Luckily for you, there is an online seminar where you can get a panorama of what is currently going on in the area of mathematical QFT. It is the webinar <a href="https://www.mis.mpg.de/applan/seminars/aqfp.html">"Analysis, Quantum Fields, and Probability"</a>. To watch live upcoming seminars you will have to join their mailing list, so they can send you the relevant Zoom links. You can also watch the previous talks on their <a href="https://www.youtube.com/channel/UC4b4DnOK-jrttpYss9zsddw">Youtube channel</a>.

QFT is a broad subject with many aspects that give rise to specific problems for mathematicians to work on. If you are interested in the renormalization group aspect, you might want to look at my previous answers:

https://mathoverflow.net/questions/397143/reading-list-recommendation-for-a-hep-ph-student-to-start-studying-qft-at-a-more/397301#397301

https://mathoverflow.net/questions/337670/formal-mathematical-definition-of-renormalization-group-flow/337692#337692