Algebraic topology. Homotopy theory. And applications. I think about configuration spaces (and their variants) of points in spaces and using them to probe questions in algebra, geometry and topology.
Kaufmann, Ralph M.; Zhang, Yongheng Permutohedral structures on E2-operads. Forum Math. 29 (2017), no. 6, 1371-1411.
Zhang, Yongheng Circle deformation in Hacon's sphere eversion. Bridges Conf. Proc., Online, Aug 2021, 265-268.
Wei, Annie; Zhang, Yongheng Wave, Boy's Surface, and Machine. Bridges Conf. Proc., Aalto, Aug 2022, 17-24.
几何y代数 Merry-Go-Round, July-December 2023.
Koytcheff, Robin; Zhang, Yongheng Cubes, cacti, and framed long knots. under review.
Zhang, Yongheng Recollection and Reflection: From Euler to Lagrange in 1Q84.
Zhang, Yongheng Line Integral and Area Without Green.
Current Teaching (Fall 2023)
- MATH 211 Multivariable Calculus
- MATH 345 Functions of a Complex Variable
Regular Office Hours
- M W 11-11:50 AM, 1-2:50 PM
- Th 9:00-10:50 AM
- SMUD 510
- MATH 105 Calculus with Algebra (f19, f22: Coraline)
- MATH 111 Introduction to the Calculus (f15)
- MATH 211 Multivariable Calculus (f15, s16, f16, s17, f17, s18, f18, s19, f19, s20, f20, s21, f21, s22, f22, s23)
- MATH 260 Differential Equations (s18: fiction by Cindy Lopez)
- MATH 345 Functions of a Complex Variable (f16: poem by Greg Carroll, f18: online game by Sai Chauhan)
- MATH 350 Groups, Rings and Fields (f17, s19)
- MATH 355 Introduction to Analysis (s16, s20)
- MATH 455 Topology (s17: 50 lessons [90MB] 50 lessons without notes [20MB])
Teaching at Purdue
- Geometry for Elementary Teachers
- Topology for High School Students (notes by Hannah Burnau)
- Calculus I, II, III
- Linear Algebra
- ODE and basic PDE
(It contains a very clear exposition on an accessible proof of the insolvability of the quintic, and much more.)
What does it feel like doing mathematical research?
Like what is described in this music video. (turn on the English translation)
By the way, we wander around and do this kind of dance a lot after school in the 1990s, before being found by parents and dragged back home.