Mi Hu

Academic interests

I am interested in Complex Dynamics in one dimension and higher dimensions.

Background

I graduated with my PhD in mathematics at the University of Parma, Italy in 2024. 

The title of my PhD thesis is Complex Dynamics Inside Fatou Sets. 

My PhD advisor is Prof. John Erik Fornæss.

Here are the research results of my thesis: 

1. M. Hu: Interior Dynamics of Fatou Sets. Annali di Matematica Pura ed Applicata (1923 -), 202 , 2903–2914, 2023. 
2. M. Hu: Dynamics inside Fatou Sets in Higher Dimensions, accepted by Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 2023.  https://doi.org/10.48550/arXiv.2301.02712
3. J. E. Fornæss, M. Hu: Orbits inside Fatou sets, preprint, 2023.  https://doi.org/10.48550/arXiv.2309.08334
4. M. Hu: Dynamics inside Parabolic Basins, preprint, 2022.  https://doi.org/10.48550/arXiv.2208.03756

Current work

I have been starting work as a researcher in the project " Dynamical Systems, Several Complex Variables, and Algebraic Geometry ", led by Prof. Tuyen Trung Truong at the Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Oslo, since 1 Aug. 2023. 

We are conducting optimization solutions and solving systems of equations with the improvement of Newton's methods combining theoretical analysis and Python programming techniques. So far, we have obtained some results in the following two papers:

1. J. E. Fornæss,  M. Hu, TT Truong, and T. Watanabe: Backtracking New Q-Newton's Method, Newton's Flow, Voronoi's Diagram and Stochastic Root finding, preprint, 2024. https://arxiv.org/abs/2401.01393
2. J. E. Fornæss, M. Hu, TT Truong, and T. Watanabe: Backtracking New Q-Newton's method, Schröder's theorem, and Linear Conjugacy, preprint, 2023.  https://arxiv.org/abs/2312.12166

Talks in Conferences

1. KAUS and Nordan, 3-5 May. 2024, Östanskär, Sweden. 
2. UiO seminar, 8 Feb. 2024, Oslo, Norway.  
3. Topics in Complex Dynamics, 19-23 Jun. 2023, Barcelona, ​​Spain.   
4. Topics in Complex Dynamics, 19-23 Apr. 2021, Barcelona, ​​Spain.  
5. Let's Face Complexity: New Bridges Between Physical and Social Sciences, Villa del Grumello, 4-8 Sept. 2017, Como, Italy.

Conferences attended 

1. Recent developments on the d-bar equation, complex dynamics and holomorphic mappings, 7-9 Dec. 2023, Oslo, Norway. 
2. Program of the National Mathematics Meeting, 31 Aug. - 2 Sept. 2022, Tromsø, Norway.
3. Geometric Methods of Complex Analysis (hybrid meeting), Oberwolfach, 16-22 May 2021, Germany. (Participant and Video Conference Assistant).