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Yizhen Zhao

Publications and source records attributed to Yizhen Zhao.

8 recordsLinked to original sources
arXiv2026

Movable Antenna Arrays with Imperfect Channel State Information in Rich Scattering Environments

The growing demand for high spectral efficiency in 6G and beyond has driven research into adaptive antenna architectures capable of exploiting the spatial structure of multipath propagation channels. Conventional base station arrays are deployed with fixed element positions and cannot adapt to the instantaneous spatial structure of the propagation channel. In contrast, movable antenna (MA) systems enable dynamic reconfiguration of antenna positions, allowing the array geometry to track the channel characteristics of the current user set. While prior MA studies have demonstrated significant gains under perfect or statistical channel state information (CSI) assumptions, the interplay between imperfect instantaneous CSI, antenna placement optimization, and precoder design has received limited attention. This paper addresses this gap by proposing a practical end-to-end framework encompassing uplink pilot transmission, MMSE channel estimation under a clustered multipath model, and downlink ZF precoding designed from estimated CSI. Antenna positions are optimized via particle swarm optimization under two objectives: sum-rate maximization and max-min fairness. Simulation results show that MA gains are most pronounced under sparse, near-LoS propagation and diminish as channel richness increases. Furthermore, we reveal a fundamental coupling between array geometry and precoder design: a fairness-oriented antenna geometry encodes spatial fairness information that is only recoverable when evaluated with a compatible power allocation strategy. A mismatched precoder can completely mask the geometric advantage, leading to misleading conclusions about the robustness of antenna placement to the choice of optimization objective. These findings provide practically relevant guidance for the design and evaluation of movable antenna systems under realistic operating conditions.

eess.SP↗
arXiv2026

The point insertion technique and open $r$-spin theories I: moduli and orientation

The papers [3,1,4,10] constructed an intersection theory on the moduli space of $r$-spin disks, and proved it satisfies mirror symmetry and relations with integrable hierarchies. That theory considered only disks with a single boundary state. In this work, we initiate the study of more general $r$-spin surfaces. We define graded $r$-spin surfaces with multiple internal and boundary states, together with their moduli spaces. In genus zero, the disk case, we define the associated open Witten bundle and prove that it is canonically oriented relative to the moduli space. We also describe a gluing construction for moduli spaces along boundaries, show that it lifts to the Witten bundle and relative cotangent line bundles, and that the result remains canonically relatively oriented. We then study the genus-one cylinder case. Here foundational difficulties arise because the Witten "bundle" is no longer an orbifold vector bundle. We resolve this by removing strata with incorrect fibre dimension, obtaining an orbibundle on the complement. The gluing method extends to genus one, and we prove that the Witten bundle again admits a canonical relative orientation. In the sequel [20], we construct a family of $\lfloor r/2\rfloor$ intersection theories in genus-zero indexed by $\mathfrak h\in\{0,\ldots,\lfloor r/2\rfloor-1\}$, where the $\mathfrak h$-th theory has $\mathfrak h+1$ boundary states, and compute their intersection numbers. The case $\mathfrak h=0$ recovers the theory of [3,1]. In the sequel [21], restricting to the $\mathfrak h=0$ case, we construct an intersection theory on the moduli space of $r$-spin cylinders and show that its potential yields, after a change of variables, the genus-one part of the $r$th Gelfand-Dikii wave function, proving the genus-one case of the main conjecture of [4].

math.AG↗
arXiv2026

Open $r$-spin theory in genus one, and the Gelfand-Dikii wave function

We construct the $g=1$ sector of the open $r$-spin theory, that is, an open $r$-spin theory on the moduli space of cylinders. This is the second construction of a $g>0$ open intersection theory, which includes descendents (the first is the all genus construction of the intersection theory on moduli of open Riemann surfaces with boundaries [23,30], whose $g=1$ case equals to the $r=2$ case of our construction). Unlike the construction of [30], in order to construct the $r$-spin cylinder theory we had to overcome the foundational problem of dimension jump loci, which in analogous closed theories has been treated using virtual fundamental class techniques, that are currently absent in the open setting. For this reason our construction is much more involved, and relies on the point insertion technique developed in [31,32]. We prove that the open $g=1$ potential equals, after a coordinate change, to the $g=1$ part of the Gelfand-Dikii wave function, thus confirming a conjecture of [7]. We also prove that our $g=1$ intersection numbers satisfy a $g=1$ recursion, also predicted in [7,15]. This recursion is the $g=1$ analogue of Solomon's famous $g=0$ Open WDVV equation [25], with descendents, and is also the universal $g=1$ recursion for $F$-Cohomological field theories [1]. Again, this is first geometric construction which is not the $g=1$ sector of [23,30], proven to satisfy this universal recursion.

math.AG↗
arXiv2024

Brauer $p$-dimension and Kato's Swan Conductor

We use Kato's Swan conductor to study the Brauer $p$-dimension of fields of characteristic $p>0$. We mainly investigate two types of fields: henselian discretely valued fields and semi-global fields. While investigating the Brauer $p$-dimension of semi-global fields, we use a Gersten-type sequence to analyse the ramification behavior of a Brauer class in a $2$-dimensional regular local ring. Using this result, we give a partial result on the Brauer $p$-dimension of function fields of algebraic curves over $\bar{k}((t))$ with good reduction.

math.AG↗
arXiv2023

The point insertion technique and open $r$-spin theories II: intersection theories in genus-zero

The papers [5, 3, 6, 19, 20] initiated the study of open $r$-spin and open FJRW intersection theories, and related them to integrable hierarchies and mirror symmetry. This paper uses a new technique, the point insertion technique, developed in the prequel [36], to define new open r-spin and open FJRW intersection theories. These new constructions provide potential candidates for theories whose existence was conjectured before: $\bullet$ K. Hori [23] predicted the existence of open $r$-spin theory with $\lfloor\frac{r}{2}\rfloor$ types of boundary states. The one constructed in [5, 3] has only one type of boundary state. In this work we describe $\lfloor\frac{r}{2}\rfloor$ open $r$-spin theories, labelled by $\mathfrak{h}\in\{0,\ldots,\lfloor\frac{r}{2}\rfloor-1\},$ where the $\mathfrak{h}$-th one has $\mathfrak{h}+1$ boundary states. We prove that the $\mathfrak{h}=0$ theory is equivalent to the [5, 3] construction, and calculate all intersection numbers for all these theories. $\bullet$ In [1] K. Aleshkin and C.C.M. Liu conjectured the existence of a quintic Fermat FJRW theory. We construct such an FJRW theory, and provide evidence that this is the conjectured theory. We also explain how the point insertion technique can be used for constructing other open enumerative theories, satisfying the same universal recursions.

math.AG↗
arXiv2019

Landau-Ginzburg/Calabi-Yau correspondence for a complete intersection via matrix factorizations

By generalizing the Landau-Ginzburg/Calabi-Yau correspondence for hypersurfaces, we can relate a Calabi-Yau complete intersection to a hybrid Landau-Ginzburg model: a family of isolated singularities fibered over a projective line. In recent years Fan, Jarvis, and Ruan have defined quantum invariants for singularities of this type, and Clader and Clader-Ross have provided a equivalence between these invariants and Gromov-Witten invariants of complete intersections. For Calabi-Yau complete intersections of two cubics, we show that this equivalence is directly related - via Chen character - to the equivalences between the derived category of coherent sheaves and that of matrix factorizations of the singularities. This generalizes Chiodo-Iritani-Ruan's theorem matching Orlov's equivalences and quantum LG/CY correspondence for hypersurfaces.

math.AG↗
arXiv2019

Infinity harmonic functions over exterior domains

In this paper, we study the infinity harmonic functions with linear growth rate at infinity defined on exterior domains. We show that such functions must be asymptotic to planes or cones at infinity. We also establish the solvability of Dirichlet problems for exterior domains.

math.AP↗