BIMSA >
Seminar on Algebraic, Complex Geometry and Singularities
NEW k-TH YAU ALGEBRAS OF ISOLATED HYPERSURFACE SINGULARITIES
NEW k-TH YAU ALGEBRAS OF ISOLATED HYPERSURFACE SINGULARITIES
Organizer
Speaker
Naveed Hussain
Time
Friday, February 24, 2023 9:00 PM - 9:45 PM
Venue
Online
Abstract
Let V be a hypersurface with an isolated singularity at the origin defined by the holomorphic function f:(Cn, 0) → (C, 0). The Yau algebra L(V) is defined to be the Lie algebra of derivations of the moduli algebra A(V):= On/(f, ∂f ∂x1 , · · · , ∂f ∂xn ), i.e., L(V) = Der(A(V), A(V)). It is known that L(V) is a finite dimensional Lie algebra and its dimension λ(V) is called Yau number. In this talk, we will discuss a new series of Lie algebras, i.e., k-th Yau algebras L k (V), k ≥ 0, which are a generalization of Yau algebra. L k (V) is defined to be the Lie algebra of derivations of the k-th moduli algebra Ak(V):= On/(f, mkJ(f)), k ≥ 0, i.e., L k (V) = Der(Ak (V), Ak (V)), where m is the maximal ideal of On. The k-th Yau number is the dimension of L k (V) which we denote as λ k (V). These numbers λ k (V) are new numerical analytic invariants of singularities. I will also present several published results with Professor Stephen Shing Toung Yau and Huaiqing Zuo which is really important to study the Lie algebra and singularity theory.
Speaker Intro
Dr. Naveed Hussain did his Master degree in pure mathematics from Government College University Faisalabad from 2013-2015. He started his PhD under the Supervision of Professor Stephen Shing Toung Yau (2015-2019) and his area of research are Lie algebras and Singularity Theory. Now he is working as Assistant Professor at Department of Mathematics and Statistics, University of Agriculture Faisalabad, Pakistan.