Hi!

I'm Morteza, currently a postdoctoral fellow at ISTA, in Herbert Edelsbrunner's research group.

Before that, I did my PhD at Sharif University of Technology under supervision of Miromid Haji Mirsadeghi & Mohammad Ali Abam. My doctoral dissertation introduced a new model of clustering algorithms for imprecise points.

In my research, I primarily explore point clouds from combinatorial, geometric, and topological perspectives, but I also have a strong interest in graph theory and other areas of combinatorics.

I also actively create math problems and propose them to national and international math competitions.

Research Interests

Discrete Geometry - Combinatorics - Computational Topology - Graph Theory

Publications and Preprints

Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, The Euclidean MST-ratio for Bi-colored Lattices, Symposium on Graph Drawing (2024). [Link]
M. Ruber, G. Rote, M. Saghafian, Grid Peeling of Parabolas, Symposium on Computational Geometry (2024). [Link]
R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Depth in Arrangements: Dehn-Sommerville-Euler Relations with Applications, Journal of Applied and Computational Topology (2024). [Link]
H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, M. Wintraecken, Brillouin Zones of Integer Lattices and Their Perturbations, SIAM Journal on Discrete Mathematics (2024). [Link]
S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, Chromatic Topological Data Analysis, Submitted (2024). [Link]
A. Jabal Ameli, F. Motiei, M. Saghafian, The Complexity of Maximizing the MST-ratio, Submitted (2024). [Link]
H. Beigy, M. Mahini, S. Qadami, M. Saghafian, Approximating Simplet Frequency Distribution for Simplicial Complexes, European Workshop on Computational Geometry (2024). [Link]
J. Pach, M. Saghafian, P. Schnider, Decomposition of Geometric Graphs into Star Forests, Symposium on Graph Drawing (2023). [Link]
R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Geometric Characterization of the Persistence of 1D Maps, Journal of Applied and Computational Topology (2023). [Link]
H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, On Angles in Higher Order Brillouin Tessellations and Related Tilings in the Plane, Discrete and Computational Geometry (2023). [Link]
H. Edelsbrunner, A. Garber, M. Saghafian, Order-2 Delaunay Triangulations Optimize Angles, Submitted (2023). [Link]
M.A. Abam, M. de Berg, S. Farahzad, M.O. Haji Mirsadeghi, M. Saghafian, Preclustering Algorithms for Imprecise Points, Algorithmica (2022). [Link]
R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Continuous and Discrete Radius Functions on Tessellations and Mosaics, Discrete and Computational Geometry (2022). [Link]
H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, Flips in Two-dimensional Hypertriangulations, Submitted (2022). [Link]
R. Biswas, S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, On the Size of Chromatic Delaunay Mosaics, Submitted (2022). [Link]
S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, Chromatic Alpha Complexes, Submitted (2022).[Link]
R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Counting Cells of Order-k Voronoi Tessellations in R^3 with Morse Theory, Symposium on Computational Geometry (2021). [Link]
S. Alipour, A. Jafari, M. Saghafian, Upper Bounds for $k$-Tuple (Total) Domination Numbers of Regular Graphs, Bulletin of the Iranian Matheathical Society (2020). [Link]
A. Ahadi, A. Dehghan, M. Saghafian, Is There any Polynomial Upper Bound for the Universal Labeling of Graphs?, Journal of Combinatorial Optimization (2017). [Link]
S. Akbari, A.H. Ghodrati, A. Jabalameli, M. Saghafian, Chromatic Number and Dichromatic Polynomial of Digraphs, (2017). [Link]
N. Anari, M.A. Fazli, M. Ghodsi, M.A. Safari, M. Saghafian, Euclidean Movement Minimization, Journal of Combinatorial Optimization (2016). [Link]
S. Bahariyan, A. Bahjati, M. Ferdosi, A. Jabalameli, M. Saghafian, M.M. Shokri, Improving the Bounds On Murty-Simon Conjecture, (2016). [Link]
S. Ehsani, S.S. Fadaee, M.A. Fazli, A. Mehrabian, S.S. Sadeghabad, M.A. Safari, M. Saghafian, A Bounded Budget Network Creation Game, ACM Transactions on Algorithms (2015). [Link]
S. Ehsani, M.A. Fazli, M. Ghodsi, M.A. Safari, M. Saghafian, M. Tavakkoli, White Space Regions, SOFSEM (2011). [Link]
M.A. Fazli, N. Nikparto, M. Saghafian, Envy Free Chain Store Pricing, CSI Symposium on Computer Science and Software Engineering (2011). [Link]

Teaching

Introduction to Graph Theory, Sharif University of Technology, Department of Mathematics, Spring 2019.
Discrete Mathematics, Sharif University of Technology, Department of Mathematics, Fall 2018.
Discrete Mathematics, Sharif University of Technology, Department of Mathematics, Fall 2017.
TA General Mathematics II, Sharif University of Technology, Department of Mathematics, Spring 2016.
TA General Mathematics I, Sharif University of Technology, Department of Mathematics, Spring 2015.

Combinatorics Teacher for IMO Preparation Camps for Austrian Students, 2021 -- present.
Invited Trainer to IMO Training Camps in Azerbaijan, Kuwait, Pakistan, Tajikistan, 2018 -- 2020.
Instructor of Mathematics Topics for Top High Schools in Iran; e.g. Allameh Helli, Farzanegan, Allameh Tabatabaei, etc., 2008 -- 2018.
Trainer of the Iranian IMO Team, 2006 -- 2018.

Olympiad Activities

2022, Member of Problem Selection Committee, Middle European Mathematical Olympiad (MEMO).
2021 -- 2022, Iranian Team Leader, International Mathematical Olympiad (IMO).
2021 -- present, Member of National Committee, Iranian National Olympiad in Informatics.
2020 -- 2022, Co-founder and Chairman of the Iranian combinatorics Olympiad (ICO), 30+ participating countries.
2018 -- present, Problem Selection Committee Member, Caucasus Mathematical Olympiad (CMO).
2014 -- 2019, Co-founder and Chairman, Iranian Geometry Olympiad (IGO), 60+ participating countries.
2013 -- 2020, Member of Jury, Sharygin Olympiad of Geometry.
2006 -- present, Author of 100+ problems in International math Competitions including three IMO problems (2011,2012,2018).

Books (in Persian)

2018, Supervisor and Scientific Editor, Bebras Problems, Fatemi Publications.
2015, Author, The Last Step to the Second Round of Math Olympiad, Fatemi Publications.
2011, Co-author, Introduction to Math Olympiad by Problem Solving, Fatemi Publications.
2009, Co-author, 250 Problems in Combinatorics, Fatemi Publications.
2009, Co-author, 250 Problems in Algebra, Fatemi Publications.
2009, Co-author, 250 Problems in Number Theory, Fatemi Publications.
2009, Co-author, 250 Problems in Geometry, Fatemi Publications.

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