Engineering topology optimization is a technique to minimize the mass of a structure while maintaining or even increasing its robustness in certain lifecycle applications. The presentation will show the technical foundation based on the finite element method with an embedded gradient based mathematical optimizer. Characteristic application solutions utilizing the method and the intriguing connection to additive manufacturing (3D printing) will also be discussed.

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## Upcoming Seminars

### Mon Oct 15, 2018

**Lei Chen (Caltech): *** Section problems*

In this talk, I will discuss a direction of study in topology: Section problems. There are many variations of the problem: Nielsen realization problems, sections of a surface bundle, sections of a bundle with special property (e.g. nowhere zero vector field). I will discuss some techniques including homology, Thurston-Nielsen classification and dynamics. Also I will share many open problems. Some of the results are joint work with Nick Salter.

**Lisa Piccirillo (UT Austin): *** TBA*

This is the second in a series of lectures on naive descriptive set theory based on an expository paper by Matt Foreman. The topics discussed will include tree representations, universality properties of Polish spaces, and subspaces of Polish spaces.

### Tue Oct 16, 2018

In 2006 Carbery raised a question about an improvement on the naïve norm inequality

(||f+g||_p)^p ≤ 2^(p-1)((||f||_p)^p + (||g||_p)^p) for two functions in Lp of any measure space. When f=g this is an equality, but when the supports of f and g are disjoint the factor 2^(p-1) is not needed. Carbery’s question concerns a proposed interpolation between the two situations for p>2. The interpolation parameter measuring the overlap is ||fg||_(p/2). We prove an inequality of this type that is stronger than the one Carbery proposed. Moreover, our stronger inequalities are valid for all p (joint work with E. A. Carlen, R. L. Frank, and E. H. Lieb).

In this talk we will discuss the mean curvature flow with surgery and how to extend it to the low entropy, mean convex setting. An application to the topology of low entropy self shrinkers will also be discussed. This is a joint work with Shengwen Wang.

### Thu Oct 18, 2018

Prof. Chen will pose a problem in the analysis of a randomized algorithm for LU factorization: https://arxiv.org/abs/1605.02353. The answer will likely use some probability tools.

### Fri Oct 19, 2018

We will discuss the use of a new tool to gather midterm feedback from your students, and how to interpret (midterm and final) teaching evaluations.