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Removability in Geometric Function Theory

Assistant Professor Malik Younsi has been awarded an NSF grant for 2021-2024 to work on Removability in Geometric Function Theory.

Previously, Prof. Younsi held another NSF grant for 2017-2020 to work on removable sets and questions in geometric function theory.

That research project involved the study of the geometric properties of conformally removable sets, including problems related to rigidity of circle domains, conformal welding and fingerprints of lemniscates. It also includes questions dealing with shapes of Julia sets and the subadditivity of analytic capacity

Graduate degrees target timelines

This page provides information about when you should accomplish various milestones in your degree and what other events must occur along the way. The target timeline is below. Consult with the Graduate Chair to ensure you have all the information you need.

PhD process

The typical time to degree for a PhD here is 5 to 6 years and the maximum length of support is 6 years. In your first couple of years, you’ll be taking classes and studying to pass your qualifying exams. It’s also a good idea during that time to try to figure out which type of math you might do research in; attending various seminars, talking to more advanced students about what they do, and asking professors about their research are a few ways you can go about accomplishing this.  We encourage you to attempt qualifying as exams as soon as you can.   They can be taken multiple times without penalty.  Study sessions are organized during the summer to help you pass a qual in August.

Even before passing your  qualifying exams, a high priority is finding an advisor. Getting up to speed on the cutting edge of research, and then doing your own, takes a lot of time and is the main reason you are a PhD student! Finding an advisor is an important decision and, while your interest in their research is a very important factor, working style should also be considered.  See the page How to choose an Advisor for more info.

Once you have an advisor you’ll need to pass a comprehensive (or specialty) exam. Your advisor will determine the format of this exam. Usually the comprehensive exam is an oral presentation or a paper which  shows that you have knowledge of the forefront of an area and have a problem you are intending on working on for your thesis.  You should form a committee around the same time as you do the comprehensive exam.

Then, you do math.

Once you’ve done math, it’s time to write it up. Actually it’s a great idea to write as you go.  As you approach completion, make sure to discuss the timing with your advisor and your committee. You should contact the graduate chair at least a month ahead of defending so that they can ensure all the various forms and announcements go out in time.

A target timeline for Phd students is below. These are targets not deadlines.  It is meant to show what, in our experience, the schedule of a Ph.D should look like. It’s designed to make sure that you move through the process smoothly as possible, that you make good use of your time, and that you give yourself the best chance of successfully completing the degree and continuing on to further opportunities. Everyone’s experience with graduate school is different. If you fall being the schedule outlined in the timeline, we will meet with you and try to help you get back on track. If this doesn’t work, other options may be explored.

PhD Target Timeline

  • Pass 3 600 level graduate courses by the end of the second semester.
  • Pass one qualifying exam by the beginning of the second year.
  • Pass second qualifying exam in January of the second year.
  • Find an advisor by beginning of third year.
  • Pass comprehensive (specialty exam) by middle of fourth year.
  • Finish at the end of year 5.



MA process

The typical time to degree for an MA here is 2 to 3 years. We typically only fund MA students on a year by year basis, subject to availability of funds as well as good progress.

In your first year, you’ll be spending a lot of your time taking classes. As suggested above for PhD candidates, it’s also suggested that you try to figure out in what general area, and with whom, you’ll want to write your MA paper. See How to choose an advisor for more info.

By the end of the fall of your second year, you will need to have chosen an advisor. You will work with them to produce a masters paper and prepare an oral presentation. As you near completion, you should discuss timing with your advisor, form a masters committee, and talk with the graduate chair to ensure all the various forms and announcements go out in time.

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Annual teaching award: Yuriy Mileyko

This year’s Teaching Award goes to Dr. Yuriy Mileyko.

Dr. Mileyko has earned high praise from students in classes from applied calculus to the graduate level. Students appreciate his clear explanations; they say he spends time showing them where the equations came from, that he is very approachable and makes it easy to ask questions, that he cares about students and wants them to succeed. A MATH 216 student writes,

Professor was nothing less than awesome. Patient, professional & approachable.

A MATH 302 student states,

Dr. Yuriy shows great passion for mathematics, & even though the course difficulty is high, his passion motivates you to learn and try your best.

And from a MATH 252A student:

Dr. Mileyko’s zest for challenging mathematics inspires students to achieve.

Of special note at this time are the extra efforts Dr. Mileyko has put into his teaching since the pandemic forced all our classes online.  His lectures have involved professional-grade animation recording with formulas moving within a slide frame and seamless glue of lecture fragments. That level of work requires a tremendous investment of time and effort besides professional software engineering skills. His students uniformly reported that the transition to online instruction went smoothly.

In addition, he was an asset to other faculty members, sharing advice on both hardware and software solutions for online teaching. Yuriy is always willing to share his wide knowledge and experience about teaching-related technology, and to spend his time and efforts to make things work. He has done that on many occasions, not only in connection with the pandemic online teaching mode. He himself has routinely applied technology in his teaching; for instance, he experimented with a flipped classroom model where the students attended a prerecorded lecture as homework to prepare for a class discussion. He is not afraid to invest his efforts in improving students’ learning.

His dedication is not lost on the students. One student says,

Dr. Mileyko did a wonderful job of engaging students, which … was amazing and invigorating!

and another writes,

He was always willing to help us and gave us all the tools we needed to succeed.

Students describe him as “enthusiastic,” “amazing,” “outstanding,” and “not only a great teacher, but a great person.”