kampusunde yer alan Feza Gursey Fizik ve
Matematik Arastirma Merkezinde matematikciler ile kuramsal  fizikcileri
bulusturmayi hedefledigimiz "Dual Perspectives" konusma dizisine 14 Nisan
Cuma gunu detaylari asagida ve ekteki posterde yer alan konusmayla devam
ediyoruz.

Butun ilgilenenleri bekleriz,

Nihat Sadik Deger, Umut Varolgunes

------------------------------------------------------

Konusma dizisinin web sayfasi: https://umutvg.github.io/dp.html

Tarih: 14 Nisan 2023, Cuma (Sabah bolumu 10:30-12:00, Oglen bolumu   
13:30-15:00)

Konusmaci: Ivan Cheltsov, University of Edinburgh

Baslik: K-moduli of Fano threefolds in the family 3-10

Ozet: Smooth Fano 3-folds are classified in 105 families (Iskovskikh, Mori,
Mukai). For the description of these families, see   
https://www.fanography.info .
We know which deformation families have K-polystable (Kahler-Einstein) members
and which do not (Araujo, Castravet, Cheltsov, Fujita, Kaloghiros, Martinez-
Garcia, Shramov, Suess, Viswanathan). Since K-polystable Fano threefolds form
good moduli spaces, it would be interesting to describe K-moduli of smoothable
Fano 3-folds (moduli that parametrize K-polystable smooth members of a given
deformation family and their K-polystable limits). This is a very   
active area of
research, but the problem has only been solved for the following 52   
deformation
families: zero-dimensional families (47 families), two one-dimensional  
  families
(families 2-24 and 2-25), cubic 3-folds (Liu, Xu), complete   
intersection of two
quadrics (Spotti, Sun), quartic double solids (Ascher, DeVleming,   
Liu). In this
talk, I will speak about K-moduli of Fano 3-folds in the family 3-10, see
https://www.fanography.info/3-10 . This is a two-dimensional family   
whose smooth
members can be obtained by blowing up a smooth quadric 3-fold along   
two disjoint
conics. We know that a general member of this family is K-stable (Kahler-
Einstein and finite automorphism groups), but some smooth members are not
K-polystable (not Kahler-Einstein), and some members have infinite   
automorphism
group (Cheltsov, Przyjalkowski, Shramov). In the talk, I will give explicit
classification of all smooth members of the family 3-10 (normal   
forms), explain
which smooth Fano 3-folds in this family are K-polystable and which are not
(Araujo, Castravet, Cheltsov, Fujita, Kaloghiros, Martinez-Garcia, Shramov,
Suess, Viswanathan), and describe all singular K-polystable members of this
family (work in progress with Alan Thompson from Loughborough). If   
time permits,
I will explain how to prove K-polystability of one singular and very symmetric
member of this deformation family.



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