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.

  • Ervin Győri

    gyori.ervin@renyi.hu

    Alfréd Rényi Institute of Mathematics, scientific advisor.

  • Gyula O.H. Katona

    ohkatona@renyi.hu

    Alfréd Rényi Institute of Mathematics, scientific advisor.

  • Ryan R. Martin

    rymartin@iastate.edu

    Professor at Iowa State University

  • Lasha Ephremidze

    le23@nyu.edu

    Research Associate, New York University Abu Dhabi, UAE

    A. Razmadze Mathematical Institute.

  • Extremal Combinatorics
  • Structural Graph Theory
  • Ramsey Theory
  • Planar Graphs
Alfréd Rényi Institute of Mathematics

Assistant Research Fellow

2018 – 2022

  • Research Area: Extremal Combinatorics, Extremal Set Theory, Graph Theory
  • Advisor: Ervin Győri

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.

Central European University, 

Budapest, Hungary

PhD
2015 – 2021

  • Research Area: Extremal Combinatorics, Graph Theory
  • Advisor: Ervin Győri

MSc
2013 - 2015

Tbilisi State University, 

Tbilisi, Georgia

visit webpage

Lecturer/ Global Teaching Fellow

2021-2022

  • Probability and Statistics
  • Discrete Mathematics

visit webpage

Online Lecturer

Winter, 2020

  • Combinatorics of finite set systems

Tutor

2018 - 2020

  • Graph Theory
  • Combinatorics 1
  • Combinatorics of Finite Sets
  • Extremal Combinatorics

visit webpage

Teaching Assistant

  • Topics in Combinatorics
    Winter, 2019
  • Quantitative Methodology
    Autumn, 2018

visit webpage

Co/Lecturer

2017 – 2019

  • Calculus for Business and Economics I
  • Calculus for Business and Economics II, Probability and Statistics

visit webpage

Module Leader

Summer, 2019

  • Advanced Graph Theory

visit webpage

Chair of Mathematics ’Circle’

2009 – 2013

  • Training students for international mathematical Olympiad
  • Teaching recreational mathematics

Doctoral Research Support Grant, CEUBPF,
Research at Institute of Pure and Applied Mathematics, Rio de Janeiro, Brazil
Nov.2019 – Feb.2020
Rustaveli National Science Foundation Grant, Project No. FR-18-2499
New approaches in modern analysis on metric spaces, multidimensional and Applied Harmonic Analysis. Applications to PDEs
2019 – 2021
Rustaveli National Science Foundation Grant, Project No. DI-18-118
Integral Operators in Non-standard Function Spaces; New Aspects of Fourier Analysis and Wavelet Theory
2019 – 2021
Fellowship for Doctoral students,
Central European University
2013 – 2015
First place at the seventy-second student scientific conference,
I. Javakhishvili Tbilisi State University Georgia
2012
Bronze medal,
International Zhautykov Olympiad, Kazakhstan
2009
Honorable mention
International Mathematical Olympiad, (IMO), Spain
2008
E. Győri A. Paulos, N. Salia, C. Tompkins, O. Zamora.
Generalized Planar Turán Numbers.
 Electronic Journal of Combinatorics, DOI: 10.37236/9603
2021
D. Ghosh, E. Győri, R. R. Martin, A. Paulos, N. Salia, C. Xiao, O. Zamora.
The Maximum Number of Paths of Length Four in a Planar Graph.
 Journal of Discrete Mathematics, DOI:10.1016/j.disc.2021.112317
2021
E. Győri, N. Salia, O. Zamora.
Connected Hypergraphs without long Berge paths.
 European Journal of Combinatorics, DOI: 10.1016/j.ejc.2021.103353
2021
D. Ghosh, E. Győri, O. Janzer, A. Paulos, N. Salia, O. Zamora.
Journal of Graph Theory, DOI: 10.1002/jgt.22745
 Journal of Combinatorial Optimization, DOI: 10.1007/s10878-020-00655-4
2021
D. Ghosh, E.Győri, A. Paulos, N. Salia, O. Zamora.
The Maximum wiener index of maximal planar graphs.
 Journal of Combinatorial Optimization, DOI: 10.1007/s10878-020-00655-4
2020
E.Győri, N. Lemons , N. Salia, O. Zamora.
The Structure of Hypergraphs without long Berge cycles.
 Journal of Combinatorial Theory, Series B, DOI: 10.1016/j.jctb.2020.04.007
2020
B. Ergemlidze, E.Győri, A. Methuku, N. Salia, C. Tompkins, O. Zamora.
Avoiding long Berge cycles, the missing cases k = r + 1 and k = r + 2.
 Combinatorics, Probability and Computing, DOI: 10.1017/ S0963548319000415, 1–13
2019
N. Salia, C. Tompkins, Z. Wang, O. Zamora.
Ramsey numbers of Bergehypergraphs and related structures.
 Electronic Journal of Combinatorics, Volume 26, Issue 4, P4.40
2019
E.Győri, N. Salia, C. Tompkins, O. Zamora.
The maximum number of P_l copies in P_k-free graphs.
 Discrete Mathematics and Theoretical Computer Science 21, 14.
2019
N. Salia, C. Tompkins, O. Zamora.
An Erdős-Gallai type theorem for vertex colored graphs.
 Graphs and Combinatorics, DOI: 10.1007/s00373- 019-02026-1.
2019
L. Ephremidze, N.Salia, I. Spitkovsky.
On a parametrization of noncompact Wavelet matreces by Wiener-Hopf factorisation.
 Transactions A. Razmadze Mathematical Institute Vol. 173 issue 3, 1.
2019
E.Győri, A. Methuku, N. Salia, C. Tompkins, M. Vizer.
On the maximum size of connected hypergraphs without a path of given length.
 Journal of Discrete Mathematics, 341(9): 26022605.
2018
B. Ergemlidze, E.Győri, A. Methuku, N. Salia.
A note on the maximum number of triangles in a C5-free graph.
 Journal of Graph Theory, 14.
2018
L. Ephremidze, N. Salia, I. Spitkovsky.
 Some Aspects of a Novel Matrix Spectral Factorization Algorithm.
Proceedings of A. Razmadze Mathematical Institute 166: 49-60.
2014
Stability of Extremal Connected Hypergraphs Avoiding Berge-Paths.
EUROCOMB 2021, European Conference on Combinatorics, Graph Theory and Applications 2021
2021
Pósa-type results for Berge Hypergraphs.
28th British Combinatorial Conference
2021
The Structure of Hypergraphs Without Long Berge Cycles.
EUROCOMB 2019, European Conference on Combinatorics, Graph Theory and Applications
2019
The Structure of Connected Hypergraphs without Long Berge Paths.
BCC 2019, 27th British Combinatorial Conference
2019
On the Maximum Size of Connected Hypergraphs without a Berge-Cycle of Given Length.
ICGT 2018, 10th international colloquium on graph theory and combinatorics
2018
D. Gerbner, D. T. Nagy, B. Patkós, N. Salia, M. Vizer.
Stability of Extremal Connected Hypergraphs Avoiding Berge-Paths.
Extended Abstracts EuroComb 2021. Trends in Mathematics, vol 14. pp. 117-122, Birkhäuser.
2021
E. Győri, A. Paulos, N. Salia, C. Tompkins, O. Zamora.
The Maximum Number of Paths of Length Three in a Planar Graph
Extended Abstracts EuroComb 2021. Trends in Mathematics, vol 14. pp. 262-266, Birkhäuser.
2021
N. Salia, C. Tompkins, Z. Wang, O. Zamora.
Ramsey numbers of Bergehypergraphs and related structures
Acta Mathematica Universitatis Comenianae, Vol. LXXXVIII, 3, pp. 1035-1042.
2019
E. Győri, N. Lemons, N. Salia, O. Zamora.
The structure of hypergraphs without long Berge cycles.
 Acta Mathematica Universitatis Comenianae, Vol. LXXXVIII, 3, pp. 767-771.
2019
E. Győri, N. Salia, C. Tompkins, O. Zamora.
The maximum number of P_l copies in P_k-free graphs.
 Acta Mathematica Universitatis Comenianae, Vol. LXXXVIII, 3, pp. 773-778.
2019
B. Ergemlidze, E.Győri, A. Methuku, N. Salia.
A note on the maximum number of triangles in a C5-free graph.
 Electronic Notes in Discrete Mathematics, 61, pp. 395-398. ISSN 1571-0653.
June 2018
L. Ephremidze, A. Gamkrelidze, N. Salia.
Numerical Comparison of Different Algorithms for Construction of Wavelet Matrices.
 IEEE First International Black Sea Conference on Communications and Networking, Proceedings, pp. 177 - 180.
2013
Survey of Recent Generalisations of Erdős-Gallai Theorems for Hypergraphs.
Open University Discrete Mathematics Seminar Series.
Nov. 2020
Ramsey numbers of Berge-Hypergraphs and Related Structures.
Which Hypergraphs are Extremal?
Combinatorics Seminar, IMPA - Institute of Pure and Applied Mathematics.
Dec.2019 & Jan.2020
Erdős-Gallai Type Theorems for Uniform Hypergraphs.
The Institute of Mathematics and Statistics, the University of Sao Paulo.
Jan.2020
Erdős-Gallai Type Theorems for Hypergraphs.
Combinatorics Seminar, .Karlsruhe Institute of Technology, KIT.
Dec.2018