Programme of the DIAMANT symposium

Hotel Van der Valk Veenendaal
29-30 November 2018


11:00-11:25 arrival and coffee
11:25-11:30 welcome
Arne Smeets (RUN) Diophantine problems for orbifold pairs
The study of Diophantine problems, i.e. of rational and integral points on algebraic varieties, is a classical and rich subfield of number theory and arithmetic geometry. I will explain how Campana's framework of "orbifold pairs" - which has its origins in birational geometry over the complex numbers - yields many new interesting Diophantine problems, which one can interpret as a way to 'interpolate' between problems having to do with rational points on the one hand, and with integral points on the other hand. I will also report on some recent work by the author on such problems: firstly, a Mordell-type conjecture over function fields; secondly, a Batyrev-Manin-type conjecture (counting points of bounded height) over number fields.
12:30-13:30 lunch
Arthur Bik (U Bern) Polynomials of bounded strength
13:30-13:55 Storing a homogeneous polynomial in K[x_1, ... ,x_n] of degree d becomes difficult very fast as n -> oo. The number of values we need to remember is a polynomial of degree d in n. However, if we only consider polynomials that can be expressed as the sum of at most k products of polynomials of lower degree, then the number of values that we need is at most k times a polynomial of degree d-1. In this talk, I will discuss joint work with Jan Draisma and Rob Eggermont stating that for every functorial family of Zariski-closed subsets X_n of K[x_1, ... , x_n]_(d) either X_n = K[x_1, ... , x_n]_(d) for all n or every polynomial f in X_n can be written as the sum of k products where k is a constant that does not depend on n or f.
Elena Kirshanova (U Lyon) Sieving algorithms for the Shortest Vector Problem
14:00-14:55 In this talk I give an overview on the complexity of the algorithms for the Shortest Vector Problem (SVP) with the focus on a particular family of algorithms: sieving algorithms. First, I explain why this problem is important and how the complexity of SVP algorithms impacts parameters for cryptographic protocols. Then, I present recent advances in memory efficient versions of sieving algorithms. I explain locality-sensitive techniques for these type of algorithms. The part of the talk is based on joint works with Gottfried Herold and Thijs Laarhoven. Finally, I present recent advances in practical aspects of sieving algorithm for SVP. I describe technical challenges that arise when one tries to make sieving algorithms practical, and how one can overcome some of them. This part of the talk is the on-going work with Martin R. Albrecht, Leo Ducas, Gottfried Herold, Eamonn W. Postlethwaite, Marc Stevens.
15:00-15:30 tea
Sam van Gool (ILLC) Pointlike sets for varieties determined by groups
15:30-15:55 I will present recent joint work with B. Steinberg in finite semigroup theory, which has applications in logic and regular language theory. Our main technical result is a characterization of the subsets of a finite semigroup that are pointlike with respect to a variety of the form H-bar. Here, H-bar denotes the variety of finite semigroups all of whose subgroups lie in a fixed variety of finite groups H. Our characterization is effective whenever H has decidable membership problem. Taking H to be the variety of solvable groups, our result gives an algorithm to decide whether two regular languages can be separated by a language definable in first order logic with modular counting quantifiers.
Sophie Huiberts (CWI) A friendly smoothed analysis of the simplex method
16:00-16:25 The simplex method for linear programming is known for its good performance in practice, although the theoretical worst-case performance is exponential in the input size. The smoothed complexity framework of Spielman and Teng (2001) aims to explain the good practical performance. In our work, we improve on all previous smoothed complexity results for the simplex algorithm on all parameter regimes with a substantially simpler and more general proof. This is joint work with Daniel Dadush.
Farbod Shokrieh (U Copenhagen) Graphs and arithmetic geometry
16:30-17:25 Graphs can be viewed as analogues of Riemann surfaces. For example there is a notion of Jacobians for graphs, which is closely related to the classical matrix-tree theorem. More classically, graphs can be viewed as electrical networks. I will explain the interplay between these points of view, as well as some recent applications to problems in arithmetic geometry.
17:30-19.00 drinks
19:00 dinner
+- 20:30 discussion about mastermath courses 2019-2020 (and 2020-2021) offered by Diamant
Renata Sotirov (Tilburg University) The Quadratic Shortest Path Problem
9:30-10:25 The quadratic shortest path problem (QSPP) is the problem of finding a path in a directed graph such that the sum of interaction costs over all pairs of arcs on the path is minimized. This problem has recently been proven NP-hard. We first classify QSPP instances into linearizable and non-linearizable instances. The linearizable QSPP instances are instances whose optimal solution can be obtained by solving the corresponding (easy) instance of the shortest path problem. We present a polynomial-time algorithm that solves the linearization problem for the QSPP, i.e., verifies whether a given QSPP instance is linearizable. For a non-linearizable instance, our algorithm generates a system of equations that is further exploited to compute lower bounds of the original problem. To the best of our knowledge, this is the first study in which the linearization problem is exploited to compute bounds for the corresponding combinatorial optimization problem. In the last part of the talk, we present a semidefinite programming relaxation for the QSPP and show how to use the alternating direction method of multipliers (ADMM) to solve the relaxation. Our approach results in solving large scale instance of the QSPP to optimality. Joint work with Hao Hu, Tilburg University.
10:30-11:00 coffee
Roland Vincze (U Maastricht) A time- and space-optimal algorithm for the many-visits TSP
11:00-11:25 The many-visits traveling salesperson problem (MV-TSP) asks for an optimal tour that visits each city a prescribed number of times. Travel costs may be asymmetric and visiting a city twice in a row may incur a non-zero cost. The fastest known exact algorithm is due to Cosmadakis and Papadimitriou (SICOMP, 1984) and has time and space complexity superexponential in the number of cities. We propose an exact algorithm that runs in single-exponential time and requires only polynomial space, which is, assuming the ETH, asymptotically optimal.
Harry Smit (UU) L-series and isogenies of abelian varieties
11:30-11:55 A theorem of Faltings states that two non-isogenous abelian varieties defined over a number field can be distinguished by the L-functions of their reductions. The global L-function does not have the same capacity, as one cannot distinguish between primes with the same characteristic. To work around this, we consider all L-functions twisted with Dirichlet characters and show that this characterises the isogeny type of an abelian variety.
12:00-13:00 lunch
Francisco Fernandes Pereira (TU/e) Entanglement-assisted quantum error correcting codes from algebraic geometry codes
13:00-13:25 The prospect of practical large-scale quantum computers and the use of quantum communication is only possible if quantum error correcting codes are implemented in them. They play the role of suppressing noise and decoherence by introducing redundancy. A few strategies can be used to improve the parameters of these codes. For example, entanglement can provide a way for quantum error correcting codes to achieve higher rates. Such codes are known as entanglement-assisted quantum error correcting codes (EAQECC). Another property of these codes is that they can attain the entanglement assisted quantum capacity of a depolarizing channel when the quantum code has maximal entanglement. In this talk we use algebraic geometry codes to construct EAQECCs that has maximal entanglement and are almost near maximal distance separable codes. We also show some examples of the possible parameters of the quantum codes that can be obtained from the presented method.
Wouter Zomervrucht (UL) Infinite Galois theory and localic groups
13:30-13:55 Recently, Bhatt and Scholze introduced a new infinite Galois theory that classifies categories of sets with a G-action, where G is a topological group. It is used to construct the pro-étale fundamental group, a refinement of the classical étale fundamental group (which is itself a generalization of the absolute Galois group of a field). Various natural questions about this infinite Galois theory are as of yet unanswered. We explain how it leads to the introduction of locales: an algebra-flavored `topology without points'. Replacing topological groups by localic groups, we answer some of the open questions.
14:00-14:30 tea
Aida Abiad Monge (U Maastricht) A spectral approach to the distance matrix of a graph
14:30-15:25 Spectral graph theory deals with the relation between the structure of a graph and the eigenvalues (spectrum) of an associated matrix, such as the Laplacian matrix or the distance matrix. In this talk, we will discuss some spectral properties of the distance matrix of a graph. It was conjectured by Graham and Lovász that the coefficients of the distance characteristic polynomial of a tree on n vertices are unimodal and have their peak at [n/2]. We will also report on recent results concerning this conjecture.
15:30 end of the symposium




Mathematics cluster DIAMANT

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NMC 2020 and Diamant symposium
14-4-2020 - 16-4-2020

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Call for PhD project proposals

NWO has issued a cluster-wide call for PhD project proposals. Researchers can apply if they are employed (i.e., hold a salaried position) at a Dutch university or a research institute recognised by NWO, and also have an appointment period for at least the duration of the application procedure and the entire duration of the research for which the grant is being applied for.

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ERC Starting Grant for Jesper Nederlof

Jesper Nederlof (TU/e) has been awarded an ERC Starting Grant of almost 1.5 ME. Nederlof will design faster algorithms for hard computational problems in computer science. The grant provides the researcher with the opportunity to further elaborate his own ideas during a period of five years.

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Full professor position in Discrete Mathematics in Delft

Delft Institute of Applied mathematics, Delft University of Technology, seeks a full Professor in the field of Discrete Mathematics. A description of the position can be found here. The deadline for applications is January 15, 2019.

ERC Starting grant for Daniel Dadush

Daniel Dadush (CWI) has been awarded an ERC Starting Grant of 1.5 ME for his proposal ‘Towards a Quantitative Theory of Integer Programming’. With this grant, Dadush aims to revolutionize the understanding of integer programming (IP), the most popular method used today for finding optimal solutions to real-world optimization problems.

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