Когда тема конференции расширяется, появляются новые секции и доклады.

In Russian, present tense is normally used in “when / whenever” clauses to talk about general or repeated situations, even if you’d use the future in English.

• Когда тема конференции расширяется, появляются новые секции и доклады.
  = Whenever / When the topic of the conference expands, new sections and talks appear.

This sentence is describing a typical pattern, not a one‑time event. That’s why both verbs are in the present:

• расширяется – expands (in general, whenever it happens)
• появляются – appear (in general, whenever that happens)

If you wanted a single specific future event, you’d more likely use future forms, e.g.:
Когда тема конференции расширится, появятся новые секции и доклады.
= When the topic expands (on that particular occasion), new sections and talks will appear.

The sentence has two clauses:

1. Когда тема конференции расширяется – a subordinate clause introduced by когда (when).
2. появляются новые секции и доклады – the main clause.

In Russian, when a subordinate clause with когда comes before the main clause, you must separate them with a comma:

• Когда … , …

If you reverse the order, you still use a comma:

• Новые секции и доклады появляются, когда тема конференции расширяется.

So the comma is just the standard rule for complex sentences with когда.

Расширяется comes from the verb расширяться (to expand, to widen). The -ся makes the verb reflexive / intransitive, so the subject “does the action to itself” or “undergoes a change”:

• расширять (что?) – to expand (something), transitive
  
  • Организаторы расширяют программу. – The organizers expand the program.
• расширяться – to expand, intransitive
  
  • Тема конференции расширяется. – The topic of the conference expands (by itself / in general).

If you said тема конференции расширяет…, you’d be saying “The topic of the conference expands something else”, which would be wrong in this context. Here the topic is what’s changing, so расширяется is needed.

In the main clause, the subject is the phrase at the end:

• новые секции и доклады – new sections and talks

This is a compound subject (two nouns joined by и), so the verb must be plural:

• появляются (3rd person plural) – appear

Word order in Russian is flexible, so the subject can come after the verb:

• появляются новые секции и доклады
  or
• новые секции и доклады появляются

Both are correct; the chosen order slightly emphasizes the fact of appearance first, and then what exactly appears.

In Russian, when you say “the topic of X”, you typically use:

• тема + Genitive

So:

• тема конференции – the topic of the conference
  
  • тема – nominative (subject of the subordinate clause)
  • конференции – genitive singular, showing possession/association: of the conference

Other similar patterns:

• программа встречи – the program of the meeting
• цели проекта – the goals of the project

In the second clause, новые секции и доклады is the subject of the verb появляются. Subjects in Russian are normally in the nominative case.

• появляются (что?) новые секции и доклады
  
  • Actually, here что? is just a way textbooks point to “who/what is appearing”, but grammatically, новые секции и доклады is the subject, not a direct object, and it’s nominative.

So their nominative forms are:

• секции – nominative plural
• доклады – nominative plural

Imperfective aspect is used here because the sentence describes a regular / typical situation, not a single completed event.

• расширяется (from расширяться) – imperfective, “keeps expanding / expands (in general)”
• появляются (from появляться) – imperfective, “appear (habitually / whenever this happens)”

For general truths, habits, or typical cause–effect patterns, Russian uses present imperfective:

• Когда идёт дождь, люди открывают зонты. – When it rains, people open umbrellas.
• Когда тема конференции расширяется, появляются новые секции и доклады.

Perfective would point more to a one‑time result:

• Когда тема конференции расширится, появятся новые секции и доклады.
  = When the topic (eventually) expands (on that occasion), new sections and talks will appear.

You could say:

• Если тема конференции расширяется, появляются новые секции и доклады.

But there is a nuance:

• когда – more like “when / whenever”, indicating a natural, expected connection: Whenever this happens, that happens.
• если – “if”, which can sound a bit more conditional / hypothetical: If this happens, then that (might) happen.

In many real contexts both could be used, but когда sounds more like a descriptive rule about how conferences are usually organized. Если puts slightly more focus on condition rather than a standard pattern.

Новые is the nominative plural form of the adjective новый (new), and it has to agree in gender, number, and case with the nouns it modifies:

• секции – feminine plural, nominative

• доклады – masculine plural, nominative
  Together they form a plural subject, so the adjective is:

• новые – nominative plural, used for “mixed” or masculine/feminine plural groups.

Examples:

• новые книги и журналы – new books and magazines
• новые секции и доклады – new sections and talks

Yes, that’s grammatically correct:

• Когда расширяется тема конференции, появляются новые секции и доклады.

Russian allows relatively free word order, especially in simple clauses. Both:

• Когда тема конференции расширяется…
• Когда расширяется тема конференции…

are acceptable. The difference is very slight:

• тема конференции расширяется – slightly more neutral, “topic of the conference” is presented as the subject first.
• расширяется тема конференции – can sound a bit more emphatic on the action “is expanding”, then naming what is expanding.

In everyday usage, the original order (тема конференции расширяется) is a bit more standard.

Here is the main stress in each word (capital letters show the stressed syllable):

• Когда́ – kogdA
• тЕма – TYEmo (stress on те)
• конференцИи – konferYEntsii (stress on и before the last)
• расширЯется – rasshirYAYetsya (stress on я in -я-ет-)
• появлЯются – poyavLYAYutsya (stress on я in -я-ют-)
• нОвые – NOvyye (stress on но)
• сЕкции – SYEktsii (stress on се)
• доклАды – dokLADy (stress on ла)

Correct stress is important in Russian; misplacing it can sometimes change the word or make it hard to understand.

Тема конференции (the topic/theme of the conference) is a very natural, common phrase. It’s built as:

• тема
  • Genitive (конференции) – “topic of the conference”

You could rephrase depending on nuance:

• тематика конференции – the conference’s subject matter / range of topics (a bit more abstract, often broader)
• темы конференции – the conference’s topics (plural, several topics)

But in your sentence, тема конференции расширяется nicely captures the idea that the scope of what the conference is about is broadening, and it’s a perfectly standard way to say it.