Research
Research
Research
Research
1,037+ open-access research outputs.
We develop a geometric procedure for finding the Ap\'ery set of any numerical semigroup with embedding dimension four. We use this method to find the Frobenius numbers, genera, Betti elements, minimal…
Superspecial curves are important objects in number theory and algebraic geometry, and the existence in genus $g \geq 4$ remains an open problem for all but finitely many characteristics $p > 0$. As a…
Let \(M\) be a closed connected oriented topological \(4\)-manifold. We prove that if \(F_1,\dots,F_r\subset M\) are pairwise disjoint connected locally flat topologically embedded nonorientable surfa…
For a one-parameter variation of biextension mixed Hodge structures, Brosnan and Pearlstein showed that the limit of the asymptotic height of the variation is given by a certain limit height of the ni…
This monograph studies $KK$-theory in its unbounded model. The central object is the $KK$-bordism group obtained by imposing the $KK$-bordism relation on unbounded $KK$-cycles. In the paradigm of nonc…
For a function $F$ represented as $F(x)=\sum_{n=0}^\infty{f_n (x) e^{2 \pi i \lambda_n x}},$ where each $f_n$ satisfies $\operatorname{spec}(f_n) \subset [0, 1]$ and $(\lambda_n)_{n\geq 0}\subset \mat…
While the numbers of superspecial curves of genus at most 3 are well understood, and several computational approaches have been developed to count superspecial curves of genus 4 with large automorphis…
We introduce a new class of formal group laws whose modulus square construction yields Buchstaber's family of polynomials. This class is related to, but does not coincide with, the family of formal gr…
We establish a logarithmic Bott localization formula for global holomorphic sections of $T_X(-\log D)$ on a compact complex manifold $X$ with simple normal crossings divisor $D$. The zero scheme is al…
By the family index theory, we generalize some well-known $SL(2,Z)$ modular forms to the family case and obtain some new anomaly cancellation formulas for the determinant line bundle and index gerbes,…
We study the set of isomorphism classes of polarized superspecial abelian varieties $(A,\lambda)$ of a fixed dimension over $\mathbb{F}_p$ with Frobenius endomorphism $\pi_A=\sqrt{-p}$ and $\ker \lamb…
Fix a smooth, projective, geometrically integral curve $C$ of genus $g \geq 2$ over a characteristic zero field. We prove that the Ceresa cycle $\mathrm{Cer}(\widetilde{C})$ of a very general ramified…
In this paper, we study a new class of mixed double phase problems that combine local and nonlocal operators. We consider two different models. The first model is driven by the fractional $p$-Laplacia…
The Gamma-limit of higher-order singular perturbations of the Perona-Malik functional is analyzed. The energies considered combine the critically scaled logarithmic term with a k-th order regularizati…
We study symplectic forms on hypersurface algebroids. These are a broad generalization of the $b^{k}$-Poisson structures studied extensively by Miranda, Scott, and collaborators, and their geometry is…
We define a new quantity, the Euler-normalized non-orientable genus, to connect a variety of ideas in the theory of non-orientable surfaces bounded by knots. This quantity is used to reframe non-orien…
The famous Ham-Sandwich theorem states that any $d$ point sets in $\mathbb{R}^d$ can be simultaneously bisected by a single hyperplane. The $\alpha$-Ham-Sandwich theorem gives a sufficient condition f…
We consider the refined $\mathrm{SU}(r)$ Vafa-Witten partition function of a smooth projective surface with non-zero holomorphic 2-form. This partition function has a vertical contribution, expressibl…
We extend the equality-type results of Ito--Takimura and Kindred for the non-orientable genera of alternating knots to the setting of two-component alternating links. We show that, for such links, a u…
For a knot $K$ in the 3-sphere and a simply connected closed 4-manifold $X$, we define the $X$-double slice genus of $K$, extending the notion from the case when $X$ is the 4-sphere. We show that for …
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