Description:

Create the research areas section with an overview page showing category tabs and research cards, plus detail pages displaying Markdown content, related publications, and members.

Tasks:

• Create src/app/(public)/research/page.tsx with category tabs and research cards
• Create src/app/(public)/research/[slug]/page.tsx with Markdown rendering
• Implement ResearchCard component with title, summary, and paper count
• Add Markdown rendering with KaTeX math formula support
• Display related publications and members on detail page
• Add breadcrumb navigation for hierarchical areas
• Add lib/db/queries/research.ts for data queries
• Ensure proper SEO metadata and static generation