# Upcoming Events

We revisit the theorem of Hironaka that one can resolve the singularities of a singular, reduced closed subscheme X of a smooth scheme Y over a field of characteristic zero, such that the singular locus of X is transformed to a simple normal crossings divisor. We propose a computable yet…

The absolute trace of a totally positive algebraic integer is defined to be the average of its conjugate elements in $\mathbb{R}$. We show that there are infinitely many totally positive algebraic integers of absolute trace at most $1.81$ but only finitely many of absolute trace at most $1.80$.…

Introduced by Mallows in statistical ranking theory, Mallows permutation model is a class of non-uniform probability measures on the symmetric group that are biased towards the identity. The general model depends on a distance metric that can be chosen from a host of metrics on permutations. In…

Khovanov homology is orginally defined for links in *S*^3, and it was extended for links in I-bundles over surface by Asaeda, Przytycki and Sikora. In this talk, we will exhibit some generalization of their construction for null homologous links in ℝℙ3. On the…

Coleman and Mazur constructed the first eigencurve, a $p$-adic analytic space which parametrizes $p$-adic overconvergent modular eigenforms of nonzero eigenvalue under the Hecke operator $U_p$. Since then, many authors have constructed analogous higher-dimensional eigenvarieties for various…

Several generalizations of Johnstone's spiked model have been considered in recent years, allowing spikes to diverge, which in turn can force the empirical eigenstructure to be consistent with the ground truth. For the simplest such extension, a covariance matrix whose eigenvalues are all one…