L\'evy processes with marked jumps I : Limit theorems

Consider a sequence (Z_n,Z_n^M) of bivariate L\'evy processes, such that Z_n is a spectrally positive L\'evy process with finite variation, and Z_n^M is the counting process of marks in {0,1} carried by the jumps of Z_n. The study of these processes is justified by their interpretation as contour processes of a sequence of splitting trees with mutations at birth. Indeed, this paper is the first part of a work aiming to establish an invariance principle for the genealogies of such populations enriched with their mutational histories. To this aim, we define a bivariate subordinator that we call the marked ladder height process of (Z_n,Z_n^M), as a generalization of the classical ladder height process to our L\'evy processes with marked jumps. Assuming that the sequence (Z_n) converges towards a L\'evy process Z with infinite variation, we first prove the convergence in distribution, with two possible regimes for the marks, of the marked ladder height process of (Z_n,Z_n^M). Then we prove the joint convergence in law of Z_n with its local time at the supremum and its marked ladder height process.Comment: 27 pages. Final version accepted for publication in Journal of Theoretical Probabilit

A Point Counting Algorithm for Cyclic Covers of the Projective Line

We present a Kedlaya-style point counting algorithm for cyclic covers $y^r = f(x)$ over a finite field $\mathbb{F}_{p^n}$ with $p$ not dividing $r$, and $r$ and $\deg{f}$ not necessarily coprime. This algorithm generalizes the Gaudry-G\"urel algorithm for superelliptic curves to a more general class of curves, and has essentially the same complexity. Our practical improvements include a simplified algorithm exploiting the automorphism of $\mathcal{C}$, refined bounds on the $p$-adic precision, and an alternative pseudo-basis for the Monsky-Washnitzer cohomology which leads to an integral matrix when $p \geq 2r$. Each of these improvements can also be applied to the original Gaudry-G\"urel algorithm. We include some experimental results, applying our algorithm to compute Weil polynomials of some large genus cyclic covers

Maximality and minimality in comparatives

In this paper, I investigate more closely the contribution of modal operators to the semantics of comparatives and I show that there is no need for a maximality or minimality operator. Following Kratzer s (1981, 1991) analysis of modal elements, I assume that the meaning of a modal sentence is dependent on a conversational background and an ordering source. For comparative environments, I demonstrate that the ordering source reduces a set of possible degrees to a single degree that is most (or least) wanted or expected, i.e., maximality and minimality readings of comparative constructions are an effect of the pragmatic meaning of the modal

Observation of Higgs boson decays to τ\tau lepton pairs

A search for Higgs boson decays to $\tau$ leptons is performed using events recorded in proton-proton collisions by the CMS experiment at the LHC at a center-of-mass energy of 13 TeV. The data set corresponds to an integrated luminosity of 35.9 $fb^{-1}$. An excess of events is observed over the expected background prediction with a significance of 4.9 standard deviations, to be compared to an expected significance of 4.7 standard deviations.Comment: Proceedings of poster at LHCP1

Search for exotic decays of the Higgs boson

Searches for exotic decays of the 125 GeV Higgs boson performed with data collected by the CMS experiment are presented. Three classes of searches are detailed: searches for invisible decays of the Higgs boson, searches for lepton flavor violating Higgs decays, and searches for decays to the Higgs boson to light pseudoscalars decaying to SM particle pairs. These analyses are based on data collected at center-of-mass energies of 8 and 13 TeV.Comment: Proceedings of LHCP1