RTG Student Geometry Seminar

from Friday
June 01, 2018 to Monday
December 31, 2018
Show events for:
Instructions for subscribing to Stony Brook Math Department Calendars

Wednesday
September 05, 2018

12:00 PM - 1:00 PM
Math Tower 5-127
Nathan Chen, Stony Brook University
An introduction to the analytic minimal model program

We will give an introduction to Kähler-Ricci Flow (KRF) and the minimal model program (MMP). The goal of this talk is to highlight the relationship between KRF and the MMP, and explain what happens in complex dimensions 1 and 2.


Wednesday
September 12, 2018

12:00 PM - 1:00 PM
Math Tower 5-127
Ben Wu, Stony Brook University
A Review of Kähler Geometry

In this talk, we will review the basic definitions in Kähler geometry and will provide some examples of Kähler manifolds. We will then review the notion of curvature and will discuss the Ricci curvature of a compact Kähler manifold. We will try to make this talk accessible to those who are not already familiar with these concepts.


Wednesday
September 19, 2018

12:00 PM - 1:00 PM
Math Tower 5-127
Tobias Shin, Stony Brook University
Kähler Ricci Flow

We will go through the definitions of the Kähler flow and provide some examples in low dimensions. We will also explain how the Kähler cone fits in and realize the first Chern class in terms of the Ricci curvature.


Wednesday
September 26, 2018

12:00 PM - 1:00 PM
Math Tower 5-127
Lisandra Hernandez Vazquez, Stony Brook University
Maximal Existence Time for Kähler-Ricci Flow

We will prove the result on maximal existence time for the Kähler-Ricci flow that was stated last time. The proof goes by showing that solutions to the flow are equivalent to solutions of a certain complex Monge-Ampère equation which, in this context, satisfy certain bounds that are uniform in time. We will finish by discussing concrete examples of the possible behaviors of the flow.


Wednesday
October 03, 2018

12:00 PM - 1:00 PM
Math Tower 5-127
Jae Ho Cho, Stony Brook University
Regularity estimates and the convergence theorem of the Kähler-Ricci flow when c1(M)<0

We will continue to consider the complex Monge-Ampère equation associated to the Kähler-Ricci flow. Especially, we will discuss about the regularity estimates based on the maximum principle. Time permitting, we will prove that when c1(M)<0, the normalized Kähler-Ricci flow starting at any Kähler metric converges to a Kähler-Einstein metric, which suggests the alternative proof of Calabi conjecture when c1(M)<0.


Wednesday
October 10, 2018

12:00 PM - 1:00 PM
Math Tower 5-127
Jean-François Arbour, Stony Brook University
Convergence of the Kähler-Ricci flow when c1(M) = 0


Wednesday
October 17, 2018

12:00 PM - 1:00 PM
Math Tower 5-127
Alexandra Viktorova, Stony Brook University
Kähler Ricci Flow on Complex Surfaces

In this talk, we will review some definitions and then discuss the Kähler-Ricci flow on surfaces of complex dimension two and Kodaira dimension minus infinity. We will consider the cases of $\mathbb{P}^{1} \times \mathbb{P}^{1}$ and the blow up of $\mathbb{P}^{2}$ at a point.


Wednesday
October 24, 2018

12:00 PM - 1:00 PM
Math Tower 5-127
Yoon-Joo Kim, Stony Brook University
Kähler Ricci Flow on Hirzebruch Surfaces

We will talk about Song and Weinkove's result on Kahler-Ricci flow (KRF) on Hirzebruch surfaces. Note that Hirzebruch surfaces have Kodaira dimension -infinity, so the first Chern class tends to be positive. Under an additional symmetry condition, they proved KRF converges within finite time and behaves exactly what we have expected, as predicted in Minimal Model Program.


Wednesday
October 31, 2018

12:00 PM - 1:00 PM
Math Tower 5-127
Marlon De Oliveira Gomes, Stony Brook University
Kahler-Ricci flow on elliptic surfaces

I will describe the behavior of the normalized Kahler-Ricci flow on a product elliptic surface. Time permitting, I will contrast this elementary case with that of a minimal elliptic surface with singular fibers.


Wednesday
November 07, 2018

12:00 PM - 1:00 PM
Math Tower 5-127
Nathan Chen, Stony Brook University
An outline of the MMP in relation to KRF

In this talk, we will go through the main steps of the minimal model program and discuss some of the difficulties in higher dimensions, in particular flips. Time permitting, we will present the conjecture of Song and Weinkove for Kähler-Ricci flow in higher dimensions.


Wednesday
November 14, 2018

12:00 PM - 1:00 PM
Math Tower 5-127
Matt Lam, Stony Brook University
The Kähler-Ricci flow on Kähler surfaces

TBA


Show events for:
Instructions for subscribing to Stony Brook Math Department Calendars