Spring 2026
Natasa Sesum
Course Description:
In the first part of the course we will cover regularity theory for second order partial differential equations and Sobolev spaces, talk about regularity properties of nonlinear PDEs. In the second part of the course we will focus on the Ricci flow, which is the example of highly nonlinear PDE system and discuss some of it basic properties, such as the regularity properties of the equation, types of singularities and Ricci solitons.
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N/A
Prerequisites:
Some basic knowledge of PDEs
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Spring 2025
Dennis Kriventsov
Course Description:
We will cover regularity theory for elliptic and parabolic equations, various approaches to existence and uniqueness, and basic estimates for dispersive equations. Other topics will be determined by student interest.
Text:
None
Prerequisites:
517 or equivalent
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Spring 2023
Sagun Chanillo
Course Description:
This course is a second course on PDE. It will focus on Boundary value problems for Elliptic second order equations. We will develop the associated Functional Analysis, Fredholm Theory and Sobolev spaces. We shall also do the Cauchy-Kowalevsky theorem and the Holmgren uniqueness theorem if not done in Math 517. Time permitting we shall do the initial value problem for Schrodinger and wave equations.
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None
Prerequisites:
Math 501, 502.
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Spring 2022
Dennis Kriventsov
Course Description:
This course is a continuation of 517, PDE I. The goal of this semester is to consider a variety of equations studied today, and look at various techniques being applied to them. We will review Sobolev spaces, spend time on various methods for elliptic regularity (including Calderon-Zygmund theory), and discuss various notions of weak and viscosity solutions. We will also consider methods in the calculus of variations and dispersive equations. The specific topics and equations covered will depend heavily on student interest.
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None
Prerequisites:
501, 502, 517 or equivalent strongly recommended; 507 helpful.
Schedule of Sections:
16:640:518 Schedule of Classes