Central morphisms and Cuspidal automorphic Representations

Let $F$ be a global field. Let $G$ and $H$ be two connected reductive group defined over $F$ endowed with an $F$-morphism $f: H\rightarrow G$ such that the induced morphism $H_{der}\rightarrow G_{der}$ on the derived groups is a central isogeny. Our main results yield in particular the following theorem: Given any irreducible cuspidal representation $\pi$ of $G(\mathbb A_F)$ its restriction to $H(\mathbb A_F)$ contains a cuspidal representation $\sigma$ of $H(\mathbb A_F)$. Conversely, assuming moreover that $f$ is an injection, any irreducible cuspidal representation $\sigma$ of $H(\mathbb A_F)$ appears in the restriction of some cuspidal representation $\pi$ of $G(\mathbb A_F)$. This theorem has an obvious local analogue

Weak Weyl's law for congruence subgroups

Let $G$ be a connected and simply connected semisimple algebraic group over $\Bbb Q$ and let $\Gamma\subset G(\Bbb Q)$ be an arithmetic subgroup. Let $K_\infty\subset G(\Bbb R)$ be a maximal compact subgroup and let $d$ be the dimension of the symmetric space $G({\mathbb R})/K_\infty$. Let $\sigma$ be an irreducible unitary representation of $K_\infty$. We prove that for every $\Gamma$ there exists a normal subgroup $\Gamma_1\subset \Gamma$ of finite index such that the quotient of the counting function of the $\Gamma_1$-cuspidal spectrum of weight $\sigma$ and $T^{d/2}$ has a positive lower bound as $T\to\infty$.Comment: 13 page

Resuscitation-promoting factors possess a lysozyme-like domain

The novel bacterial cytokine family – resuscitation-promoting factors (Rpfs) – share a conserved domain of uncharacterized function. Predicting the structure of this domain suggests that Rpfs possess a lysozyme-like domain. The model highlights the good conservation of residues involved in catalysis and substrate binding. A lysozyme-like function makes sense for this domain in the light of experimental characterization of the biological function of Rpfs

La formule des traces tordue d'apr\`es le Friday Morning Seminar

Based on the notes of the Friday Morning Seminar held in the IAS in 1983-1984 (often quoted as Morning Seminar on the Trace Formula), we give a complete and detailed proof of the Twisted Trace Formula in its primitive form i.e. its noninvariant form. ----- Notre ambition est de donner, en nous basant pour l'essentiel sur les notes du Friday Morning Seminar de l'IAS en 1983-1984 (souvent cit\'e sous le nom de Morning Seminar on the Trace Formula), une version compl\`ete de la preuve de la formule des traces dans le cas tordu dans sa version primitive c'est-\`a-dire non invariante

Distinguished non-Archimedean representations

For a symmetric space (G,H), one is interested in understanding the vector space of H-invariant linear forms on a representation \pi of G. In particular an important question is whether or not the dimension of this space is bounded by one. We cover the known results for the pair (G=R_{E/F}GL(n),H=GL(n)), and then discuss the corresponding SL(n) case. In this paper, we show that (G=R_{E/F}SL(n),H=SL(n)) is a Gelfand pair when n is odd. When $n$ is even, the space of H-invariant forms on \pi can have dimension more than one even when \pi is supercuspidal. The latter work is joint with Dipendra Prasad

Opioid prescribing practices and training needs of Québec family physicians for chronic noncancer pain

Abstract : AIM: To examine medical practices and training needs of Québec family physicians with respect to pain management and opioid prescription for chronic noncancer pain (CNCP). METHODOLOGY: An online survey was carried out in 2016. RESULTS: Of 636 respondents (43.0% men; 54.3% ≥ 50 years old), 15.2% and 70.9% felt very or somewhat confident that they could properly prescribe opioids for CNCP. Concerns related to abuse (72.5% strongly/somewhat agree), dependence (73.2%), and lack of support (75.4%) were the main barriers reported. Only 19.7% always/often screened their patients for risks of abuse and dependence using a screening tool. About two-thirds of participants (65.7%) had recently (last five years) taken part in continuing education programs on opioid use for CNCP and 73.4% on CNCP management. Patient evaluation and differential diagnoses of chronic pain syndromes were rated as a top priority for further training. CONCLUSIONS: This study provides insights into Québec family physicians' concerns, practices, and needs with respect to the management of CNCP. Physicians' difficulties around the application of strategies to mitigate the problem of opioid abuse and addiction are worrying. The need to better train physicians in the field of pain and addiction cannot be emphasized enough

Dirac cohomology, elliptic representations and endoscopy

The first part (Sections 1-6) of this paper is a survey of some of the recent developments in the theory of Dirac cohomology, especially the relationship of Dirac cohomology with (g,K)-cohomology and nilpotent Lie algebra cohomology; the second part (Sections 7-12) is devoted to understanding the unitary elliptic representations and endoscopic transfer by using the techniques in Dirac cohomology. A few problems and conjectures are proposed for further investigations.Comment: This paper will appear in `Representations of Reductive Groups, in Honor of 60th Birthday of David Vogan', edited by M. Nervins and P. Trapa, published by Springe

Antimicrobial treatment improves mycobacterial survival in nonpermissive growth conditions

Antimicrobials targeting cell wall biosynthesis are generally considered inactive against nonreplicating bacteria. Paradoxically, we found that under nonpermissive growth conditions, exposure of Mycobacterium bovis BCG bacilli to such antimicrobials enhanced their survival. We identified a transcriptional regulator, RaaS (for regulator of antimicrobial-assisted survival), encoded by bcg1279 (rv1219c) as being responsible for the observed phenomenon. Induction of this transcriptional regulator resulted in reduced expression of specific ATP-dependent efflux pumps and promoted long-term survival of mycobacteria, while its deletion accelerated bacterial death under nonpermissive growth conditions in vitro and during macrophage or mouse infection. These findings have implications for the design of antimicrobial drug combination therapies for persistent infectious diseases, such as tuberculosis

Mass equidistribution of Hilbert modular eigenforms

Let F be a totally real number field, and let f traverse a sequence of non-dihedral holomorphic eigencuspforms on GL(2)/F of weight (k_1,...,k_n), trivial central character and full level. We show that the mass of f equidistributes on the Hilbert modular variety as max(k_1,...,k_n) tends to infinity. Our result answers affirmatively a natural analogue of a conjecture of Rudnick and Sarnak (1994). Our proof generalizes the argument of Holowinsky-Soundararajan (2008) who established the case F = Q. The essential difficulty in doing so is to adapt Holowinsky's bounds for the Weyl periods of the equidistribution problem in terms of manageable shifted convolution sums of Fourier coefficients to the case of a number field with nontrivial unit group.Comment: 40 pages; typos corrected, nearly accepted for