Title of Seminar: Infosys Chandrasekharan Random Geometry Colloquium
Title of Talk: An overview of the Dimension Drop Conjecture on the space of lattices
Speaker: Aratrika Pandey, IIT Bombay
Date: September 23, 2024
Time: 14:00:00 Hours
Venue: A-369
Abstract: Let $G$ be a Lie group and $\Gamma$ be a lattice in $G$ and $X=G\slash \Gamma$. Dimension Drop Conjecture states the set of points in $X$ whose $g_t$ trajectory misses some open set $U$ is not of full Hausdorff dimension. We will first discuss the setup and the history of the problem for $G=SL_{n}(\mathbb{R})$. Then, we will discuss a technique that has been used to prove the conjecture in this specific case. This talk is based on the paper https://www.sciencedirect.com/science/article/pii/S0001870823002013?via%3Dihub.
Title of Talk: An overview of the Dimension Drop Conjecture on the space of lattices
Speaker: Aratrika Pandey, IIT Bombay
Date: September 23, 2024
Time: 14:00:00 Hours
Venue: A-369
Abstract: Let $G$ be a Lie group and $\Gamma$ be a lattice in $G$ and $X=G\slash \Gamma$. Dimension Drop Conjecture states the set of points in $X$ whose $g_t$ trajectory misses some open set $U$ is not of full Hausdorff dimension. We will first discuss the setup and the history of the problem for $G=SL_{n}(\mathbb{R})$. Then, we will discuss a technique that has been used to prove the conjecture in this specific case. This talk is based on the paper https://www.sciencedirect.com/science/article/pii/S0001870823002013?via%3Dihub.