Programme of the DIAMANT symposium, Thursday 5 April 2018
For the programme of the NMC 2018 (3-4 April 2018) please refer to this page.
The Diamant symposium will take place in room 63 of Koningshof. The dinner on Wednesday will take place in room Binnenhof.
Wednesday | |
19:00 | dinner (Binnenhof) |
Thursday | room 63 |
Christian Haase (FU Berlin) | Some facets of marginal polytopes |
9:00-9:55 | In this talk, I would like to introduce a class of convex polytopes which appear under different names in different fields of mathematics. For instance, they go by the name of marginal polytopes in statistics, they are called partial constraint satisfaction polytopes in combinatorial optimization. They occur as representation polytopes of abelian permutation groups, and they are used in tensor decomposition analysis. In the general setting, a polytope in the family is specified by a simplicial complex D with vertices labeled by positive integers. If all labels are equal to 2 (binary case), and if D is a graph, the polytope is a cut polytope. In spite of their many uses, the facet structure of marginal polytopes remains mysterious --- particularly so in the non-binary case. In joint work with Benjamin Nill and Andreas Paffenholz, we describe a generalization of the cycle inequalities for cut polytopes to non-binary labels together with a polynomial time separation algorithm if the size of the vertex labels is bounded. |
Arthur Bik (U Bern) | Noetherianity of dualized adjoint representations up to locally diagonal groups |
10:00-10:25 | Finite-dimensional vector spaces are Noetherian, i.e. every descending chain of Zariski-closed subsets stabilizes. For infinite-dimensional spaces this is not true. However it can be true for some group G acting on the space that every descending chain of G-stable closed subsets stabilizes. We call spaces for which this holds G-Noetherian. Recently, Draisma proved that polynomial functors of finite degree are Noetherian, which gives many representations of the infinite-dimensional general linear group that are Noetherian up to the action of the group. Eggermont and Snowden improved this result to encompass algebraic representations of infinite-dimensional classical groups. In this talk we will go in the opposite direction. We restrict ourselves to a specific representation, the dual of the adjoint representation, but we consider a wider class of groups, those that are the limit of a sequence of diagonal embeddings between classical groups. We prove that such representations are Noetherian up to the group action. |
10:30-11:00 | coffee break |
Hao Hu (UvT) | On linearization for the quadratic shortest path problem |
11:00-11:25 | Given an instance of the quadratic shortest path problem (QSPP) on a digraph G, the linearization problem for the QSPP asks whether there exists an instance of the linear shortest path problem on G such that the associated costs for both problems are equal for every s-t path in G. We prove here that the linearization problem for the QSPP on directed acyclic graphs can be solved in O(nm^3) time, where n is the number of vertices and m is the number of arcs in G. By exploiting this linearization result, we introduce a family of lower bounds for the QSPP on acyclic digraphs. The strongest lower bound from this family of bounds is the optimal solution of a linear programming 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 optimization problem. Numerical results show that our approach provides the best known linear programming bound for the QSPP. |
Jan-Willem van Ittersum (UU) | Harmonic shifted symmetric functions and the Bloch-Okounkov theorem |
11:30-11:55 | By the Bloch-Okounkov theorem, certain functions defined by sums over partitions are quasimodular. The space of quasimodular forms is closed under differentiating, which induces a sl_2-action on quasimodular forms. This mapping preserves this sl_2-action. A linear subspace of these functions on partitions - those in the kernel of a certain operator, called the space of harmonic shifted symmetric functions - are actually modular. We find an explicit basis for this kernel using an analogue of the Kelvin transform. |
12:00-13:30 | lunch |
Frits Spieksma (TU/e, KU Leuven) | Practical combinatorial optimization |
13:30-14:25 | Combinatorial optimization is a field that provides results and insights relevant in different domains. In this talk we intend to illustrate this claim by focusing on a number of specific results. As a first example, we consider the Circle Method (which dates back to 1851); this method is widely used to generate schedules for round-robin tournaments. An indicator for the fairness of a schedule is the so-called carry-over effect value. We prove that, for an even number of teams, the Circle Method generates a schedule with maximum carry-over effect value, answering an open question. As a second example, we consider the allocation of kidneys in live kidney exchange. Given a number of pairs, each pair consisting of a patient and a donor, incompatibility of the donor with the patient often prohibits a direct transplantation from the donor of a pair to the patient of that pair. Still, by using the fact that the donor of one pair may be compatible with the patient of another pair, and vice versa, transplantations may be possible. We review some of the existing models that are used for solving this problem. Finally, we consider the operation of a set of locks located along a waterway. Ships that travel along a waterway may have to wait in front of a waterway, and the amount of waiting time depends on the precise operation of these locks. We will investigate the computational complexity of the resulting problems, and discuss solution strategies. |
Lasse Grimmelt (UU) | Vinogradov's theorem with Fouvry-Iwaniec primes |
14:30-14:55 | Vinogradov showed in 1937 that every sufficiently large odd integer can be written as the sum of three primes. We consider this problem restricted to primes p, such that p=k^2+l^2 for some integer k and prime l. Fouvry and Iwaniec showed in 1997 that there are infinitely many of such primes. We extend their work to arithmetic progressions and combine it with B. Green's transference principle and several sieve related ideas to show that every sufficently large integer x with x = 3 mod 4 can be written as the sum of three such primes. |
15:00-15:30 | tea break |
Sjabbo Schaveling (UL) | Knot invariants using the quantum double construction on sl_3 |
15:30-15:55 | In this talk I will briefly explain the concept of quantum enveloping algebras. I will construct them using the quantum double construction. I will go into the connection between quantum groups and knot invariants, and explain how we created knot invariants with this construction. |
Djordjo Milovic (UCL) | Spins of ideals and arithmetic applications to one-prime-parameter families |
16:00-16:55 | We will define three similar but different notions of "spin" of an ideal in a number field, and we will show how a number-field version of Vinogradov's method (a sieve involving "sums of type I" and "sums of type II") can be used to prove that spins of prime ideals oscillate. Such equidistribution results have applications to the distribution of 2-parts of class groups of quadratic number fields and 2-Selmer groups of quadratic twists of elliptic curves in families parametrized by prime numbers. Parts of this talk are joint work with Peter Koymans. |
17:00 | end of the symposium |