Assistant Research Fellow
2018 – 2022
- Extremal Combinatorics, Extremal Set Theory, Graph Theory
- Advisor: Ervin Győri
salianika@gmail.com
Extremal problems are a natural and important area of research in mathematics. They involve studying the interplay between global and local properties of a mathematical structure, such as a graph, a hypergraph, a set system, or a function. In particular, extremal problems in hypergraphs are of significant interest due to their numerous applications in various fields of mathematics, computer science, and physics. In recent years, the study of extremal problems in hypergraphs has become increasingly important due to its relevance to quantum computing and artificial intelligence. Hypergraphs are a natural and powerful tool for modeling complex systems, and networks, and understanding their structure is crucial for developing efficient algorithms and computational methods.
The study of extremal problems is often challenging and involves various difficulties. One of the main challenges is determining the order of the extremal function, which describes the largest or the smallest possible value of a parameter with given properties. In some cases, the asymptotic behavior of the extremal function is known, but determining the exact value for every possible structure size remains an open question. Once exact results are obtained, including the structure of the extremal objects, the focus shifts to questions of stability and saturation. Stability problems seek to understand how close a model is to the extremal structure as it approaches given properties. On the other hand, saturation problems aim to understand how rich the model is if another property holds strongly. These questions are of great interest and have numerous applications.
I study the exact results and structural stability of extremal hypergraphs. I aim to develop new approaches using known probabilistic and algebraic techniques and tools for analyzing hypergraphs and answering fundamental questions in the field. Such results might have significant implications for various areas of mathematics and computer science and will contribute to the ongoing efforts to understand the structure of complex systems.
Combinatorics is a field uniquely suited to involving undergraduate students in research. With carefully structured guidance and foundational knowledge provided over a semester, students can quickly progress to tackling meaningful, open questions. The accessibility of combinatorial problems allows students to develop both technical skills and an appreciation for the depth of mathematical exploration, opening the door to a variety of engaging research directions.
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Lasha Ephremidze
le23@nyu.edu
Research Associate, New York University Abu Dhabi, UAE
A. Razmadze Mathematical Institute.
Central European
University,
Budapest, Hungary
PhD
2015 – 2021
- Research Area: Extremal Combinatorics, Graph Theory
- Advisor: Ervin Győri
MSc
2013 - 2015
- Thesis Title: Graphs with Isomorphic DFS Spanning Trees
- Advisor: Ervin Győri
Tbilisi State
University,
Tbilisi, Georgia
BSc, Exact and Natural
Sciences
2009 - 2013
Professor
2023 –
- Math 531 - Real Analysis
- Math 467 - Graph Theory
- Math 463 - Combinatorics
- Math 407 - Applied Game Theory
- Math 201 - Calculus III
Lecturer
Summer, 2022
- Graph Theory
Online Lecturer
Winter, 2020
- Combinatorics of finite set systems
Tutor
2018 - 2020
- Graph Theory
- Combinatorics 1
- Combinatorics of Finite Sets
- Extremal Combinatorics
Co/Lecturer
2017 – 2019
- Calculus for Business and Economics I
- Calculus for Business and Economics II, Probability and Statistics
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, Z. He, Z. Lv, N. Salia, C. Tompkins, K. Varga, X. Zhu.
Exact results for generalized extremal problems forbidding an even cycle.Accepted at Journal of Graph Theory
2025
E. Győri, N. Salia.
Linear three-uniform hypergraphs with no Berge path of a given length.Journal of Combinatorial Theory, Series B
2025
E. Győri, B. Li, N. Salia, C. Tompkins.
A note on universal graphs for spanning trees.Discrete Applied Mathematics
2025
N. Salia, D. Tóth.
Intersecting families of polynomials over finite fields.Finite Fields and Their Applications
2025
P. L. Erdős, E. Győri, T. Róbert Mezei, N. Salia, M. Tyomkyn.
On the small quasi-kernel conjecture.Information Theory and Related Fields, Lecture Notes for Computer Science. (Accepted)
2025+
2024
E. Győri, A. Paulos, N. Salia, C. Tompkins, O. Zamora.
The maximum number of pentagons in a planar graph.Journal of Graph Theory.
2024
Z. Lv, E. Győri , Z. He, N. Salia, C. Tompkins, X. Zhu.
The maximum number of copies of an even cycle in a planar graph.Journal of Combinatorial Theory, Series B.
2024
S. Jiang, H. Liu, N. Salia
How connectivity affects the extremal number of trees.Journal of Combinatorial Theory, Series B.
2024
D. Gerbner, D. Nagy, B. Patkós, N. Salia, M. Vizer
Stability of extremal connected hypergraphs avoiding Berge-paths.European Journal of Combinatorics.
2024
Z. Lv, E. Győri, Z. He, N. Salia, C. Xiao, X. Zhu
Maximum number of cliques in graphs with bounded odd circumference.Annals of Combinatorics.
2024
P. Frankl, E. Győri , Z. He, Z. Lv, N. Salia, C. Tompkins, K. Varga, X. Zhu
Extremal results for graphs avoiding a rainbow subgraph.Electronic Journal of Combinatorics.
2024
Z. Lv, E. Győri , Z. He, N. Salia, C. Tompkins, K. Varga, X. Zhu
Generalized Turan number for the edge blow-up graph.Discrete Mathematics.
2024
X. Zhu, E. Győri , Z. He, Z. Lv, N. Salia, C. Tompkins, K. Varga
Edges not covered by monochromatic bipartite graphs.SIAM Journal on Discrete Mathematics.
2023
B. Ergemlidze, E. Győri , A. Methuku, N. Salia, C. Tompkins
3-uniform hypergraphs avoiding a cycle of length four.Electronic Journal of Combinatorics.
2023
X. Zhu, E. Győri , Z. He, Z. Lv, N. Salia, C. Xiao
version of Dirac's theorem and its applications for generalized Tur\'an problems.Bulletin of the London Mathematical Society.
2023
A. Grzesik, E. Győri , N. Salia, C. Tompkins
Subgraph densities in K_r-free graphs.Electronic Journal of Combinatorics.
2023
2023
2022
A Grzesik, E. Győri A. Paulos N. Salia, C. Tompkins, O. Zamora
The maximum number of paths of length three in a planar graph.Journal of Graph Theory.
2022
2022
E. Győri A. Paulos, N. Salia, C. Tompkins, O. Zamora.
Generalized Planar Turán Numbers.Electronic Journal of Combinatorics.
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.
2021
E. Győri, N. Salia, O. Zamora.
Connected Hypergraphs without long Berge paths.European Journal of Combinatorics.
2021
D. Ghosh, E. Győri, O. Janzer, A. Paulos, N. Salia, O. Zamora.
Journal of Graph Theory.Journal of Combinatorial Optimization.
2021
D. Ghosh, E.Győri, A. Paulos, N. Salia, O. Zamora.
The Maximum wiener index of maximal planar graphs.Journal of Combinatorial Optimization.
2020
E.Győri, N. Lemons , N. Salia, O. Zamora.
The Structure of Hypergraphs without long Berge cycles.Journal of Combinatorial Theory.
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.
2019
N. Salia, C. Tompkins, Z. Wang, O. Zamora.
Ramsey numbers of Bergehypergraphs and related structures.Electronic Journal of Combinatorics.
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.
2019
N. Salia, C. Tompkins, O. Zamora.
An Erdős-Gallai type theorem for vertex colored graphs.Graphs and Combinatorics.
2019
L. Ephremidze, N.Salia, I. Spitkovsky.
On a parametrization of noncompact Wavelet matreces by Wiener-Hopf factorisation.Transactions A. Razmadze Mathematical Institute.
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.
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.
2018
L. Ephremidze, N. Salia, I. Spitkovsky.
Some Aspects of a Novel Matrix Spectral Factorization Algorithm.Proceedings of A. Razmadze Mathematical Institute.
2014
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