You and Asuka have been on good terms since coming to the Miniature Garden. She was the first friend that You made when they first arrived. She has shown concerned for You's safety such as when You bet her life when challenging the Griffin and when she came back wounded after battling a corrupt Galdo Gasper in a Gift Game.
In various parts of the story, they are seen to go together in training, shopping and even finding the same mentor to train under.
Initially put off by Izayoi's demeanor and cocky attitude, Asuka has since come to respect Izayoi's strength and intelligence. She was surprised and complimented him when he won Black Rabbit's Gift Game, revealing that he was smarter than he appeared to be, albeit his method stayed true to his brute way of going about things. Izayoi also promises to hold a Festival to honor the sun together with her and the others of the Community. Later on in the battle with Ratten, it is written in the light novel that she pulled through when she remembered her promise with Izayoi and broke free from Ratten's flute enchantments.
Her mentor who teaches her to have patience and not to use her full potential. This is because he believes in keeping the best cards hidden till the time calls for them to be placed on the pile. He also said to Izayoi:
"Her Gift is very strong. I've not heard of evaporating a metal bar with just a Gift that's supposed to give a small spark for kindling fire."
when Izayoi asked him about his appraisal of her current strength. To help reduce expenses and the wastage of Gifts that comes from the incompatibility of attacks, he provides her with lessons on strategizing battle plans. Though this is only implied by his words that needn't be clear for Izayoi to understand.