Hello and welcome to the Student Geometry and Analysis Seminar (SGAS) at the University of Toronto. This seminar’s wide range of topics focuses on the interplay between geometry and analysis and includes (but is not limited to):

- Analysis & PDEs :
*microlocal analysis, nonlinear PDEs, inverse problems, geometric measure theory, optimal transport, stochastic analysis* - Differential Geometry
- Riemannian-Lorentzian Geometry :
*quantitative geometry and metric geometry on Ricci and scalar curvature, general relativity* - Geometric Analysis :
*Ricci flow, (gradient and skew) mean curvature flows, minimal surfaces, Kähler-Einstein metric, CSCK metric* - Symplectic Geometry :
*Floer homology and geometric invariants, geometric fluids and Hamiltonian systems*

- Riemannian-Lorentzian Geometry :
- Dynamical systems :
*geodesic flow and other dynamical applications in geometry*

- Wenkui Du (wenkui.du@mail.utoronto.ca)
- David Knapik (david.knapik@mail.utoronto.ca)
- Xinze Li (xbryanli.li@mail.utoronto.ca)

**September 30: Aram-Alexandre Pooladian (NYU)***Leveraging entropic regularization to approximate optimal transport maps*

Optimal transport and its variants have gained significant interest over the past decade, primarily due to computational advancements by way of entropic regularization. In this talk, I will introduce the notions of regularized and unregularized optimal transport (for the squared-Euclidean cost, specifically), and talk about my recent work on approximating the optimal transport map, or Monge map, on the basis of entropic regularization. This is a foundational aspect of statistical optimal transport, which I will only mention briefly for the sake of motivation (joint work with Jon Niles-Weed)

**September 21 & 23: Yushan Jiang (CUNY)***Dynamical Systems and Ergodic Theory: Some Topics Related to Subsurfaces in Three Manifolds*

Dynamical systems and ergodic theory have so many wonderful applications in different fields like geometry, topology, complex analysis, number theory and so on. One fantastic field which connects almost all such branches is hyperbolic geometry. In this talk, I will briefly introduce hyperbolic plane and space (2 & 3 dim) and some related dynamical systems (geodesic/frame flow and horocycle flow). Also I need to say a word about some terms in ergodic theory. Then I would like to talk (without proof) some famous applications in 3-manifolds theory (post-Thurston era). One is Surface Subgroup Conjecture (related to geodesic/frame flow and the famous Virtual Haken Conjecture). The other one is about the rigidity of the closures of immersed totally geodesic subsurfaces (related to unipotent group action and the famous Ratner theorems).

**September 16: Minghao Miao (Nanjing University & Beijing International Center for Mathematical Research)***Kahler-Einstein metric on Fano manifold*

In this talk, I will survey some recent progress of Yau-Tian-Donaldson conjecture, which relate certain algebro-geometric stability condition with the existence of Kahler-Einstein metric on Fano manifold. Another canonical metric, Kahler-Ricci soliton will also be discussed in a parallel setting.