Session II.3 - Real-Number Complexity
Thursday, June 15, 15:30 ~ 16:00
Characterisations of good convex cones
Vera Roshchina
UNSW Sydney, Australia - This email address is being protected from spambots. You need JavaScript enabled to view it.
There are many properties of facial structure of convex sets that coincide in a lower-dimensional setting but differ in higher dimensions. This talk will cover several such different properties and their relations, including facial exposure, facial dual completeness (niceness), amenability and projectional exposure. Even though the definitions of these properties have a different nature, they form a neat hierarchy. Based on an example of sufficient and necessary conditions for niceness obtained using lexicographic tangents, an argument can be made about a possibility to explain these different notions and their relations using a unified approach.
Joint work with Bruno Lourenço (The Institute of Statistical Mathematics/SOKENDAI, Japan) and James Saunderson (Monash University, Australia).