# Complex Analysis, Harmonic Analysis, & Complex Geometry Seminar

@Rutgers - New Brunswick

Welcome to the homepage of Complex Analysis, Harmonic Analysis, and Complex Geometry seminar at Rutgers University - New Brunswick.

To subscibe please send an email to ayush.khaitan@rutgers.edu

Times: Fridays, 10:30 - 11:30 a.m. Eastern Time

Location: Hill 705, Department of Mathematics, Hill Center - Busch campus

110 Frelinghuysen Road, Piscataway, NJ 08854

Schedule Fall 2023

## September 8th: Eiji Inoue (RIKEN iTHEMS)- Introduction to optimal degeneration problems

Abstract: Optimal degeneration is a 'test configuration' of a projective variety X which degenerates the variety X to a variety Y K-semistable in an extended sense. It is characterized as a maximizer of a certain quantity for test configurations. The conjectural existence of optimal degeneration is important as it completes the proof of the YTD conjecture and more importantly it clarifies the right treatment of K-unstable varieties in moduli theory.

There are various frameworks of optimal degeneration depending on the choice of the quantity (normalized Donaldson-Futaki invariant, H-entropy, mu-entropy, ...), which corresponds to choosing a certain extended framework of K-stability for 'spacetime' (relative K-stability, modified D-stability, muK-stability, ...).

I would like to sketch the blueprint of optimal degeneration problem and report where we are now in the long way to go.

## September 15th: Ved Data (IISc, Bangalore)- Minimal slopes and singular solutions for some complex Hessian type equations on Kahler manifolds

## September 29th: K. Han (Seoul National University)- The notions of first integral and involutivity, and some applications to control problems

The notion of first integral came from the classical mechanics. The constants of motion, namely, the total enegy and the angular momentum in the Newtonian mechanics are typical examples of the first integral. I will survey briefly how these notions have been generalized along the lines of exterior differential systems, including the Frobenius theorem on integrability. Then we shall discuss the partial integrability and the notion of weak first integral, and as applications, the affine control problems with prescribed obstacles and the stability of population dynamics of Kolmogorov type.