Description
14:00 Matszangosz Ákos: Real problems in enumerative geometry
Abstract: Enumerative geometry deals with counting objects satisfying geometric conditions, such as:
How many lines lie on a smooth cubic surface?
How many lines intersect four generic lines in 3-space?
Such problems are classically studied over the complex field, where the answer is a single number. Over the reals, the answer depends on the given configuration, so the answer is a list of possible numbers. In this talk I will discuss lower bounds to the number of possible solutions.
14:20 Nagy Dániel: Set systems with forbidden subposets
Abstract: Let us consider set systems consisting of subsets of an n element set that do not realize certain configurations of inclusion. Such a forbidden structure can be described by a partially ordered set (poset). The general question is to find the largest set system avoiding a given poset. The talk provides a brief introduction to this topic then we will discuss recent research, various generalizations and open problems.
14:40 Niko Laaksonen: Prime Geodesic Theorem and Arithmetic
Abstract: The prime geodesic theorem (PGT) states that the lengths of primitive closed
geodesics on a hyperbolic surface have an asymptotic behaviour similar to the
usual prime numbers. Therefore, the PGT can be thought of as a geometric analogue
of the classical prime number theorem, where the role of the non-trivial zeros
of the Riemann zeta function is replaced by the eigenvalues of the Laplace
operator. On the other hand, for certain arithmetic surfaces the PGT also
has close connections to class numbers of binary quadratic forms and special
values of Dirichlet L-functions. By combining these two points of view, we show
how to obtain new estimates for the remainder in the PGT in three-dimensional
hyperbolic space.
15:00 Bencs Ferenc: Some results on the roots of the independence polynomial
Abstract: In this talk we will define the independence polynomial, that also appears in the literature as a partition function of a statistical physics model, and we will investigate the closure of the possible roots of these polynomials. We would like to understand for a given graph family (e.g. graphs of degree at most $\Delta$ ) what the zero-free open connected sets of $\mathbb{C}$ that contain 0 are, and how they are influenced by the graph family. In the talk we will give some examples of such graph classes and some of their zero-free regions.
15:20 Mészáros András: Limiting entropy of determinantal processes
Abstract: We extend Lyons's tree entropy theorem to general determinantal measures. As a byproduct we show that the sofic entropy of an invariant determinantal measure does not depend on the chosen sofic approximation.