Background

I am an Assistant Teaching Professor and the Director of MS in Applied Mathematics and MS in Operations Research in the Department of Mathematics at Northeastern University. From 2016 to 2019, I was a Postdoctoral Fellow at the University of Nevada, Reno. (Mentor: Chris Rogers). I received my Ph.D. degree in Mathematics from Northeastern University in 2016. (Advisor: Alexandru I. Suciu). In those years, I also had many very nice discussions with Kiyoshi Igusa and Richard Porter. I received my M.S. degree in Mathematics at Nankai University in Tianjin in 2010. (Advisors: Liu, Xiugui, and Wang, Xiangjun). My B.S. degree in Mathematics and applied mathematics is obtained from Hebei Normal University in 2007.

Here is my CV. My accounts on MathSciNet, Google Scholar, arXiv, ResearchGate.

I am organizing the Northeastern Applied and Interdisciplinary Mathematics (AIM) Seminar

Research Interests

My research interests are in Algebraic Topology and Group Theory, and their relation with Algebra, Geometry, Combinatorics, and Data Science. Currently, I am interested in applications to data science,  machine learning, and deep learning. More specifically,

• •  Rational homotopy theory: moduli spaces of C-infinity structures, formality properties, and Massey products.
  • Cohomology jumping loci: characteristic varieties and resonance varieties of spaces and CDGA models.
  • Combinatorial group theory, especially various Lie algebras associated to finitely generated groups.
  • Configuration spaces, pure virtual braid groups, pure welded braid groups, fundamental groups of algebraic varieties, picture groups from the quiver representations, etc.
  •  Topological data analysis.

When I worked on my MS degree, I did some computations on the stable homotopy theory of spheres. See the RESEARCH page for my publications and seminar notes.

Teaching

Here are not the full teaching materials. They only have some lecture notes and syllabus. The main purpose is to help students to register for courses. Ongoing class websites are on Northeastern/Canvas including assignments, computer labs, exams, final projects, etc. See the TEACHING page, RESOURCES pageandPOSTSfor more information.

Graduate Courses:

• MATH 5110-Applied Linear Algebra and Matrix Analysis
• MATH 7243-Machine Learning and Statistical Learning Theory 1
• MATH 7339-Machine Learning and Statistical Learning Theory 2
• MATH Summer course: Rational Homotopy Theory. 
• MATH 7741  Readings in Probability and Statistics (No notes)
• MATH 7978- Independent Study (No notes)

Undergraduate Courses:

• MATH 4570- Matrix Methods in Data Analysis and Machine Learning
• MATH 3081-Probability and Statistics
• MATH 2331-Linear Algebra
• MATH 2321- Calculus 3 for Science and Engineering
• MATH 182 Calculus 2 (at University of Nevada, Reno)
• MATH 1231 Calculus for Business and Economics