In this article, we survey some results on geometric methods to study quiver representations, and applications of these results to sheaves, equivariant sheaves and parabolic bundles.
Amrutiya, Sanjay(Cornell University Library, 2018-10)
In this note, we prove that the F-fundamental group scheme is birational invariant for smooth projective varieties. We prove that the F-fundamental group scheme is naturally a quotient of the Nori fundamental group scheme. ...
Tyagi, Jagmohan(European Mathematical Society (EMS), 2018-10)
In this note, we establish Leighton's variational lemma for fractional Laplace equations. We use the classical techniques to establish this variational lemma. We also point out several questions concerning the zeros of the ...
Recently Dixit, Kesarwani, and Moll introduced a generalization Kz,w(x) of the modified Bessel function Kz(x) and showed that it satisfies an elegant theory similar to Kz(x). In this paper, we show that while K12(x) is an ...
Berndt, Bruce C.; Dixit, Atul; Kim, Sun; Zaharescu, Alexandru(Elsevier, 2018-11)
Letrk(n) denote the number of representations of the positive integernas thesum ofksquares. We rigorously prove for the first time a Vorono ?? summation formula forrk(n), k?2,proved incorrectly by A. I. Popov and later ...
Amrutiya, Sanjay; Dubey, Umesh(Cornell University Library, 2018-08)
In this note, we give a construction of the moduli space of filtered repre- sentations of a given quiver of fixed dimension vector with the appropriate notion of stability. The construction of the moduli of filtered ...
Mehta, Ranjana; Saha, Joydip; Sengupta, Indranath(Association for Computing Machinery, 2018-08)
Bresinsky defined a class of monomial curves in A4 with the property that the minimal number of generators or the first Betti number of the defining ideal is unbounded above. We prove that the same behaviour of unboundedness ...
We consider a certain class of multiplicative functions f:N→C. Let F(s)=∑∞n=1f(n)n−s be the associated Dirichlet series and FN(s)=∑n≤Nf(n)n−s be the truncated Dirichlet series. In this setting, we obtain new Hal\'asz-type ...
Quasilocal formulations of black hole are of immense importance since they reveal the essential and minimal assumptions required for a consistent description of black hole horizon, without relying on the asymptotic boundary ...
In this paper we compute Gr�bner bases for determinantal ideals of the form , where X and Y are both matrices whose entries are indeterminates over a field K. We use the Gr�bner basis structure to determine Betti numbers ...
Dixit, Atul; Maji, Bibekananda(Cornell University Library, 2018-06)
A generalization of a beautiful q-series identity found in the unorganized portion of Ramanujan's second and third notebooks is obtained. As a consequence, we derive a new three-parameter identity which is a rich source ...
In 1914, Hardy proved that infinitely many non-trivial zeros of the Riemann zeta function lie on the critical line using the transformation formula of the Jacobi theta function. Recently the first author obtained an integral ...