1.  These talks (and the written reports for them) should be directed at an your peer audience of master’s level graduate students in mathematics. The level of the material you are presenting should be what might be found in a special topics upper level undergraduate or graduate course. The style of presentation should be instructional (what you would expect to see in a lecture). The scope of each talk should be an important theorem in the subject with necessary definitions and examples. The written report should be lively, but essentially textbook in style.
2. In preparing your presentation, remember the things that have made lectures in your mathematics courses accessible and include them. (Also remember the things that have made them difficult, boring or otherwise unattractive, and exclude them.) This is a tall order.
3. Since you are not teaching an entire course, just one short lecture's worth, choose your talk topic carefully for interest value and your ability to present it in context of (a) your seminar topic and (b) the mathematical subject of which it is a part.
4. Your talks should be a subset of a short independent study you undertake of the mathematical subject(s) needed to better investigate and understand technical aspects of your seminar topic. The study should comprise several chapters of appropriate text materials that you will read, discuss and use for exercises to gain some mastery of the subject.

Don't forget your announcement should be posted two days before you speak, and set aside time to rehearse your talk.