Assistant Research Fellow
2018 – 2022
- Extremal Combinatorics, Extremal Set Theory, Graph Theory
- Advisor: Ervin Győri
salianika@gmail.com
Mathematics is the science that lays the groundwork for all other sciences. Combinatorics and Graph Theory are fields of mathematics that have played a similar role within mathematics. They emerged as independent disciplines with the rise of computer science and its need for discrete structures and found applications in various branches of mathematics. Extremal combinatorics is a sub-field of combinatorics that explores how local properties affect global properties of combinatorial structures. These questions are not only beautiful in their own right but also find applications in number theory, discrete geometry, and theoretical computer science, to name a few.
A typical problem in extremal combinatorics is to find the largest or the smallest size of a combinatorial object that satisfies certain constraints. For example, how many edges can a graph have if it does not contain a certain subgraph? This is a so-called forbidden subgraph problem (also referred to as the Turán problem), one of the most classic and important problems in the area. Addressing it for the forbidden 4-cycle C_4, a remarkable theorem of Erdős says that the maximum number of edges in a C_4-free graph is of order n^{3/2}, where n is the number of vertices. Erdős used this theorem in order to prove an asymptotic result for a famous number theory problem, namely the maximum number of bounded integers with distinct products.
Extremal combinatorics is an active and rich field, with many open problems and recent breakthroughs. Some of the current research directions include Ramsey theory, Turán type problems including generalized Turán problems, stability and saturation problems for discrete structures, extremal problems for hypergraphs and set systems, for graphs with a bounded degree or girth, for graphs with forbidden induced subgraphs, and for graphs with algebraic or geometric structure. The goal of this project is to pursue further research in these areas and address a number of long-standing open problems, with a particular focus on Turán numbers of bipartite graphs, extremal problems in geometric settings, and Turán problems for hypergraphs.
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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
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
S. Jiang, H. Liu, N. Salia
How connectivity affects the extremal number of trees.Journal of Combinatorial Theory, Series B , (Accepted).
2024+
D. Gerbner, D. Nagy, B. Patks, N. Salia, M. Vizer
Stability of extremal connected hypergraphs avoiding Berge-paths.European Journal of Combinatorics, (Accepted).
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, Series B.
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, 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
My arXiv identifier:
