**November 27, 2019 at 11:45**

**Speaker(s):**
**Pilar Bayer and Christian Blum**

**Center(s): **Universitat de Barcelona and Artificial Intelligence Research Institute (CSIC)

We are glad to announce the program for the 7th Math Colloquium BCAM-UPV/EHU that will take place on ** Wednesday, November 27th,** at BCAM’s facilities (Sala Aketxe, Edificio Sede) located at the Leioa Campus of the University of the Basque Country.

**PROGRAM:**

11:45-12:45 Pilar Bayer (Universitat de Barcelona)

__Computation of special values of arithmetic automorphic functions:__ The simplest example of automorphic function is provided by the exponential function e^2πit, which is invariant under the action of the additive group of the integers. Its values at rational numbers are the roots of the unity. They are algebraic numbers in one to one correspondence with the vertices of the regular polygons. The division points of the circle together with the division points of rational elliptic curves with complex multiplication (extra symmetries), play an essential role in algebraic number theory. Modular curves and, more generally, Shimura curves, are highly symmetric objects. As a consequence, they are a source of automorphic functions. In the study of diophantine equations, the knowledge of special points where these functions take algebraic values has became very important.

As a result of joint work with Montserrat Alsina, Jordi Guàrdia and Artur Travesa, I shall present a method to compute arithmetic automorphic functions attached to quaternionic Shimura curves and explain how to determine special algebraic values of them.

**13:00-14:00 Christian Blum (Artificial Intelligence Research Institute, Spanish National Research Council)**

__Construct, Merge, Solve & Adapt: A Recent Hybrid Approach for Combinatorial Optimization: __Construct, Merge, Solve & Adapt (CMSA) is a recent hybrid algorithm for solving combinatorial optimization problems. This algorithm provides a means for taking profit from exact techniques (such as, for example, general-purpose integer linear programming (ILP) solvers) in the context of problem instances that are much too large for solving them with the exact technique directly. In this presentation, the standard CMSA algorithm is first introduced by means of examples. Subsequently, the focus of the presentation will shift to some recent developments. The first one deals with a problem-independent version of CMSA for solving any combinatorial problem that can be modelled as a binary integer linear program. And the second one is about a comparison of CMSA with another hybrid technique known as large neighbourhood search (LNS). This comparison is supported by a new way of graphically showing the search behaviour of algorithms by means of merged local optimal networks.

**14:00 Lunch at "Sala Kurkudi" **