Related papers: A remark to "A note on the Fundamental Group of a …
We define the notion of fundamental group of an algebraic stack, prove a comparison theorem between the fundamental group of a stack over the complex numbers and that of the associated analytic orbifold, show that this notion coincides with…
We consider the realization of fundamental groups of $AF$-algebras in a certain class. We find the fundametal groups of $AF$-algebras with finite dimensional trace space which is not realizable as a fundamental group of von Neumann…
In this note, we study a certain class of trigonometric series which is important in many problems. An unproved statement in Zygmund's book [5] will be proved and generalized. Further discussions based on this problem will also be made…
Dual canonical bases are expected to satisfy a certain (double) triangularity property by Leclerc's conjecture. We propose an analogous conjecture for common triangular bases of quantum cluster algebras. We show that a weaker form of the…
In this note we rectify the proof of Theorem 3.11 in [arXiv:2403.02876]. We also present a set of examples at the end discussing various cases.
We study (support) $\tau$-tilting modules over the trivial extensions of finite dimensional algebras. More precisely, we construct two classes of (support)$\tau$-tilting modules in terms of the adjoint functors which extend and generalize…
We give a counterexample of Morrison's cone conjecture for a strict Calabi-Yau threefold.
We study the integral Hodge conjecture in complex codimension $2$ and $3$ for approximations to the classifying space of groups of type A. In degree two, we prove a conjecture of Ben Antieau, extending his two counterexamples to a general…
We correct the proof of Theorem 4.1 from [C. R. Math. Acad. Sci. Soc. R. Can. \textbf{44} (2022), no. 4, 88--112].
Lecture notes on Finsler Geometry
We investigate the group gradings on the algebra of upper triangular matrices over an arbitrary field, viewed as a Lie algebra. These results were obtained a few years early by the same authors. We provide streamlined proofs, and present a…
This is a survey article on the theory of finite complex reflection groups. No proofs are given but numerous references are included.
I prove the group theory analogues of some Lie and Leibniz algebra results on F-hypercentral and F-hypereccentric modules.
The arithmetic fundamental lemma conjecture of the third author connects the derivative of an orbital integral on a symmetric space with an intersection number on a formal moduli space of $p$-divisible groups of Picard type. It arises in…
Some notes and observations on analytic functions defined on an annulus
The article provides a counterexample to a conjecture by Blocki-Zwonek.
This note provides a formula for the character of the Lie algebra of the fundamental group of a surface, viewed as a module over the symplectic group.
Recently Breuillard and Tointon showed that one reasonable formulation of the polynomial Freiman-Ruzsa conjecture fails for nonabelian groups. We improve and simplify their construction.
In this short note we introduce a new metric on certain finite groups. It leads to a class of groups for which the element orders satisfy an interesting inequality. This extends the class CP_2 studied in our previous paper [16].
In this paper, we introduce the notion of weak core and central weak core inverse in a {\it proper $*$-ring}. We further elaborate on these two classes by producing a few representations and characterizations of the weak core and central…