Lihan Wang

 Courses Taught at CSULB

Math 224 – Calculus III

Math 361A – Introduction to Mathematical Analysis I

Math 364A/B – Ordinary Differential Equations I & II

Math 562 – Elements of Complex Analysis

Math 566 – Topics in Complex Analysis

Math 697 – Directed Study

Research Interests

Geometric Analysis · Differential Geometry · Partial Differential Equations

Can we hear the shape of a drum from the sound it produces?
This classic question captures the essence of a deep area of mathematics known as geometric analysis. At its heart, this field investigates how the shape or geometry of an object affects its vibrational properties — the “sound” it makes — often encoded in the eigenvalues of certain differential operators.

My research explores these connections in general settings, especially in higher-dimensional or curved spaces, where the relationship between geometry and analysis becomes more intricate. I’m particularly interested in how geometric structures influence the behavior of solutions to partial differential equations.

While the work is primarily theoretical, the underlying ideas have broad and impactful applications:

• Medical imaging (e.g., X-rays, CT scans, MRI): Recovering internal structures from boundary measurements.
  
  

• Geophysical exploration: Using seismic waves to detect underground formations like oil reservoirs or fault lines.
  
  

• Quantum mechanics: Understanding how the shape of a space influences the behavior of particles and energy levels.
  
  

• Acoustics and vibration analysis: Designing materials and structures with specific resonance properties.
  
  

• Computer graphics and shape recognition: Extracting geometric information from data in 3D modeling and animation.
  
  

• Machine learning and data science: Employing geometric and spectral techniques to understand the shape of data.
  
  

These connections demonstrate how deep mathematical questions can lead to insights across both the physical sciences and modern technologies.

If you're curious about how geometry and analysis interact — or what it means to “listen” to the shape of space — feel free to reach out or stop by to chat.

📘 Learn more about my research in articles:
Theories Taking Shape (CSULB Quest, 2024)

Bang the Drum (CSULB 2020) 

Recent Professional Activity:

Invited speaker:

• UCSD Undergraduate Research Mini-course in Complex Variables and Complex Geometry, July 21, 2025 -  July 26, 2025. UCSD_Undergraduate research_minicourse 

• Differential Geometry and PDE Seminar,  University of Washington, April 2, 2025 

• American Mathematics Society (AMS) 2025 Spring Central Sectional Meeting,  Special Session on Advances in Geometric Analysis, University of Kansas, March 29-30, 2025.

•  Analysis Seminar, UC San Diego, December 5, 2024.

• Geometry and Topology Seminar, UC Riverside, May 31, 2024.

• Math Lecture Series, Wichita Sate University, March 29, 2024.

• Differential Geometry Seminar, UC Irvine, Feberbury 27, 2024.

Conference organization: 

•  American Mathematics Society(AMS) Fall Western Sectional Meeting – Special Session on Topics in Geometric Analysis
  October 26–27, 2024, UC Riverside.

• AMS Spring Western Sectional Meeting – Special Session on Recent Advances in Differential Geometry
  May 4–5, 2024, San Francisco State University.

• AMS Spring Eastern Sectional Meeting – Special Session on Recent Advances in Differential Geometry
  April 1–2, 2023, Virtually. 

Book editor:

• Recent Advance in Differential Geometry and Related Areas, to appear in AMS volumes 2025.