Dynamic graph prompting freezes a pre-trained temporal backbone and adapts it to label-scarce downstream tasks using lightweight prompts. However, existing methods operate within a single, fixed embedding space. In this work, we reveal that temporal shifts in local clustering and degree heterogeneity actively reorganize the edge curvature spectrum---indicating that the optimal representation geometry dynamically evolves with local topology over time. We formalize this unaddressed mismatch as geometry under-adaptation. To overcome this limitation, we propose CurvPrompt, a topology-routed geometry prompting framework for dynamic graphs. Instead of relying on a single space, CurvPrompt maintains a bank of curvature-diverse Riemannian experts, each paired with a learnable prompt. A topology-aware gate dynamically routes each node--time instance to a sparse subset of experts, constructing a personalized mixed-curvature representation. To ensure parameter efficiency and training stability under extreme label scarcity, CurvPrompt employs soft routing during pre-training to build a continuous topology--geometry mapping, and transitions to hard Top-K routing with uniform weights during downstream adaptation. Extensive experiments across four benchmark datasets show that CurvPrompt significantly advances few-shot link prediction while delivering strong, consistent performance on node classification tasks, validating the necessity of geometry-adaptive prompting.
With the rapid advancement of large language models (LLMs), classic graph learning tasks have greatly benefited from LLMs, including improved encoding of textual features, more efficient construction of graphs from text, and enhanced reasoning over knowledge graphs. In this paper, we ask a complementary question: How can graphs help LLMs? We address this question from three perspectives: 1) graphs provide an up-to-date knowledge source that helps reduce LLM hallucinations, 2) graph-based prompting techniques-such as Chain-of-Thought (CoT), Tree-of-Thought (ToT), and Graph-of-Thought (GoT)-enhance LLM reasoning capabilities, and 3) integrating graphs into LLMs improves their understanding of structured data, expanding their applicability to domains such as e-commerce, code, and relational databases (RDBs). We further outlook some future directions including designing sparse LLM architectures based on graphs and brain-inspired memory systems.