On geometric Langlands theory and stacks

R.Langlands conjectured the existence of a bridge between two parts of number theory. This correspondence, called 'Langlands conjecture' was proved by L. Lafforgue who obtained a Fields medal for his work. G. Laumon gave a geometric translation of a part of the theorem, called 'geometric Langlands correspondence'. The latter was proved by E. Frenkel, D. Gaitsgory and K. Vilonen for the case of finite fields and the group GL-n- of invertible matrices. A statement and a proof of the complex case should be obtained by mimicking the proof for finite fields. However, it does not appear anywhere in the literature. In this thesis, we chose a different approach. Our first aim was to make a correct statement and proof for simple cases. More precisely, we deal with cases where the two difficult objects "stacks" and "perverse sheaves", which appear in the original statement, are not involved. We also state and prove the correspondence in a new context, namely the case of singular curves. A large part of the thesis is devoted to making the objects appearing in the geometric statement, such as stacks, mor explicit. These objects are categories with glueing properties. They are now widely used but references are rare and often difficult to read. We thus give numerous examples of stacks and treat in detail explicit ones. We chose for instance to work on the case of trangles in order to get a better understanding of the interest of stacks. Another important example is the stack Bun-n-x of vector bundles or rank -n- over curve x. This is an interesting stack which plays an important role in the geometric Langlands correspondance

Genetic characterization of congenital tufting enteropathy: epcam associated phenotype and involvement of SPINT2 in the syndromic form.

International audience: Congenital tufting enteropathy (CTE) is a rare and severe enteropathy recently ascribed to mutations in the epcam gene. Here we establish SPINT2, previously ascribed to congenital sodium diarrhea, as a second gene associated with CTE and report molecular and immunohistochemistry data in 57 CTE patients. Inclusion criteria were early onset diarrhea and intestinal insufficiency with the typical histological CTE abnormalities. The clinical phenotype was registered, the entire coding regions of epcam and SPINT2 sequenced, and immunostaining of EpCAM and SPINT2 performed on intestinal biopsies. An epcam mutation was involved in 41 patients (73 %) who mainly displayed isolated digestive symptoms. Mutations severely affected gene expression since the EpCAM signal on intestinal tissues was either undetectable or low and irregular. Twelve other patients (21 %) carried mutations in SPINT2, and were phenotypically characterized by systematic association with keratitis (p G (abnormal splicing) was significantly associated with a better outcome (p = 0.032) with milder PN dependency to weaning in some cases. Finally, four patients (7 %) with isolated digestive symptoms had no detectable epcam or SPINT2 mutation. Two candidate genes, Elf3 and Claudin7, were excluded from this population. Our study allows us to separate CTE patients into at least three genetic classes, each with specific phenotypes. The genetics approach raises the question of the distinction between two congenital enteropathies. Our findings should help improve the diagnosis of CTE, guide toward strategies of long-term PN management, and limit indications for intestinal transplantation to life-threatening PN complications

Rare predicted loss-of-function variants of type I IFN immunity genes are associated with life-threatening COVID-19

BackgroundWe previously reported that impaired type I IFN activity, due to inborn errors of TLR3- and TLR7-dependent type I interferon (IFN) immunity or to autoantibodies against type I IFN, account for 15-20% of cases of life-threatening COVID-19 in unvaccinated patients. Therefore, the determinants of life-threatening COVID-19 remain to be identified in similar to 80% of cases.MethodsWe report here a genome-wide rare variant burden association analysis in 3269 unvaccinated patients with life-threatening COVID-19, and 1373 unvaccinated SARS-CoV-2-infected individuals without pneumonia. Among the 928 patients tested for autoantibodies against type I IFN, a quarter (234) were positive and were excluded.ResultsNo gene reached genome-wide significance. Under a recessive model, the most significant gene with at-risk variants was TLR7, with an OR of 27.68 (95%CI 1.5-528.7, P=1.1x10(-4)) for biochemically loss-of-function (bLOF) variants. We replicated the enrichment in rare predicted LOF (pLOF) variants at 13 influenza susceptibility loci involved in TLR3-dependent type I IFN immunity (OR=3.70[95%CI 1.3-8.2], P=2.1x10(-4)). This enrichment was further strengthened by (1) adding the recently reported TYK2 and TLR7 COVID-19 loci, particularly under a recessive model (OR=19.65[95%CI 2.1-2635.4], P=3.4x10(-3)), and (2) considering as pLOF branchpoint variants with potentially strong impacts on splicing among the 15 loci (OR=4.40[9%CI 2.3-8.4], P=7.7x10(-8)). Finally, the patients with pLOF/bLOF variants at these 15 loci were significantly younger (mean age [SD]=43.3 [20.3] years) than the other patients (56.0 [17.3] years; P=1.68x10(-5)).ConclusionsRare variants of TLR3- and TLR7-dependent type I IFN immunity genes can underlie life-threatening COVID-19, particularly with recessive inheritance, in patients under 60 years old