STGS Geometry Module

	Date	Title	Speaker	Keywords

Feb²³
Feb²³	20^th	The Demailly systems with the Vortex ansatz	Arindam Mandal	Demailly's system, Vortex bundle, Nonlinear elliptic PDE

Jan²³
	23^rd	On the positivity of ample vector bundles	Arindam Mandal	Positivity of vector bundles, Griffiths conjecture, Demailly's approach
	16^th	How to determine whether a simply connected smooth surface is parabolic or hyperbolic depending on growth of curvature functions	Gobinda Sau	Simply connected surface, Growth of curvature functions
	9^th	Vortex Bundle and Hermite-Einstein metric (part 2)	Kartick Ghosh	Vortex equation, Hermitian-Yang-Mills equation, Vortex bundle
	2^nd	Vortex Bundle and Hermite-Einstein metric (part 1)	Kartick Ghosh	Vortex equation, Hermitian-Yang-Mills equation, Vortex bundle

Nov²²
	28^th	Positivity of differential forms (part 3)	Anantadulal Paul (Postdoc, ICTS)	Positivity of differential form, Griffiths conjecture on positivity, Schur forms
	23^rd	Coupled Kähler Einstein and Yang-Mills equations (part 2)	Kartick Ghosh	Kähler-Einstein equation, Yang-Mills equation and Moment map
	16^th	Coupled Kähler Einstein and Yang-Mills equations (part 1)	Kartick Ghosh	Kähler-Einstein equation, Yang-Mills equation and Moment map
	7^th	Positivity of differential forms (part 2)	Anantadulal Paul (Postdoc, ICTS)	Positivity of differential form, Griffiths conjecture on positivity, Schur forms

Oct²²
	31^st	Positivity of differential forms (part 1)	Anantadulal Paul (Postdoc, ICTS)	Positivity of differential form, Griffiths conjecture on positivity, Schur forms
	21^st	Ricci Flow and Uniformization (part 2)	Gobinda Sau	Ricci flow, Uniformization theorem, PDE theory
	17^th	Ricci Flow and Uniformization (part 1)	Gobinda Sau	Ricci flow, Uniformization theorem, PDE theory
	10^th	Gromov-Hausdorff convergence along Kähler-Ricci flow	Sivaram P.	Gromov-Hausdorff convergence, Calabi ansatz, Kähler-Ricci flow

Sep²²
	28^th	Gromov-Hausdorff convergence	Sivaram P.	Gromov-Hausdorff metric, Hausdorff metric, Gromov-Hausdorff convergence
	19^th	The Calabi and Mabuchi Functionals and their Critical Points	Rajas Sandeep Sompurkar	Calabi Functional, Mabuchi Functional, Extremal Kähler Metrics, cscK Metrics, Higher Extremal Kähler Metrics, hcscK Metrics
	12^th	$L^{2}$ extension and interpolation	Arindam Mandal	Interpolation in $C$
	5^th	Lebrun-Simanca deformation (part 2)	Kartick Ghosh	Extremal metrics, holomorphic vector fields

Aug²²
	29^th	Lebrun-Simanca deformation (part 1)	Kartick Ghosh	Extremal metrics, holomorphic vector fields
	22^th	Heat kernel on a Riemannian manifold and Heat kernel estimates	Gobinda Sau	Heat Kernel, Fundamental Solution
	15^th	$J$ equation and Stability (part 2)	Sivaram P.	Test configuration, $J$ equation, Stability
	1^st	$J$ equation and Stability (part 1)	Sivaram P.	Test configuration, $J$ equation, Stability

July²²
	25^th	Heat kernel and Parabolic maximum Principle	Gobinda Sau	Heat Kernel, Parabolic Maximum Principle
	18^th	Lectures On K-stability (part 3)	Kartick Ghosh	Test configuration, Donaldson-Futaki invariant, K-stability
	11^th	Lectures On K-stability (part 2)	Kartick Ghosh	Moment map, Scalar curvature, Hilbert polynomials, Flat limits
	4^th	Lectures On K-stability (part 1)	Kartick Ghosh	Moment map, symplectic/algebraic quotient construction, Geometric invariant theory, stable/semi-stable/poly-stable points, Hilbert-Mumford criterion

June²²
	27^th	Toric Varieties (part 4)	Adithya Upadhya	Compactness of Toric varieties
	23^rd	Toric Varieties (part 3)	Adithya Upadhya	Orbit-Cone Correspondence
	20^th	Toric Varieties (part 2)	Adithya Upadhya	Fans, Orbit-Cone correspondence
	13^th	Toric Varieties (part 1)	Adithya Upadhya	Affine/Projective/General Toric varieties, Normal toric varieties
	6^th	Futaki Invariant and Localisation formula for it (part 2)	Kartick Ghosh	Blow-Up of a manifold, K-stability

May²²
	30^th	Futaki Invariant and Localisation formula for it (part 1)	Kartick Ghosh	KE/cscK metric, Futaki invariant, Localisation formula
	23^rd	Mabuchi Functional	Sivaram P.	cscK Metric

Apr²²
	25^th	Chern character map in complex setting	Anantadulal Paul (Postdoc, ICTS)	Chern Character map, $\partial \bar{\partial}$ exact forms
	11^th	PDEs on Manifolds	Gobinda Sau	Vector bundles, Sections of vector bundle, Connections
	4^th	Image of Chern character map	Anantadulal Paul (Postdoc, ICTS)	Chern character map, Exact forms

Mar²²
	28^th	Chern-Weil Theory	Anantadulal Paul (Postdoc, ICTS)	Characteristic classes, Chern Character, Gauss-Bonnet theorem
	21^st	Hörmander's theorem with $L^{2}$ estimates on a compact Kähler manifold (part 2)	Kartick Ghosh	Bochner-Kodaira Identity
	7^th	Hörmander's theorem with $L^{2}$ estimates on a compact Kähler manifold (part 1)	Kartick Ghosh	$\bar{\partial}$ operators and their adjoints

Feb²²
	28^th	Hörmander's Theorem on the solution of the $\bar{\partial}$ equation with $L^{2}$ estimates (part 3)	Arindam Mandal	Bochner-Kodaira Identity
	21^st	Hörmander's Theorem on the solution of the $\bar{\partial}$ equation with $L^{2}$ estimates (part 2)	Arindam Mandal	Functional Analysis Lemma, Hilbert Space adjoint, Formal adjoint
	14^th	Hörmander's Theorem on the solution of the $\bar{\partial}$ equation with $L^{2}$ estimates (part 1)	Arindam Mandal	$\bar{\partial}$ equation, Distribution theory, Unbounded operators
	7^th	Kähler Geometry (part 4)	Sivaram P.	Complex geometry, Kähler geometry

Jan²²
	31^st	Kähler Geometry (part 3)	Sivaram P.	Complex geometry, Kähler geometry
	24^th	Kähler Geometry (part 2)	Sivaram P.	Connection on Holomorphic Vector Bundle, Chern connection
	17^th	Kähler Geometry (part 1)	Rajas Sandeep Sompurkar	Complex geometry, Kähler geometry