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Fan Gao

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Published work

8 published item(s)

preprint2026arXiv

3DGS$^3$: Joint Super Sampling and Frame Interpolation for Real-Time Large-Scale 3DGS Rendering

3D Gaussian Splatting (3DGS) enables high-quality real-time 3D rendering but faces challenges in efficiently scaling to ultra-dense scenes and high-resolution due to computational bottlenecks that limit its use in latency-sensitive applications. Instead of optimizing the splatting pipeline itself, we propose \textbf{3DGS$^3$}, a unified post-rendering framework that jointly performs super sampling and frame interpolation through differentiable processing of low-resolution outputs to achieve both high-resolution and high-frame-rate rendering. Our \textbf{Gradient\- \-Aware Super Sampling (GASS)} module leverages the continuous differentiability of 3DGS to extract image gradients that guide a GRU-based refinement network to enable high-fidelity super sampling. Furthermore, a \textbf{Lightweight Temporal Frame Interpolation (LTFI)} module based on a compact U-Net-like backbone fuses temporal and differentiable spatial cues from consecutive frames to synthesize temporally coherent intermediate frames. Experiments on public datasets demonstrate that 3DGS$^3$ achieves superior rendering efficiency and visual quality when compared with state-of-the-art methods and remains compatible with existing 3DGS acceleration techniques. The code will be publicly released upon acceptance.

preprint2022arXiv

Genuine pro-$p$ Iwahori--Hecke algebras, Gelfand--Graev representations, and some applications

We study the Iwahori-component of the Gelfand-Graev representation of a central cover of a split linear reductive group and utilize our results for three applications. In fact, it is advantageous to begin at the pro-$p$ level. Thus to begin we study the structure of a genuine pro-$p$ Iwahori-Hecke algebra, establishing Iwahori-Matsumoto and Bernstein presentations. With this structure theory we first describe the pro-$p$ part of the Gelfand-Graev representation and then the more subtle Iwahori part. For the first application we relate the Gelfand-Graev representation to the metaplectic representation of Sahi-Stokman-Venkateswaran, which conceptually realizes the Chinta-Gunnells action from the theory of Weyl group multiple Dirichlet series. For the second we compute the Whittaker dimension of the constituents of regular unramified principal series; for the third we do the same for unitary unramified principal series.

preprint2021arXiv

Restrictions, L-parameters, and local coefficients for genuine representations

We consider the restriction and induction of representations between a covering group and its derived subgroup, both on the representation-theoretic side and the L-parameter side. In particular, restriction of a genuine principal series is analyzed in detail. We also discuss a metaplectic tensor product construction for covers of the symplectic similitudes groups, and remark on the generality of such a construction for other groups. Furthermore, working with an arbitrary irreducible constituent of a unitary unramified principal series, we prove a multiplicity formula for its restriction to the derived subgroup in terms of three associated R-groups. Later in the paper, we study an unramified L-packet on how the parametrization of elements inside such a packet varies along with different choices of hyperspecial maximal compact subgroups and their splittings. We also investigate the genericity of elements inside such an L-packet with respect to varying Whittaker datum. Pertaining to the above two problems, covers of the symplectic similitudes groups are discussed in detail in the last part of the paper.

preprint2020arXiv

On the wavefront sets associated with theta representations

We study a conjectural formula for the maximal elements in the wavefront set associated with a theta representation of a covering group over $p$-adic fields. In particular, it is shown that the formula agrees with the existing work in the literature for various families of groups. We also recapitulate the results of an analogous formula in the archimedean case, which motivated the conjectural formula in the $p$-adic setting.

preprint2014arXiv

The Gindikin-Karpelevich Formula and Constant Terms of Eisenstein Series for Brylinski-Deligne Extensions

We firstly discuss properties of the L-group for Brylinski-Deligne (BD) extensions constructed by M. Weissman. Secondly, the Gindikin-Karpelevich (GK) formula for arbitrary BD extensions is computed and expressed in terms of naturally defined elements of the group. We show that the GK formula can be interpreted as Langlands-Shahidi type L-functions associated with the ajoint action of the L-group of the Levi on certain Lie algebras. As a consequence, the constant term of Eisenstein series for BD extensions could be expressed in terms of global (partial) Langlands-Shahidi type L-functions. In the end, we use this to determine the residual spectrum of BD covers of some semisimple rank one groups.

preprint2014arXiv

The Langlands-Weissman Program for Brylinski-Deligne extensions

We describe an evolving and conjectural extension of the Langlands program for a class of nonlinear covering groups of algebraic origin studied by Brylinski-Deligne. In particular, we describe the construction of an L-group extension of such a covering group (over a split reductive group) due to Weissman, study some of its properties and discuss a variant of it. Using this L-group extension, we describe a local Langlands correspondence for covering (split) tori and unramified genuine representations, using work of Savin, McNamara, Weissman and W.W. Li. Finally, we define the notion of automorphic (partial) L-functions attached to genuine automorphic representations of the BD covering groups.