Related papers: Around Quillen's theorem A

We prove a generalization of Lopes's theorem, that is, of the converse of Brolin's theorem.

In this manuscript we review the construction of the Teichm\"{u}ller TQFT in [AK1], upgrading it to a theory dependent on an extra odd integer $N$ using results developed in [AK3]. We also describe how this theory is related with quantum…

We study Rubin's variant of the $p$-adic Birch and Swinnerton-Dyer conjecture for CM elliptic curves concerning certain special values of the Katz two-variable $p$-adic $L$-function that lie outside the range of $p$-adic interpolation.

We give a new proof of some cases of the Baum-Connes conjecture along the lines of a proof of the Farrell-Jones conjecture.

We prove some new results related to Tanaka's formula.

We prove a new cross theorem for separately holomorphic functions.

We give q-analogues of Wilson's theorem for the primes congruent 1 and 3 modulo 4 respectively. And q-analogues of two congruences due to Mordell and Chowla are also established.

I expound here in a more detailed way a proof of an important Serini's theorem, which I have already sketched in a previous Note. Two related questions are briefly discussed.

An alternative computational approach to the Collatz (3n+1) conjecture is presented that may be theoretically capable of confirming the conjecture.

We show that Isserlis' theorem follows as a corollary to the invariant tensor theorem for isotropic tensors.

We give a new proof of Lucas' Theorem in elementary number theory.

In this work, we state and prove versions of the linear and bilinear $T(b)$ theorems involving quantitative estimates, analogous to the quantitative linear $T(1)$ theorem due to Stein.

We prove an abstract linking theorem that can be used to show existence of solutions to various types of variational elliptic equations, including Schr\"{o}dinger--Poisson--Slater type equations.

New version of my 1998 article. The method of proof of the main results follows the original, but there are many simplifications/streamlining of arguments, especially Lemma 3.6 (new Lemma 3.7). Fixed small error in proof of lower bound for…

We provide a Kingman-like Theorem for arbitrary finite measures and a version of Birkhoff's Theorem for bounded observable. As an application, we show that Birkhoff's limit exists for some continuous observable, in an example of Bowen.

We prove the Aspinwall-Morrison formula by relating their calculation to Gromov-Witten theory.

We give a short, new proof of a recent result of Hanlon-Hicks-Lazarev about toric varieties. As in their work, this leads to a proof of a conjecture of Berkesch-Erman-Smith on virtual resolutions and to a resolution of the diagonal in the…

We give a new proof of a lemma by L. Shepp, that was used in connection to random coverings of a circle.

An observation on Hall-Littlewood polynomials.

We prove some symmetric $q$-congruences.