I study representations of associative algebras, or quiver representations, using algebra, category theory, combinatorics, and algebraic geometry. I am interested in various homological conjectures, most importantly the finitistic dimension conjecture, and their related invariants, such as the delooping level, the derived delooping level, the phi and psi dimensions, representation dimensions, and more. Some of my research interests are:
Finitistic dimension conjecture
Frieze varieties
Tilting theory, tau-tilting theory
I also work on applications of machine learning in finance. Specifically, I leverage theoretical and engineering innovations for cross-sectional asset pricing problems.
Pure Math Research:
4. Homological invariants of left and right serial path algebras. Submitted for publication. arXiv: 2506.02307
3. Symmetry of derived delooping level, Algebras and Representation Theory. arXiv: 2406.00253
2. Derived delooping levels and finitistic dimension, with Kiyoshi Igusa. Advances in Mathematics. 464 (2025). arXiv: 2311.00661
1. Spectral decimation of the magnetic Laplacian on the Sierpinski gasket: Solving the Hofstadter-Sierpinski butterfly, with Joe P. Chen. Communications in Mathematical Physics. 380, 187-243 (2020). A MATLAB code for generating the Hofstadter-Sierpinski butterfly is provided in the appendix of the paper. arXiv: 1909.05662.
Machine Learning Research:
1. R. Guo and Haochen Qiu, Pursuing Top Growth with Novel Loss Function. Submitted for publication. arXiv: 2502.17493
Talks:
13. Some applications of the delooping and derived delooping levels, Maurice Auslander Distinguished Lectures and International Conference, Woods Hole Oceanographic Institution, Quissett Campus, Woods Hole, MA, 2025
12. Some Techniques of the Finitistic Dimension Conjecture and Their Applications, Representations Theory and Related Topics Seminar (RTRTS), Northeastern University, Boston, MA, 2025
11. Upper Bounds of the Finitistic Dimensions: Survey and Recent Developments, WALKS (Working ALgebra Knowledge Seminar), Syracuse University, Syracuse, NY, 2024
10. Derived Delooping Levels and Finitistic Dimension, Maurice Auslander Distinguished Lectures and International Conference, Woods Hole Oceanographic Institution, Quissett Campus, Woods Hole, MA, 2024
9. Derived Delooping Levels and Finitistic Dimension, AMS Spring Central Sectional Meeting, University of Wisconsin-Milwaukee, Milwaukee, WI, 2024
8. Stable Module Theory and the Finitistic Dimension Conjecture, 49th Annual New York State Regional Graduate Mathematics Conference, Syracuse University, Syracuse, NY, 2024
7. Representation Dimension, Graduate Student Seminar, Brandeis University, Waltham, MA, 2024
6. Contravariantly Finite Subcategories, Graduate Student Seminar, Brandeis University, Waltham, MA, 2023
5. Frieze Varieties of Acyclic Quivers, Graduate Student Seminar, Brandeis University, Waltham, MA, 2022
4. Spectral decimation of the magnetic Laplacian on the Sierpinski gasket: Hofstadter’s butterfly, determinants, and loop soup entropy, AMS Fall Eastern Sectional Meeting, Binghamton University, Binghamton, NY, 2019
3. The magnetic spectrum on the Sierpinski gasket (Outstanding Poster Award), Joint Mathematics Meetings Poster Session, Baltimore, MD, 2019
2. Self-similar energies on Sierpinski gasket type fractals, SPUR/REU Undergraduate Research Forum, Cornell University, Ithaca, NY, 2018
1. The magnetic spectrum on the Sierpinski gasket, Hudson River Undergraduate Mathematics Conference (HRUMC), St. Lawrence University, Canton, NY, 2018