[PHK_seminar] [Cohomology]Wednesday 20 Mar, K V Subrahmanyam

[Igor Khavkine]

Dear All,

The video recording of the talk by K V Subrahmanyam from last week is 
now available on YouTube at

   https://youtu.be/wGv6XutOSnw

It has also been recorded at the ResearchSeminars announcement

   https://researchseminars.org/talk/PHK-cohomology-seminar/99/

Best,

Igor

On 3/18/24 13:00, sender of seminar announcement via phk_seminar wrote:
> Wednesday, 20 March 2024 - 13:30 to 14:30
> Place: ZOOM meeting
> 
> Speaker: K V Subrahmanyam, Chennai Mathematical Institute
> Title: Stabilizer limits and Orbit closures with applications to 
> Geometric Complexity Theory
> 
> Abstract
> 
> Let $G\subseteq GL(X)$ be a reductive group acting on a finite 
> dimensional vector space $V$ over $\C$. A central problem in Geometric 
> Complexity Theory is the study points $y,z\in V$ where (i) $z$ is 
> obtained as the leading term of the action of a 1-parameter subgroup 
> $\lambda (t)\subseteq G$ on $y$, and (ii) $y$ and $z$ have large 
> distinctive stabilizers $K,H \subseteq G$.
> 
> We address the question: under what conditions can (i) and (ii) be 
> simultaneously satisfied, i.e, there exists a 1-PS $\lambda \subseteq G$ 
> for which $z$ is observed as a limit of $y$.
> 
> 
> Using $\lambda$, we develop a leading term analysis which applies to $V$ 
> as well as to ${\mathcal G}= Lie(G)$ the Lie algebra of $G$ and its 
> subalgebras ${\cal K}$ and ${\cal H}$, the Lie algebras of $K$ and $H$ 
> respectively.
> 
> Through this we construct the Lie algebra $\hat{\cal K} \subseteq {\cal 
> H}$ which connects $y$ and $z$ through their Lie algebras. Here 
> $\hat{\cal K} is the leading term Lie algebra obtained from ${\cal K}$ 
> by the adjoint action of $\lambda(t)$. We develop the properties of 
> $\hat{\cal K}$ and relate it to the action of ${\cal H}$ on 
> $\overline{N}=V/T_z O(z)$, the normal slice to the orbit $O(z)$.
> 
> 
> We examine the case when a semisimple element belongs to both ${\cal H}$ 
> and ${\cal K}$. We call this a {\em alignment}. We describe some 
> consequences of alignment and relate it to existing work on lower bounds 
> in the case of the determinant and permanent.
> 
> We also connect alignment to {\em intermediate $G$-varieties} $W$ which 
> lie between the orbit closures of $z$ and $y$, i.e. $\overline{O(z)} 
> \subsetneq W \subsetneq O(y)$. These have a direct bearing on 
> representation theoretic as well as geometric properties which connect 
> $z$ and $y$.
> 
> 
> This is joint work with Bharat Adsul and Milind Sohoni.
> 
> -----------------------------------------------------------------------------------------------------------------------
> 
> We shall open ZOOM at 13.15 for virtual coffee
> 
> Join Zoom Meeting
> 
> https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09 <https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09>
> 
> MeetingID:99598413922
> 
> Passcode:Galois
> 
> 
> For more information see the seminar web page at
> https://www.math.cas.cz/index.php/events/seminar/16
> 
> Cohomology in algebra, geometry, physics and statistics mailing list
> phk_seminar at math.cas.cz
> https://list.math.cas.cz/listinfo/phk_seminar@math.cas.cz
> 
> 
> _______________________________________________
> phk_seminar mailing list
> phk_seminar at math.cas.cz
> https://list.math.cas.cz/listinfo/phk_seminar