He Wang

Personal academic website of He Wang, Associate Teaching Professor in Mathematics at Northeastern University.

Welcome!

I am an Associate Teaching Professor in the Department of Mathematics at Northeastern University. I serve as a Program Director for MS Applied Mathematics, MS Mathematics, MS Statistics and MS Statistics-Connect. My academic background is in algebraic topology, group theory, and their connections with algebra, geometry, data science, and artificial intelligence.

Before joining Northeastern as a faculty member, I was a Postdoctoral Fellow at the University of Nevada, Reno from 2016 to 2019, working with Chris Rogers. I received my PhD in Mathematics from Northeastern University in 2016 under the supervision of Alexandru I. Suciu. I received my MS in Mathematics from Nankai University in 2010 and my BS in Mathematics and Applied Mathematics from Hebei Normal University in 2007.

My research and teaching connect algebraic topology, group theory, applied mathematics, linear algebra, machine learning, stochastic processes, topological data analysis, and AI-enhanced mathematics education.

He Wang profile photo

He Wang

Associate Teaching Professor
Director for MS Programs
Department of Mathematics
Northeastern University

Research and Scholarly Interests

My research interests are in algebraic topology and group theory, together with their connections with algebra, geometry, combinatorics, data science, and AI. I am also interested in applications to machine learning, deep learning, and topological data analysis. See the Research page for publications, abstracts, and seminar notes.

Algebraic Topology and Homotopy Theory

Rational homotopy theory, moduli spaces of \(C_\infty\)-structures, formality, Massey products, spectral sequences, and stable homotopy computations.

Groups, Lie Algebras, and Jumping Loci

Cohomology jumping loci, characteristic varieties, resonance varieties, Chen ranks, lower central series ranks, holonomy Lie algebras, and formality properties of finitely generated groups.

Configuration Spaces and Braid-Type Groups

Configuration spaces, pure braid groups, pure virtual braid groups, pure welded braid groups, McCool groups, fundamental groups of algebraic varieties, and related combinatorial structures.

Topological Data Analysis

Persistent homology, simplicial complexes, shape of data, computational topology, and the use of algebraic-topological ideas in data science.

Random Graphs and RAAGs

Random right-angled Artin groups, clique complexes, Betti numbers, resonance varieties, Chen ranks, and probabilistic algebraic topology.

Mathematics of AI

Linear algebra, probability, optimization, and geometry as foundations for machine learning and artificial intelligence.

Teaching

My teaching combines mathematical structure, computational experimentation, real data, and project-based learning. The materials on this website are mainly lecture notes, syllabi, course pages, and public resources. Full course sites, assignments, computer labs, exams, and projects are usually hosted on Northeastern Canvas.

Graduate Courses

Undergraduate Courses

Teaching Projects

Program Leadership

I serve as a program director for graduate programs in the Department of Mathematics at Northeastern University. My work includes curriculum development, student advising, interdisciplinary program planning, experiential learning, industry connections, and support for graduate student success.

Graduate programs in the Department of Mathematics

Seminars, Student Activities, and Outreach

AIM Seminar

I organize the Northeastern Applied and Interdisciplinary Mathematics Seminar, which supports conversations across mathematics, computation, modeling, and applications.

Data Club

I organize the Northeastern Graduate Math Data Club for MS students in the mathematics department. The club supports student learning in Python, SQL, data science, machine learning, projects, career preparation, and peer collaboration.

Talks and Teaching Innovation

My talks and posters include topics in algebraic topology, group theory, matrix methods, AI in mathematics education, and machine learning in the applied mathematics curriculum. See the Talks page for selected talks, posters, and workshop materials.