Likelihood Geometry is the geometric study of the maximum likelihood estimation problem to an algebraic variety serving as a statistical model. In this talk, basic notions of algebraic statistics and likelihood geometry will be introduced before discussing the maximum likelihood degree of a toric variety (also known as a log-linear model in the statistics context) in more detail.

Numerical semigroups are the cofinite subsemigroups of the natural numbers containing 0. We discuss the concept of counting numerical semigroups and introduce the notion of counting by the maximum primitive (generator) of the semigroup. For any positive integer $n$, let $A_n$ denote the set of numerical semigroups whose maximum primitive is $n$, and let $N_f$ denote the set of numerical semigroups whose Frobenius number is $f$.

The Grassmann convexity conjecture by B. Shapiro and M. Shapiro admits
several equivalent formulations.
One of them gives a conjectural formula for the maximal total number
of real zeros of the consecutive Wronskians of an arbitrary
fundamental solution to a disconjugate linear ordinary differential
equation with real time.
Another formulation is in terms of convex curves in the nilpotent
lower triangular group.
There is a very elementary formulation in terms of lists of vectors in $\mathbb{R}^k$.

The theoretical discovery of hyperbolic geometry first got its actual tactile example in 1868 when Eugenio Beltrami created a negatively curved surface from paper annuli and named it a pseudosphere. Later the name pseudosphere got attached to a surface created by a tractrix rotating around its axis. However, mathematicians found more useful for theoretical purposes using different, non-tactile models such as Klein or Poincare disc models or half-plane model. Those are traditionally used in college textbooks.

Vamos considerar a conectividade de coberturas por dominós usando movimentos locais.
Em particular, nos concentraremos no movimento conhecido como flip, no qual dois dominós adjacentes são removidos e recolocados em outra posição.
Em dimensão 2, é possível ligar quaisquer duas coberturas de uma região simplesmente conexa por meio de uma sequência de flips.
No entanto, em dimensão 3, existem regiões simplesmente conexas onde flips não são suficientes para conectar qualquer par de coberturas.

In his paper from 2012, Nicolas Thiéry gives a formula for computing the Cartan matrix of a finite monoid (which can be seen as a measure of how "not semisimple" the algebra over the monoid is) in terms of number of fixed points under a conjugacy like action and the character table of the monoid.

Any Poisson bracket on a differentiable manifold can be written locally as the sum of two commuting Poisson brackets: a Poisson bracket of
a symplectic form and a Poisson bracket that vanishes at a point. This is the so-called Weinstein splitting. The result is strictly local; in
general, it is impossible to globalize the two local Poisson structures.  It turns out that for holomorphic Poisson structures on compact Kähler
manifolds admitting a simply connected compact symplectic leaf, the local Weinstein splitting globalizes and produces a global splitting of

A ring (associative with identity) is called a fine ring if every nonzero element in it is the sum of a unit and a nilpotent element.  G. Cǎlugǎreanu and T.Y. Lam initiated the study of fine rings in  "Fine rings: a new class of simple rings.", J. Algebra Appl. (2016). In this talk, we review known results and discuss some new developments of this study.

The tunneling effect predicted by B.Josephson (Nobel Prize, 1973) concerns the Josephson junction: two superconductors

separated by a narrow dielectric. It states existence of a supercurrent through it and equations governing it. The overdamped Josephson junction

is modeled by a family of differential equations on 2-torus depending on 3 parameters. In this talk we are going to study these parameters.

A tangle T is a pair formed by a ball and collection of properly embedded disjoint arcs in B. Tangles are useful for decomposing links and have presence in applications in science. In this talk we will discuss the case where the unknot and split links have decompositions with a given tangle T as factor. As an application we obtain a complete classification for tangles up to seven crossings with such properties. 

This is joint work with António Salgueiro.