# Graph Limits & Graph Homomorphism Density Inequalities

Graph limits is a recently developed powerful theory in studying large (weighted) graphs from a continuous and analytical perspective. It is particular useful when studying subgraph homomorphism density, which is closely related to graph property testing, graph parameter estimation, and many central questions in extremal combinatorics. In this talk, we will show how the perspective of graph limits helps with graph homomorphism inequalities and how to make advances in a common theme in extremal combinatorics: when is the random construction close to optimal? We will also show some hardness result for proving general theorems in graph homomorphism density inequalities.

Speaker Bio

Fan Wei completed her PhD in mathematics in 2019 from Stanford University, under the supervision of Jacob Fox. She spent one year as a post-doctoral member at the Institute for Advanced Study being part of Avi Wigderson's CSDM (computer science and discrete math) program and funded through Founders' Circle Member. She is currently an instructor at Princeton University math department, where she has and is funded by Simons Foundation, Algorithms & Geometry Unit, and NSF grant.

Prior to that, she received bachelors degree in Mathematics from MIT, and a Master of Advanced Study with Distinction from Cambridge University, UK. She has also had internships at Microsoft Research New England and Microsoft Research Redmond Theory group. Fan Wei's research is on extremal combinatorics, probabilistic combinatorics, applications of combinatorics to theoretical computer science. She is especially interested in using tools from probability, analysis and algebra to analyze large networks or other combinatorial objects.