Yutan Zhang 张宇谭

photo
Department of Mathematics
Indiana University Bloomington

Alumni of University of Notre Dame
Greater China Scholar

PHI BETA KAPPA

zhangyut [swiss roll] iu DOT edu
yzhang66 [swiss roll] alumni DOT nd DOT edu

Linkedin: yutan-zhang
Curriculum Vitae: (please contact)

About

I am a third-year Ph.D. student (advised by Professor Peter Sternberg) and Associate Instructor in the Department of Mathematics at Indiana University Bloomington. I obtained B.S. in Mathematics and Scientific Computing from the University of Notre Dame. My research interests include Liquid Crystal models, calculus of variations, analysis and partial differential equations, with a general interest in the philosophy of mathematics and mathematical finance.

Research

  1. Well-posedness of the Nonlinear Schrödinger Equations on the Line. (advised by Alex Himonas with Fangchi Yan).
    Senior Thesis at University of Notre Dame (CurateND link).

  2. Determinantal inequalities in minors of totally positive matrices. (with Jack Hertzog, Julian Kaufmann, and Emma Laboe).

Teaching and Mentoring

Indiana University Bloomington

University of Notre Dame

Conferences Attended

  1. Midwestern Workshop on Asymptotic Analysis, October 11-13, 2024, Indiana University Bloomington
  2. The Notre Dame PDE Workshop, May 3-5, 2024, University of Notre Dame
  3. 87th Midwest PDE Seminar, May 5-7, 2023, University of Notre Dame

Expository Writings

  1. Introduction to the Feynman-Kac Formula. (link). 2024/12/12.
    I gave a presentation as partial fulfillment of the project in Probability.

  2. Nonexistence of Solutions of Certain PDEs. (link). 2024/12/11.
    This is the note for the lecture I gave as part of the final assesment for PDE II.

  3. Derivation of the Heston Model Option Pricing Formula. (with Luke Marushack, Tiantian Wei, Yuchen Yang, and Jiachen Zhao) (link). 2023/05/01.
    We gave a joint presentation as fulfillment of the project in Mathematical Methods in Financial Economics (MMFE). Also for MMFE we jointly worked on a cryptocurrrency paper and gave its presentation.

  4. History, Derivation, and Solution of the Black-Scholes-Merton PDE. (with Jacob Gose and Julian Kaufmann) (link). 2022/12/05.
    We gave a joint presentation as fulfillment of the PDE class project. On April 12, 2023, I gave a lecture on this topic to the graduate Topics in PDE and Analysis.

  5. Group Actions, Pólya's Theorem, and Applications in Tempered Music. (link). 2022/05/05.

Personal Interests

I am an enthusiast of classical music, ballet, and figure skating, and can often be found in concert halls, opera houses, and art museums.

Like many mathematicians, I hold the philosophical position of structuralism, a view that, I quote from Steward Shapiro, "mathematics is the science of structures". In the words of G.H. Hardy, "a mathematician, like a painter or a poet, is a maker of patterns". I have always believed that mathematics at its root is art, and I enjoy finding connections between mathematics, arts, and music. As Jacques Hadamard argued, a lot of mathematical inventions happen unconsciously in the very early stage. Hardy made the further claim that, "Beauty is the first test: there is no permanent place in the world for ugly mathematics".

This page is maintained by Yutan Zhang (ZYT).

This page is last updated on 2026/09/08.