Topics in continuous optimization

The course will be structured as a student seminar. 

 

Working in groups of 2 or 3 on each topic, the students give two presentations per group:

 

* One about mathematical background that is necessary to approach the topic at hand.
* One about the main contributions of the topic itself.

 

The presentations will be open to the public. They are followed by class discussions (for course participants only).

 

Students may also be asked to prepare lecture notes, exercises and / or a blog post about their work.

 

The course is structured to foster conversations both about the technical contents themselves and about the oral presentations.

 

Illustrative list of papers (not exhaustive; students are welcome to propose papers too, but the instructor will determine if they are of broad enough appeal):

 

1. Rod Flow: A Continuous-Time Model for Gradient Descent at the Edge of Stability
https://arxiv.org/abs/2602.01480

 

2. Basic Inequalities for First-Order Optimization with Applications to Statistical Risk Analysis
https://arxiv.org/abs/2512.24999

 

3. On Approximate Computation of Critical Points
https://arxiv.org/abs/2601.21917

 

4. The matrix-vector complexity of $Ax = b$
https://arxiv.org/abs/2602.04842

 

5. Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop
https://arxiv.org/abs/2602.05394