Yifei Zhu

I'm an assistant professor at Southern University of Science and Technology (SUSTech) in Shenzhen, China. From 2013 to 2016, I was a visiting assistant professor at Northwestern University. I received my Ph.D. from the University of Minnesota in 2013. My advisor was Tyler Lawson.

My research interests are in algebraic topology and related fields, particularly in its connections to algebraic geometry and number theory via objects such as formal groups, elliptic curves, and modular forms. A central theme in my research is elliptic cohomology and power operations, which combines the classical methodology of cohomological computations in algebraic topology with modern inputs from arithmetic moduli of elliptic curves in number theory, with applications to unstable homotopy. More generally, I study moduli spaces in various aspects, including geometric, arithmetic, computational, combinatorial, categorical. I am also interested in applying topology to physics, such as homotopy classification of energy band structures geared towards quantum materials, and to data science, such as speech signal processing through time-delay embedding and persistent homology. Here's a less formal but ancient account of me.

Vita

Email: zhuyf@sustech.edu.cn (my alumnus account zyf@umn.edu , which I've also been using for academic purposes, will be closed on Dec 7, 2024 and replaced by zyf@alumni.umn.edu . All three are merged in one place.)

Conferences: International Workshop on Algebraic Topology (IWoAT, annually since 2018), Computer-assisted research in geometry and topology (Sep 2024), Arithmetic and Topology (since 2022), Great Bay Area Topology Conference: Topological data analysis and deep learning (Nov 2024, upcoming)

Topology seminars and Mathematics Colloquium at SUSTech

Papers

With Pingyao Feng, Qingrui Qu, Siheng Yi, Zhiwang Yu, and Haiyu Zhang, Topology-enhanced machine learning for consonant recognition, Preprint. [A poster on this work presented at Spires 2024 with contributions by Zeyang Ding and Yuhe Qin]

With C. T. Chan, Jing Hu, Hongwei Jia, Xiaoping Ouyang, Yixiao Wang, and Ruo-Yang Zhang, Non-Hermitian swallowtail catastrophe revealing transitions among diverse topological singularities, Nat. Phys. 19 (2023), 1098–1103. [Nat. Phys. News & Views by Savannah Garmon; Phys.org feature by Ingrid Fadelli]

With C. T. Chan, Jing Hu, Hongwei Jia, Yixin Xiao, Ruo-Yang Zhang, and Shuang Zhang, Topological classification for intersection singularities of exceptional surfaces in pseudo-Hermitian systems, Commun. Phys. 6 (2023), 293.

Norm coherence for descent of level structures on formal deformations, J. Pure Appl. Algebra 224 (2020), 106382, 35 pp. [A sequel to Remark 1.3 by Hongxiang Zhao, a former undergraduate student; Xuecai Ma's recent work on spectral realization of classifying rings for these level structures]

Morava E-homology of Bousfield–Kuhn functors on odd-dimensional spheres, Proc. Amer. Math. Soc. 146 (2018), 449–458.

Semistable models for modular curves and power operations for Morava E-theories of height 2, Adv. Math. 354 (2019), 106758, 29 pp.

The Hecke algebra action and the Rezk logarithm on Morava E-theory of height 2, Trans. Amer. Math. Soc. 373 (2020), 3733–3764.

The power operation structure on Morava E-theory of height 2 at the prime 3, Algebr. Geom. Topol. 14 (2014), 953–977.

Presentations

Topological analysis and deep learning of human speech data, Symposium on Artificial Intelligence and Mathematics, Chongqing, 2024

Explicit examples of Higgs bundles from physics and bulk–edge correspondence, Interdisciplinary Mathematical Workshop, Chongli, 2024

Higher-periodic homotopy types through Lubin–Tate towers, Conference on p-adic Geometry and Related Topics, Beijing International Center for Mathematical Research, Beijing, 2024

Moduli, moduli, moduli, International Workshop on Algebraic Topology, Beijing International Center for Mathematical Research, Beijing, 2023

Power operations in elliptic cohomology and related arithmetic topics, Special Session on Algebraic and Geometric Topology, AMS–CMS Joint International Meeting, Shanghai, 2018

Toward calculating unstable higher-periodic homotopy types, Electronic Computational Homotopy Theory Seminar, Zoom, 2018

Symmetry encoded by norm maps, International Workshop on Loop Spaces, Supersymmetry and Index Theory, Chern Institute of Mathematics, Tianjin, 2017

Power operation calculations in elliptic cohomology, AMS Special Session on Homotopy Theory, Joint Meetings, Baltimore, 2014

Teaching and advising

MAT7064, Topics in Geometry and Topology, Fall 2024

MAT8021, Algebraic Topology

MA323, Topology

I've also taught MAT8024, 8010, MA327, 301, 215, 107a, 102a, 101a at SUSTech and Math 300, 240, 234, 230 and, as a substitute, graduate Algebraic Number Theory at Northwestern.

Weird surfaces: Möbius band, Klein bottle, and swallowtail, International Day of Mathematics public lecture, SUSTech, 2022

Here's a page for a research group at SUSTech.

Here's a link to former students and their theses.

Here are photos from the 2023 IWoAT summer school.