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Xinchun Ma

Publications and source records attributed to Xinchun Ma.

3 recordsLinked to original sources

The recent anomalously weak polar field does not imply a weak field at solar cycle 25 minimum

The ongoing solar cycle 25 has progressed past its peak of sunspot numbers, being stronger than the previous cycle 24. However, the present polar field is rather weak compared to previous cycles at the same evolution phase, particularly in the northern hemisphere, where it has been decreasing since mid-2025 till present. A prominent poleward surge is observed to cause the decrease of the polar field. This raises concerns to the polar field at cycle 25 minimum, which is the precursor to the strength of the next cycle 26. To predict whether the polar field at cycle 25 minimum will be weak as expected, we use observation-based statistical properties to predict the active region emergence during the latter half of cycle 25, and use a surface flux transport model to simulate the evolution of the large-scale magnetic field. We predict the polar field at cycle 25 minimum to be $-5.62\pm1.61$G in the north and $5.51\pm1.48$G in the south, both stronger than those at cycle 24 minimum. This is because the poleward surge causing the temporal decrease of the polar field originates from a group of active regions that produces net increase to the polar field, instead of active regions with non-Joy's tilt. Our results suggest the weak polar field at present is unlikely to cause a weak minium and an exceptionally weak cycle 26, clarifying that the short term evolution should not be simply correlated to the long term properties of the solar large-scale field.

astro-ph.SR

From Cherednik algebras to knot homology via cuspidal D-modules

We show that the triply-graded Khovanov-Rozansky homology of the $(m,n)$ torus knot can be recovered from the finite-dimensional representation $\mathrm{L}_{m/n}$ of the rational Cherednik algebra at slope $m/n$, endowed with the Hodge filtration coming from the cuspidal character D-module. Our approach involves expressing the associated graded of the cuspidal character D-module in terms of a dg module closely related to the action of the shuffle algebra on the equivariant K-theory of the Hilbert scheme of points on the plane, thereby proving the rational master conjecture. As a corollary, we identify the Hodge filtration with the inductive and algebraic filtrations on $\mathrm{L}_{m/n}$.

math.RT

Rational Cherednik Algebras and Torus Knot Invariants

The HOMFLY polynomial of the $(m,n)$ torus knot $T_{m,n}$ can be extracted from the doubly graded character of the finite-dimensional representation $\mathrm{L}_{\frac{m}{n}}$ of the type $A_{n-1}$ rational Cherednik algebra as observed by Gorsky, Oblomkov, Rasmussen and Shende. It is furthermore conjectured that one can obtain the triply-graded Khovanov-Rozansky homology of $T_{m,n}$ by considering a certain filtration on $\mathrm{L}_{\frac{m}{n}}$. In this paper, we show that two of the proposed candidates, the algebraic filtration and the inductive filtration, are equal.

math.RT