This collection of high-quality articles in the field of combinatorics, geometry, algebraic topology and theoretical computer science is a tribute to Jiķ Matouek, who passed away prematurely in March 2015. It is a collaborative effort by his colleagues and friends, who have paid particular attention to clarity of exposition something Jirka would have approved of.
The original research articles, surveys and expository articles, written by leading experts in their respective fields, map Jiķ Matoueks numerous areas of mathematical interest.
Simplex Range Searching and Its Variants: A Review: Pankaj K.
Agarwal.- Fair Representation by Independent Sets: Ron Aharoni, Noga Alon,
Eli Berger, Maria Chudnovsky, Dani Kotlar, Martin Loebl, and Ran
Ziv.- Computing Heegaard Genus Is NP-Hard: David Bachman, Ryan Derby-Talbot,
and Eric Sedgwick.- Approximation-Friendly Discrepancy Rounding: Nikhil
Bansal and Viswanath Nagarajan.- A Tverberg Type Theorem for Matroids: Imre
Barany, Gil Kalai, Roy Meshulam.- Gershgorin Disks for Multiple Eigenvalues
of Non-Negative Matrices: Imre Bįrįny and József Solymosi.- Computing the
Partition Function of a Polynomial on the Boolean Cube: Alexander Barvinok.-
Siegel's Lemma Is Sharp: József Beck.- On Codimension One Embedding of
Simplicial Complexes: Anders Björner and Afshin Goodarzi.- Around Brouwer's
Fixed Point Theorem: Anders Björner, Jiri Matousek, and Günter M.
Ziegler.- Beyond the Borsuk-Ulam Theorem: The Topological Tverberg
Story: Pavle V. M. Blagojevic and Günter M. Ziegler.- One-Sided
Epsilon-Approximants: Boris Bukh and Gabriel Nivasch.- A Note on Induced
Ramsey Numbers: David Conlon, Domingos Dellamonica Jr., Steven La Fleur,
Vojtech Rödl, and Mathias Schacht.- ARRIVAL: A Zero-Player Graph Game in NP \
coNP: Jerome Dohrau, Bernd Gärtner, Manuel Kohler, Jiri Matousek, and Emo
Welzl.- Constant-Factor Approximation for TSP with Disks: Adrian Dumitrescu,
and Csaba D. Toth.- Transport-Entropy Inequalities and Curvature in
Discrete-State Markov Chains: Ronen Eldan, James R. Lee, and Joseph
Lehec.- Bounding Helly Numbers Via Betti Numbers: Xavier Goaoc, Pavel Patak,
Zuzana Patakova, Martin Tancer, and Uli Wagner.- Ruled Surface Theory and
Incidence Geometry: Larry Guth.- Approximating the k-Level in
Three-Dimensional Plane Arrangements: Sariel Har-Peled, Haim Kaplan, and
Micha Sharir.- Schrijver Graphs and Projective Quadrangulations: Tomas Kaiser
and Matej Stehlik.- Near-Optimal Lower Bounds for nets for Halfspaces and Low
Complexity Set Systems: Andrey Kupavskii, Nabil H. Mustafa, and Janos
Pach.- Random Simplicial Complexes - Around the Phase Transition: Nathan
Linial and Yuval Peled.- Nullspace Embeddings for Outerplanar Graphs: Laszlo
Lovasz and Alexander Schrijver.- Homology of Spaces of Directed Paths in
Euclidean Pattern Spaces: Roy Meshulam and Martin Raussen.- Sperner's
Colorings and Optimal Partitioning of the Simplex: Maryam Mirzakhani and Jan
Vondrak.- Teaching and Compressing for Low VC-Dimension: Shay Moran, Amir
Shpilka, Avi Wigderson, and Amir Yehudayo.- Restricted Invertibility
Revisited: Assaf Naor and Pierre Youssef.- Rational Polygons: Odd Compression
Ratio and Odd Plane Coverings: Rom Pinchasi and Yuri Rabinovich.- First Order
Probabilities for Galton{Watson Trees: Moumanti Podder and Joel
Spencer.- Crossing-Free Perfect Matchings in Wheel Point Sets: Andres J.
Ruiz-Vargas and Emo Welzl.- Network Essence: Page Rank Completion and
Centrality-Conforming Markov Chains: Shang-Hua Teng.- Anti-Concentration
Inequalities for Polynomials: Van Vu.
Jiķ Matouek studied at Charles University in Prague, where he also took his doctorate and worked since 1986 till his early decease. He was a full professor at Charles University since 2000. Since 2012 he was also a full professor at ETH Zurich.
He was internationally very active, visited many institutions and delivered distinguished lectures, for example, at the European Congress of Mathematicians in 1996 and at the International Congress of Mathematicians in 1998. He was awarded the Prize of EMS for young researchers in 1996 and the Prize of the Czech Learned Society in 2000.
Jiķ Matouek was a brilliant and outstanding mathematician and computer scientist. Although his research focused on combinatorics, discrete geometry and algorithmics, his interests ranged well beyond these areas. He was a recognised expert in fields including algorithmic geometry, topological methods, discrepancy theory and linear programming.
Jiķ Matouek passed away on March 9, 2015.
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