Seminar

Title: An Introduction to Discrete Quantum Walks

Abstract:

We will introduce the concept of a discrete quantum walk, prove some of its properties, discuss its relation to different graph structures, and construct interesting walks from these structures such as self-dual embeddings.

Title: Coloring (cap even hole)-free graphs

Abstract:

An even cycle of length 4 or more is called an even hole. A cap is a cycle of length at least 5 with exactly one chord and that chord creates a triangle with the cycle. In this talk we consider (cap, even hole)-free graphs, i.e., graphs that do not contain any even hole or cap as an induced subgraph.

Title: A short proof of a forgotten result

Abstract:

Title: A Stochastic Gradient Method with an Exponential Convergence Rate for Finite Training Sets

Abstract:

We will be discussing the paper (having the same title) by Roux, Schmidt, and Bach.  The authors propose a new stochastic gradient method for optimizing the sum of
 a finite set of smooth functions, where the sum is strongly convex.


Title: How we solve linear programs

Abstract:

Linear programming is one of the most fundamental tools in optimization, and its theoretical complexity is well understood. In practice though, things are quite different: Which types of problems can we really solve? What sizes? With what algorithms?

Title: Coordinate Descent Algorithms

Abstract:

We will be discussing the survey of Stephen J. Wright on coordinate descent algorithms. Coordinate descent algorithms solve optimization problems by successively performing approximate minimization along coordinate directions or coordinate hyperplanes. They have been used in applications for many years, and their popularity continues to grow because of their usefulness in data analysis, machine learning, and other areas of current interest.

Title: Progress on Continuous Quantum Walks

Abstract:

I will discuss the progress we’ve made in our work on continuous walks. I will start with old stuff (last November) and continue on to current stuff (this week).

Title: Extended odd holes and their blockers

Abstract:

Title: Some matrix problems in quantum information science

Abstract:

In this talk, we present  some matrix results and techniques in solving certain optimization problems arising  in quantum information science.

No quantum mechanics background is required.

Title: The Paulsen problem, continuous operator scaling, and smoothed analysis

Abstract:

The Paulsen problem is a basic open problem in operator theory: Given vectors u_1, ..., u_n in R^d that are eps-nearly satisfying the Parseval's condition and the equal norm condition, is it close to a set of vectors v_1, ..., v_n in R^d that exactly satisfy the Parseval's condition and the
equal norm condition? Given u_1,..., u_n, we consider the squared distance to the set of exact solutions.