Related papers: Around Quillen's theorem A
We prove an extension of the Quillen Theorem Bn for homotopy fibres to a similar result for homotopy pullbacks and use this to obtain sufficient conditions on a pullback diagram of categories to guarantee that it be a homotopy pullback.
We review our construction of the Teichm\"uller TQFT. We recall our volume conjecture for this TQFT and the examples for which this conjecture has been established. We end the paper with a brief review of our new formulation of the…
We survey the classical results of the Dirichlet Approximation Theorem.
We give a new proof of the butterfly theorem, based on the use of several expressions involving the scale factor between the two wings.
We generalise the work of Sarnak-Tsimerman to twisted sums of Kloosterman sums and thus give evidence towards the twisted Linnik-Selberg Conjecture.
We present some further results on Liouville type theorems for some conformally invariant fully nonlinear equations.
We extract the Abhyankar-Moh-Suzuki theorem from the Lin-Zaidenberg theorem.
We give "hybrid" proofs of the $q$-binomial theorem and other identities. The proofs are "hybrid" in the sense that we use partition arguments to prove a restricted version of the theorem, and then use analytic methods (in the form of the…
In this note we provide a new proof of the Tikhonov theorem for the infinite time interval and discuss some of its applications.
We revisit the proof of solidity of KM (Kelley-Morse theory of classes), as presented in the 2016 paper "Variations on a Visserian theme", so as to indicate the role of the scheme of class collection in the proof.
We give a short and relatively elementary proof of the Hilton-Milner Theorem.
We give a counting based proof of the Graham Pollak Theorem
In this note, we prove a theorem covering Chartrand, Kaigars, and Lick's theorem in [Proc. Amer. Math. Soc. 32 (1972), 63-68]. As an application, we give a simpler proof of theorem proved by Mader [J. Graph Theory 65 (2010), 61-69. (Theorem…
Here we give a short survey of our new results. References to the complete proofs can be found in the text of this article and in the litterature.
In this paper, we prove a theorem which adds a new member to the famous G\"oellnitz-Gordon identities. We construct a "new system of recurrence formulas" in order to prove it.
The article summarizes some developments about a singular versions of the Sturm Comparison and Separation theorems where the coefficients or the interval of definition may be unbounded.
We prove stronger variants of a multiplier theorem of Kislyakov. The key ingredients are based on ideas of Kislaykov and the Kahane-Salem-Zygmund inequality. As a by-product we show various multiplier theorems for spaces of trigonometric…
We prove an endpoint version of the Stein-Tomas restriction theorem, for a general class of measures, and with a strengthened Lorentz space estimate. A similar improvement is obtained for Stein's estimate on oscillatory integrals of…
We settle in the affirmative the Graham-Sloane conjecture.
We present in this work a new and simple proof of the false centre theorem.