Date September 18 (Thursday), 2025
Venue KIAS Building 1 (Room 1503), Seoul, Korea
Time 9:30 - 16:00
Joint event
KIAS Colloquium at 16:30, Room 1503
Gram Matrices for Isotropic Vectors by Professor Bernd Sturmfels (MPI)
Registration Please submit your registration by 11:59 p.m. on September 11 (Korean Standard Time)
Martin Bridson (U of Oxford)
KyeongRo Kim (KIAS)
Amie Wilkinson (U of Chicago)
Pengyu Yang (Morningside Center of Mathematics)
Bernd Sturmfels (MPI)
9-9:30 Registration/Coffee
9:30 - 10:30 KyeongRo Kim
10:30- 11:00 Coffee Break
11:00-12:00 Martin Bridson
12:00 - 13:30 Lunch
13:30 - 14:30 Pengyu Yang
2:30 - 3:00 Tea time
15:00 - 16:00 Amie Wilkinson
16:30 - 17:30 Bernd Sturmfels (KIAS Colloquium)
KyeongRo Kim
Ping-pong dynamics of hyperbolic-like actions
Abstract: In dimension 1, the dynamical properties of a group action and the algebraic properties of the group are highly intertwined. When the action satisfies the uniformly bounded fixed point condition, this relationship becomes especially apparent. In the real line, such a relationship has been completely revealed by Holder and Solodov under the at most 1 fixed point condition. However, in the circle, the relationship is still mysterious even under the at most 2 fixed point condition. For this case, Bonatti conjectured a structure theorem. In this talk, I will introduce the conjecture of Bonatti, and discuss related questions. Also, I will introduce recent progress about Bonatti conjecture. This talk is based on a joint work with Michele Triestino.
Martin Bridson
Common finite covers and quasitrees
Abstract: Sam Shepherd and I proved that if two finite simplicial complexes have isomorphic universal covers and
free fundamental groups, then they have a common finite cover. In the 1-dimensional case (graphs), this is Leighton's Theorem. I shall discuss various extensions of Leighton's Theorem and examples that illustrate its limitations, with a focus on coverings by quasitrees. I shall then outline a proof of our theorem, which involves the construction of auxiliary CAT(0) cube complexes
Pengyu Yang
Birkhoff generic points on affine subspaces in horospheres
Abstract: We discuss Birkhoff genericity on affine subspaces of horospheres for diagonal flow in homogeneous spaces, and its application to Diophantine approximation. Joint work in progress with Shah.
Amie Wilkinson
Dynamical Symmetry
Abstract: The centralizer Z(f) of a diffeomorphism f: M--> M of a closed manifold M is the group of all diffeomorphisms commuting with f; it is the collection of dynamical symmetries of f. The centralizer of f always contains the group <f> generated by f as a normal subgroup, and conjecturally the two typically coincide (that is, ``the generic diffeomorphism has only trivial symmetries''). In this talk, I will describe some results and conjectures in a project with Danijela Damjanovic, Chengyang Wu and Disheng Xu that addresses the question: what happens when Z(f) is bigger than <f>?
Bernd Sturmfels (colloquium)
Gram Matrices for Isotropic Vectors
We discuss the algebraic geometry of low rank symmetric matrices that have zero blocks along the main diagonal. In theoretical physics, these arise as Gram matrices for kinematic variables in quantum field theories.
Contact : Homin Lee (KIAS)
hominlee (at) kias (dot) re (dot) kr