Planes, Trains, and…Number Theory. Meet Kübra Benli, incoming PIMS PDF at the University of Lethbridge.

By Ruth A. Situma, Program and Communications Manager

My questions to Kübra are a reminder that she will have to board a plane across the Atlantic Ocean one more time. A current PDF in Nancy, France, she will be moving to Lethbridge, Alberta to begin her PIMS PDF tenure later this summer. She’s always enjoyed the train rides in Europe — fast and efficient means to get her through the cities she wished to travel to. (I’m tempted to remind her that there are no high-speed trains in Lethbridge like there are in France). When I asked how she was settling in, and what the transition was like, she said, “When I arrived, we had all been working online, and I created an appropriate working space at home, but I had to wait until the end of the lockdown to start meeting the people.. ”

In 2020, after completing her Ph.D. at the University of Georgia, Kübra decided to fly back to her home in Turkey. She spent her time giving online lectures and was invited to speak at the PIMS-Lethbridge Number Theory and Combinatorics seminar. It was here that her connection to PIMS began, just before she moved to Nancy, for her first fellowship. “When France began opening up, we started having seminars in person, I could give talks in person and the communication of my research started to be smoother” she notes. Her appointment as a PIMS PDF at the University of Lethbridge is nothing short of hard work. Though the PIMS PDF Awards are highly competitive, her move to Alberta can be seen as the formalization of a pre-existing relationship that began in 2020.

I connected with Kübra late in January, our exchange has been edited for clarity.

Kübra, enjoying the sights and sounds of Strasbourg. The trip from Nancy to Strasbourg is less than two hours on the SNCF operated speed trains (TGV and TER).

What field are you in and how did you get there?

My research is on analytic/elementary number theory. My first research experience was when I was pursuing my M.S. studies at Bogazici University, Istanbul. Then I moved to the US for my Ph.D. studies, where I worked with Prof Paul Pollack on problems on prime numbers in certain settings. Here in Nancy, I have been working with Prof Thomas Stoll on the sum of digits function in regular setting as well as in the setting with Zeckendorf digits. With Prof Ng and Prof Kadiri, our plan is to obtain some explicit results in number theory. Some of my publications in this area include:

1. Small prime kth power residues, Proc. Amer. Math. Soc. 148 (2020), no. 9, pp. 3801–3809.

2. On the number of prime factors of the composite numbers resulting after a change of digits of primes, J. Théor. des Nombres Bordeaux 31 (2019), no. 3, pp. 689–696.

3. Small prime kth power residues for k = 2; 3; 4: a quadratic reciprocity approach (with P. Pollack), Proc. Amer. Math. Soc. 147 (2019), pp. 987–994.

At Institut Élie Cartan de Lorraine we have been currently working on writing up some of our results from our research. We also have another project at hand. I hope to continue our collaboration with Prof Stoll even after leaving Nancy. Besides, at the University of Lethbridge, I will start a new project(s) on explicit number theory with Prof Kadiri and Prof Ng. Back in September 2020, I was invited to give an online talk in the PIMS-Lethbridge Number Theory and Combinatorics seminar, and that is when I really connected with Prof. Kadiri and Prof. Ng. I’m excited to be part of their projects and I look forward to the move to Alberta.

It’s common for PDFs to teach a course. Are you teaching any this semester? What is the experience like?

In my current postdoc, I do not have teaching obligations. I taught PreCalculus and Calculus courses as an instructor of record at the University of Georgia while I was pursuing my Ph.D. I find teaching very valuable for my academic development, on the other hand, focusing on research for a year has been equally great.

Parc de la Pépinière in Nancy, France — the idealyic location to unwind.

What do you do to balance your research and life and what do you look forward to, when you get to Lethbridge?

It has been tricky as we are going through some weird times. I like to travel and explore new places when it is feasible. At home, when we are in the lockdown, I like to read, I like 2D and 3D puzzles.

I really enjoy that traveling is easier in Nancy, than it is in the US, especially where I was in Athens, Georgia. This is what I will miss the most from France. However, I am looking forward to being a part of a successful research group, and starting teaching again at Lethbridge.

Tramlines in Nancy, France. The tram offers easy commutes within the city.

Kübra Benli received her B.S and M.S. degrees at Bogazici University in Istanbul, her M.S. supervisor was Prof. Cem Yalcin Yildirim. She then received her Ph.D. at the University of Georgia under the supervision of Prof. Paul Pollack in 2020. Since May 2021, she has been a postdoctoral fellow at the Institute Elie Cartan de Lorraine in Nancy, France working under the project ARITHRAND. She will begin her PIMS postdoctoral fellow at the University of Lethbridge later in 2022. Her research is on analytic/elementary number theory, with recent work focusing on counting primes in certain settings. She has also been working on some combinatorial problems. Her master thesis was published as a joint work and she has four publications, three of which are single-authored as a result of her Ph.D. research.

Kübra will be speaking at the PIMS Emergent Research Seminar Series, on February 23, 2022, at 9:30 AM Pacific. Details on her talk, Small prime $k$th power residues modulo $p$}, can be found here

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The Pacific Institute for the Mathematical Sciences — a consortium of 10 universities promoting research in and application of the mathematical sciences of the highest international calibre.

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Pacific Institute for the Mathematical Sciences

Pacific Institute for the Mathematical Sciences

PIMS — A consortium of 10 universities promoting research in and application of the mathematical sciences of the highest international calibre.

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