Current Research Activities

Applied mathematics, Mathematical biology and medicine: developing analysis methods for applied mathematics (PDEs, ODEs, SDEs, and stochastic processes) and constructing mathematical models for biological and medical problems. I have the following ongoing projects.

  1. Collective dynamics of solid tumors and their microenvironment: a project of U54 FHCRC-NMSU partnership, I am the leader at NMSU (Eric Holland is the leader at Fred Hutchinson Cancer Research Center); collaborators include Philip Maini in the Centre for Mathematical Biology at the University of Oxford. One sub-project was funded by National Institute of Health (NIH) for which I was the Principal Investigator (PI). Since 2017, two sub-projects were completed. We currently work on two sub-projects, OPN functions and abscopal effects. 
  2. Brain tumor growth with therapies and virotherapy: collaborating with E. Antonio Chiocca in Harvard Medical School, Avner Friedman in the Ohio State University, Jin Wang in the University of Tennessee Chattanooga; one sub-project was funded by National Science Foundation (NSF) for which I was the PI. Since 2012, we completed 5 sub-projects. Since July 2021, we work on the oncolytic crash problem initiated by Eric Bartee in Medical School at University of New Mexico. 
  3. Potassium in tumor growth and viral infection: this is a new project initiated by Eric Bartee in Medical School University of New Mexico since September 2020, collaborators including Xianyi Zeng in Lehigh University and Mary Ballyk in NMSU. One sub-project was completed in August 2022. We currently work on T cell exhaustion.
  4. Optimization of CAR T cell therapy: in January 2022, I started to develop this project with Cameron Turtle in FHCRC now in Sydney Medical School the University of Sydney, currently working on stochastic variability in silicon clinical trials, and a grant proposal.
  5. Stem cell biology: collaborating with Ting Xie at the Stowers Institute for Medical Research, Angelique Bordey in Yale University, and Philip Maini in CMB Oxford. Project: Virtual stem cell - a digital platform for regenerative medicine collaborating with Jie Zheng in Nanyang Technological University, was supported by the Ministry of Education of Singapore for which I was a co-PI (returned because PI left to Shanghai Tech University). We completed 1 project, and are currently studying traffic of neural stem cells in SVZ.
  6. Disease ecology: collaborating with Jingan Cui at Beijing University of Architecture and Civil Engineering, it was funded by NNSFC (National Natural Science Foundation of China) and I was a co-PI. Since 2010, we have completed studies on avian influenza and cholera.
  7. Stochastic differential equations (SDEs): developing analysis methods for qualitative study of Ito SDEs, I have a book project with AMS.

Past research projects:

  1. Topology: quantum invariants of knots and 3-manifolds, and representations of braid groups on tangent bundle of Lie groups.
  2. Algebraic structures in genetics: evolution algebras and coalgebraic structure of genetic inheritance (I defined).
  3. Coalescent theory: colored coalescent theory and coalescent random walks (I defined).

 Current and Past Visiting Scholars:

  1. Hanchun Yang, from Yunnan University, Feb. 2017 - May 2017.
  2. Ben Niu, from Harbin Institute of Technology, March 2017 - Feb 2018.
  3. Yuxiao Guo, from Harbin Institute of Technology, March 2017 - Feb 2018.
  4. Jiantao Zhao, from Heilongjiang University, March 2018 - Feb 2019.

  Current and Past Graduate Students:

  1. Tuan Phan, Ph.D student, 2016 -  December 2020, now postdoctoral fellow in Institute for Modeling Collaboration & Innovation, University of Idaho.
  2. Farhana Sarower, Master, 2016 - 2018, Ph.D candidate, 2018 - May 2023, now assistant professor of instruction in Department of Mathematics at University of Texas at Austin.
  3. Chau Hoang, Master, 2018 fall - 2020; Ph.D candidate, 2020 -
  4. Yumi Maharjan, Master, 2020 fall -  2023 spring.  
  5. Ulrich Kemmo Tsafack, Fall 2016 --- 2018, Master.
  6. Donovan Simpson, Fall 2022 ---, Master student.

 Research Meetings: Mathematical Biology Seminar, Spring 2017, Wednesday 2:30 - 3:30pm, SH 235,  Starting from 2020 fall, we move to online Zoom meeting, Friday 6-8pm (in order for participants from different time zones).

 Research Summary: This is a summary of my research in case you are interested in.

 Invited Talks and Conferences: in Professional Services.   

 Notice: # If you are interested in working with me towards your thesis (Ph.D, Master, or even Bachelor honor thesis), or just on some project, you are more than welcome to talk to me, and I may support you financially. 

  --- 07/26/2023 updated          

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