Mathematics/Physics Graduation Internship: Double bounded symmetric matrix solver

ASML

Introduction

Are you a master’s student in Mathematics or Physics (with a strong affinity with mathematics) looking for a graduation internship? Are you interested in linear algebra? Do you want to think of clever mathematical ticks to solve a complex problem? Then this internship might be interesting to you!

Background information

Our research team is a part of the wafer alignment department. Our focus is on novel models and novel modeling techniques to improve corrections for wafer deformations in the xy-plane. This also involves machine learning and linear regression applications. Our aim is to improve on-product overlay.

Your assignment

For multiple applications, such as improving post bonding wafer overlay, we are looking for a least squares solver method that solves for a matrix under the constraint of being symmetric and being two-side bounded. This is also referred to in literature as the symmetric Procrustes problem.

The solution for the unbounded Procrustes problem is known and can be solver using the singular value decomposition. For the single-bounded (positive semidefinite) problem in many cases a (bounded) solution does not exist. For the double bounded problem a solution should always exist, but no literature was found on this.

We are looking for clever mathematical tricks to directly solve the problem, but if that is not possible, numerical/iterative optimization algorithms may also be considered.

Your Profile

To be a perfect match for this internship, you:

  • Are a masters student studying Mathematics or Physics (with a strong affinity with mathematics)
  • Strong background in linear algebra
  • Familiar with singular value decomposition, eigenvalue decomposition, properties of symmetric matrices. 

This is a master's graduation internship for a minimum of 3 months, for 3-5 days a week, starting as soon as possible.

Please note that we can only consider students who are enrolled at a school for the entire duration of the internship.

Other Information

Diversity and inclusion

ASML is an Equal Opportunity Employer that values and respects the importance of a diverse and inclusive workforce. It is the policy of the company to recruit, hire, train and promote persons in all job titles without regard to race, color, religion, sex, age, national origin, veteran status, disability, sexual orientation, or gender identity. We recognize that diversity and inclusion is a driving force in the success of our company.

Change the world – one nanometer at a time

Become an intern at a Dutch company that’s a global industry leader. You’ll gain valuable experience in a highly innovative environment – one that sparks your imagination and creativity. In addition to a monthly internship allowance of maximum €600 (plus a possible housing and free public transport), you’ll get practical guidance from experts in the field and the chance to work in and experience a dynamic team environment.

ASML - be part of progress

ASML is a high-tech company headquartered in the Netherlands. We manufacture the complex lithography machines that chipmakers use to produce integrated circuits, or computer chips. What we do is at the heart of all the electronic devices that keep us informed, entertained and connected. Every day, you use electronics that simply wouldn’t exist without our machines.

Behind ASML’s innovations are engineers who think ahead. The people who work at our company include some of the most creative minds in physics, electrical engineering, mathematics, chemistry, mechatronics, optics, mechanical engineering, computer science and fields which are not technical oriented.

We believe we can always do better. We believe the winning idea can come from anyone. We love what we do – not because it’s easy, but because it’s hard.

Students - getting ready for real-world R&D!

We’re a global team of about 40,000 people of 120 different nationalities and counting. Headquartered in Europe’s top tech hub, the Brainport Eindhoven region in the Netherlands, our operations are spread across Europe, Asia and the US.

In such an environment, your colleagues may be sitting next door, or they could be thousands of kilometers away in a different country – or even working for a different company.

An internship at ASML is the opportunity to get to know not only the world of the semiconductor industry, but yourself – you’ll discover just what excites you most. Will you design a part of the machine, or make sure it gets built to the tightest possible specifications? Will you write software that drives the system to its best performance, or work side-by-side with the engineers of our customers in a fab, optimizing a system to the requirements of the customer? Anything is possible!

How will you be part of progress?

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Confirmed an hour ago. Posted 30+ days ago.

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