A Journey Through Discrete Mathematics

1. Simplex Range Searching and Its Variants: A Review
Pankaj K. Agarwal

2. Fair Representation by Independent Sets
Ron Aharoni, Noga Alon, Eli Berger, Maria Chudnovsky, Dani Kotlar, Martin Loebl, Ran Ziv

3. Computing Heegaard Genus is NP-Hard
David Bachman, Ryan Derby-Talbot, Eric Sedgwick

4. Approximation-Friendly Discrepancy Rounding
Nikhil Bansal, Viswanath Nagarajan

5. A Tverberg Type Theorem for Matroids
Imre Bárány, Gil Kalai, Roy Meshulam

6. Gershgorin Disks for Multiple Eigenvalues of Non-negative Matrices
Imre Bárány, József Solymosi

7. Computing the Partition Function of a Polynomial on the Boolean Cube
Alexander Barvinok

8. Siegel’s Lemma Is Sharp
József Beck

9. On Codimension One Embedding of Simplicial Complexes
Anders Björner, Afshin Goodarzi

10. Using Brouwer’s Fixed Point Theorem
Anders Björner, Jiří Matoušek, Günter M. Ziegler

11. Beyond the Borsuk–Ulam Theorem: The Topological Tverberg Story
Pavle V. M. Blagojević, Günter M. Ziegler

12. One-Sided Epsilon-Approximants
Boris Bukh, Gabriel Nivasch

13. A Note on Induced Ramsey Numbers
David Conlon, Domingos Dellamonica, Steven La Fleur, Vojtěch Rödl, Mathias Schacht

14. ARRIVAL: A Zero-Player Graph Game in NP ∩ coNP
Jérôme Dohrau, Bernd Gärtner, Manuel Kohler, Jiří Matoušek, Emo Welzl

15. Constant-Factor Approximation for TSP with Disks
Adrian Dumitrescu, Csaba D. Tóth

16. Transport-Entropy Inequalities and Curvature in Discrete-Space Markov Chains
Ronen Eldan, James R. Lee, Joseph Lehec

17. Bounding Helly Numbers via Betti Numbers
Xavier Goaoc, Pavel Paták, Zuzana Patáková, Martin Tancer, Uli Wagner

18. Ruled Surface Theory and Incidence Geometry
Larry Guth

19. Approximating the k-Level in Three-Dimensional Plane Arrangements
Sariel Har-Peled, Haim Kaplan, Micha Sharir

20. Schrijver Graphs and Projective Quadrangulations
Tomáš Kaiser, Matěj Stehlík

21. Near-Optimal Lower Bounds for ε-Nets for Half-Spaces and Low Complexity Set Systems
Andrey Kupavskii, Nabil H. Mustafa, János Pach

22. Random Simplicial Complexes: Around the Phase Transition
Nathan Linial, Yuval Peled

23. Nullspace Embeddings for Outerplanar Graphs
László Lovász, Alexander Schrijver

24. Homology of Spaces of Directed Paths in Euclidean Pattern Spaces
Roy Meshulam, Martin Raussen

25. Sperner’s Colorings and Optimal Partitioning of the Simplex
Maryam Mirzakhani, Jan Vondrák

26. Teaching and Compressing for Low VC-Dimension
Shay Moran, Amir Shpilka, Avi Wigderson, Amir Yehudayoff

27. Restricted Invertibility Revisited
Assaf Naor, Pierre Youssef

28. Rational Polygons: Odd Compression Ratio and Odd Plane Coverings
Rom Pinchasi, Yuri Rabinovich

29. First Order Probabilities for Galton–Watson Trees
Moumanti Podder, Joel Spencer

30. Crossing-Free Perfect Matchings in Wheel Point Sets
Andres J. Ruiz-Vargas, Emo Welzl

31. Network Essence: PageRank Completion and Centrality-Conforming Markov Chains
Shang-Hua Teng

32. Anti-concentration Inequalities for Polynomials
Van Vu

Keywords: Mathematics, Algorithms, Combinatorics, Geometry, Operations Research, Management Science, Algebraic Topology, Mathematics of Computing