Title of Seminar: Algebraic Geometry Preprint Seminar 2023
Title of Talk: Morphism between homogeneous varieties
Speaker: A.J. Parameswaran, TIFR, Mumbai
Date: October 3, 2023
Time: 16:00:00 Hours
Venue: AG-77
Abstract: There are many classical and obvious results on morphisms: like $\mathbb{P}^n$ cannot map (nonconstant) to $\mathbb{P}^m$ if $m < n$, every nonconstant map of $\mathbb{P}^n$ is finite and so on. We will racall some results of Tango on morphisms of Grassmannians. We will sketch a proof of the fact that every map of $\mathbb{P}^2$ to $\mathrm{SL}_{n/B}$ is constant and conclude that if $\mathrm{SL}_{n/P}$ to $\mathrm{SL}_{m/B}$ is a nonconstant map then the parabolic $P$ is a Borel subgroup of $\mathrm{SL}_n$. We will extend this to showing some examples of maps of $\mathbb{P}^3$ to homogeneous spaces by minimal parabolic subgroups and draw the attention to the recent conjecture of Shrawan Kumar.
Title of Seminar: Infosys Chandrasekharan Random Geometry Colloquium
Title of Talk: Polyhedral-like approximations of strongly $\mathbb C$-convex domains
Speaker: Purvi Gupta, IISc
Date: October 3, 2023
Time: 16:30:00 Hours
Venue: A-369
Abstract: Polyhderal approximations of convex bodies have been studied extensively in both affine and stochastic geometry. Of particular interest are the asymptotics of the approximation error as a function of the complexity of the approximating polyhedra. This analysis yields invariant combinatorial and geometric data associated to the underlying convex body. In this talk, we will discuss the motivation to study polyhedral-like approximations of domains satisfying notions of convexity that are suited for complex analysis. In particular, we will focus on the notion of $\mathbb C$-convexity, which is a natural analogue of convexity in complex projective spaces. We will introduce a suitable notion of polyhedra in this context, and present some (optimal and random) approximation results in the spirit of several results in real convex geometry.
Title of Talk: Morphism between homogeneous varieties
Speaker: A.J. Parameswaran, TIFR, Mumbai
Date: October 3, 2023
Time: 16:00:00 Hours
Venue: AG-77
Abstract: There are many classical and obvious results on morphisms: like $\mathbb{P}^n$ cannot map (nonconstant) to $\mathbb{P}^m$ if $m < n$, every nonconstant map of $\mathbb{P}^n$ is finite and so on. We will racall some results of Tango on morphisms of Grassmannians. We will sketch a proof of the fact that every map of $\mathbb{P}^2$ to $\mathrm{SL}_{n/B}$ is constant and conclude that if $\mathrm{SL}_{n/P}$ to $\mathrm{SL}_{m/B}$ is a nonconstant map then the parabolic $P$ is a Borel subgroup of $\mathrm{SL}_n$. We will extend this to showing some examples of maps of $\mathbb{P}^3$ to homogeneous spaces by minimal parabolic subgroups and draw the attention to the recent conjecture of Shrawan Kumar.
Title of Seminar: Infosys Chandrasekharan Random Geometry Colloquium
Title of Talk: Polyhedral-like approximations of strongly $\mathbb C$-convex domains
Speaker: Purvi Gupta, IISc
Date: October 3, 2023
Time: 16:30:00 Hours
Venue: A-369
Abstract: Polyhderal approximations of convex bodies have been studied extensively in both affine and stochastic geometry. Of particular interest are the asymptotics of the approximation error as a function of the complexity of the approximating polyhedra. This analysis yields invariant combinatorial and geometric data associated to the underlying convex body. In this talk, we will discuss the motivation to study polyhedral-like approximations of domains satisfying notions of convexity that are suited for complex analysis. In particular, we will focus on the notion of $\mathbb C$-convexity, which is a natural analogue of convexity in complex projective spaces. We will introduce a suitable notion of polyhedra in this context, and present some (optimal and random) approximation results in the spirit of several results in real convex geometry.