During my PhD I worked on a specific topic. My thesis is published at my university website. This has been done one year ago. Today, I found that one professor (not my supervisor and not from the same institute. I do not know them personally) give a presentation on a conference about the same idea as mine. Even their future work are the same a my other PhD chapter. They expressed their idea as a novel one. Do I need to contact them? If so, what should I tell them? I do not know if they know about my thesis or not. Also, my work was built up on existing work. They even do not cite any existing works. I do not know why, but may be they do not know about these works. So I do not suggest any bad thing about them. Just would like to know what should do for this situation. I respect the professor so much. So again no bad suggestion about her or any one of her group. She may at the beginning of the research and did not update her literature review yet.
You do not "need" to contact them. The fact that your work was on a university website does not mean that anyone has seen it.
Unless there are subtler clues that they just copied your work, you should treat that work as completely independent of yours.
If you email them, do not express any doubts about their honesty, etc. This would in-any-case terminally alienate them. Rather, say that you have similar interests, as visible in your thesis, which actually obtains some similar results.
Do NOT make any remarks about how your thesis was on-line for a year, and "should have been cited", etc. Things don't really work that way.
Again, most often it's not that people are cheating, but that they have similar ideas, due to similar contexts...
Similar research lines often pop up at similar times, when the tools, mood, and fashions hit favourable winds.
Many good research ideas come, historically, in at least pairs. Unless you have a strong reason to assume that the prof had seen your work, I would not assume that. Start under the assumption of good faith in absence of any evidence to the contrary.
The easiest and most neutral way to let the prof know about your work is a friendly mail such as: Dear Prof. X, I have seen your interesting presentation/paper at Y. I have worked on this topic in my thesis (Alice 2020) [add full reference at the end of your mail], which you might be interested in - you can obtain it from http://this-is-my-thesis.
You have now told them you did the work. The reference lists the precise time. They cannot in future claim to not know about your work. And, who knows, perhaps you even have a future collaborator.
Sure you can (and should) contact the professor. But you should not accuse them of any misconduct (yet) since, based on your question, it sounds very plausible that they haven't seen your Ph.D. thesis and came up with the same ideas independently (great minds think alike).
You should contact them to make them aware of your thesis. Do not make any specific requests (e.g., that they revise the conference slides to give you credit for prior work, or that they revise any articles in their pipeline to cite your thesis).
Perhaps you may want to look up their university's Dean of Research, or someone with a similar title, and cc them. I wouldn't do it on the first e-mail, but I might cc the department chair, especially if I knew them.
Dear Prof. X,
I became aware of the presentation you gave at a conference X and was surprised by the similarities between your work and my 2019 Ph.D. thesis posted at URL. Your slide X says X, while my thesis (section X, page X) says X.
Cite all the similarities, omit none, no "etc's", and be as detailed and specific as posisble, and quote the text from your thesis, do not paraphrase or summarize.
You describe idea X as novel, but it is found my thesis (section X, page X, saying X).
I trust that you have found my thesis to be of interest. I hope we can correspond more about X.
Then you wait for their response (or the lack thereof) and proceed accordingly.