Assistant Research Fellow
2018 – 2022
- Research Area: Extremal Combinatorics, Extremal Set Theory, Graph Theory
- Advisor: Ervin Győri
' Cogito, Ergo Sum '
Nánási st. 1/B, app. 414, 1031, Budapest, Hu
Guram Panjikidze 22, app. 40, 0160, Tbilisi, Geo
+36 70 259 5264
nikasalia@yahoo.com
My research centers on a branch of discrete mathematics known as extremal combinatorics, which studies the maximum or minimum size of discrete structures under given constraints. For example, a classical question studied by Mantel in 1907 asks, `What is the maximum number of edges that a triangle-free graph with a given order can have?'. Thus extremal combinatorics can be thought of as solving certain optimization problems and as such has many real-life applications. The fast development of this field in the last century was driven by its close relations with computer science and many other fields of mathematics. Since we are all naturally fascinated by everyday objects that are extreme for various properties such as speed, color or size, in much the same way extremal objects in mathematics are inherently fascinating for me. In addition to their natural beauty, the problems that I work on encourage elegant mathematics that uses a variety of techniques. In particular, we often use algebraic and probabilistic methods to construct large graphs with given properties to derive the desired lower bound, whilst for the upper bound one may also apply the probabilistic method, the celebrated regularity lemma and even elementary arguments such as induction, double-counting or the pigeonhole principle.
le23@nyu.edu
Research Associate, New York University Abu Dhabi, UAE
A. Razmadze Mathematical Institute.
Simply speaking, I love teaching and when I teach my favorite topics of mathematics I am a passionate teacher. My love of teaching was developed by the following two factors. Firstly, I was taught by great teachers who never stopped inspiring me including my mother. Secondly, I enjoy doing mathematics. This led me to pursue all the teaching opportunities I had during my life. Since I was a successful student of the best math school in Georgia, I was fortunate enough to have a chance to be a teacher from early on in my career. I started my teaching career when I was just a high-school student. During my final year, there was a reform in the educational system and teachers were required to pass proficiency exams. One of the exam topics was graph theory. Unfortunately, this field of mathematics is not much appreciated in Georgia and was therefore not widely known. But I was a kid who was fascinated with graph-theoretical problems. Hence I was the one who gave several short talks to my teachers about topics from graph theory. I believe this was one of the proudest moments of my life in which I decided I wanted to be an educator. After graduating high school, I was an instructor for bright students. I was training them for math and computer science Olympiads, both national and international. At the same time, I was a leader of a small group of young children interested in recreational mathematics. During those years I have seen the sparkling and shining eyes of children each and every time they have seen the beauty of the patterns they found in the math problems.
During my Ph.D. studies, I had various teaching opportunities in Hungary. When the pandemic hit in 2020, all the lectures moved online. As the professor of Combinatorics of Finite Set Systems was not able to teach online, I took over his duties and finished the second half of the semester. This was the best teaching experience of my life since my students were motivated, bright undergraduate students from all over the USA who came to Hungary with the desire to learn mathematics. At the same time, I was teaching the subject I loved most. This was such an uplifting experience that it helped me to live with harsh pandemic regulations.
But I have not always been so fortunate. I have been teaching Probability and Statistics and Calculus at Metropolitan University Budapest for several semesters. Since the students were not majoring in technical fields, they were not motivated and eager to study. Moreover, sadly the majority of them could not even solve quadratic equations at the beginning of the semester. At first, it was a frustrating experience. Soon after, I realized that my duties in the classroom are to motivate and develop learning habits in my students that will make them want to succeed. Also, I have realized that the syllabus is not a rule book that I need to follow no matter what, but it is a recommended road on which I need to walk with students at a pace determined by the majority of the group. At the same time, I needed to deal with the brightest students to keep them engaged. I made sure that I always had some extracurricular activities ready for them. For the rest of the students, who were not as skilled as the majority of the group, I needed to work extra hours to make sure they could catch up with the group. This was hard work but when I saw the results and feedback at the end of the semester I was proud of what I had achieved.
Teaching at the Milestone Institute was also an empowering teaching experience. The Milestone Institute is a private organization for talented kids who want to continue their studies in the top universities of the world. My goal as a mentor was to prepare students for university life and help them for future decision-making about their professions. I had 25 highly motivated high-school students whom I was teaching my favorite topics from graph theory. This was the first time I have developed my own syllabus and I was teaching students the way I thought best for them. Fortunately, my enthusiasm was rewarded and the vast majority of students were happy with the time they spent with me.
For two semesters I was a teaching assistant at Central European University for two different courses Topics in Combinatorics and Quantitative Methodology. Since Combinatorics was my field of expertise and the students were fellow Ph.D. students this was not a difficult task. Sometimes students would appear in my office with specific questions which I was ready to answer and show them a path towards the solution. To be a teaching assistant of Quantitative Methodology was very challenging since this was a subject with which I was not completely familiar, therefore I needed many hours to prepare for each and every meeting. Furthermore, it occasionally happened that I had no answer to the given questions. Genuinely it was a very stressful experience for me which taught me very important lessons.
Right now I have very exciting and important teaching duties. I am teaching online at the Asian University for Women. This university is located in Bangladesh and is dedicated to growing a new generation of educated independent women in Asia. I am very privileged to take part in empowering future female leaders of Asia. One of the main goals for me is to nurture scholarship habits and abilities in my students. The students are highly motivated individuals from various backgrounds- abilities, knowledge, facilities, religion, and culture. Therefore it is extremely challenging to teach such a diverse audience. But during these semesters, I have improved my online teaching skills and developed new techniques that can be used efficiently to enhance online teaching.
The beauty and power of mathematical thinking have changed our lives. Naturally, we consider mathematics to be the core of basic education. Without mathematical literacy, not only do our career opportunities shrink, but we also miss the true beauty of the world in which we live. Teaching, in general, is a hard job; it requires not only proficiency in the field and responsibility, but also you need to be an educator, philosopher, psychologist, negotiator and most importantly a friend.
I believe that an educator's main goals are to make students curious and teach them how to think outside of the box and be brave. To teach mathematics, we need to steal their attention briefly, make them wonder about an authentic mathematical problem. It is important not to rush the audience to an answer, since, otherwise, we will rob them of the opportunity to learn; instead, we should help them to pursue the truth while raising new questions. In short, we should give them loads of time to struggle alone to teach them to be tenacious, courageous and to persevere in the case of difficulty. This will make them passionate about the world of logical thinking. Furthermore, if they come up with an answer, we should not tell them if it is true or not; instead, we should encourage them to engage in group discussions and convince each other of their truth. Meanwhile, it is important to control the engagement of every individual. Hence inclusivity is an important variable.
Budapest, Hungary
Tbilisi, Georgia