Rutgers University--Department of Mathematics
Graduate Student Job Talk Seminar: Guidelines for Preparing your Talk

• You are doing interesting work in mathematics.
• You will be a good mathematical colleague: you have a broader understanding of mathematics than outside your little area.
• You will be a good instructor: you demonstrate an awareness of your audience, you are able to communicate in an engaging manner, and the level of your talk is appropriate to the audience.

Here are some considerations in planning your talk.

• Know what kind of audience you will have. Academic job talks rarely consist of specialists in your field. In a research oriented department, the audience will typically consist of faculty and graduate students in a variety of areas, most of whom will not be familiar with your thesis area, and many of whom will not even know the basics in the subject. At a four year college, the audience will consist of faculty and undergraduate students, who will typically not know the contents of our first year graduate courses. You should decide which of these two audiences you are aiming at, and plan your talk accordingly.
• Here is an article entitled How to Get a Teaching Job at a Liberal-Arts College
• When going on an actual interview, it may be a good idea to ask your hosts what level talk they would like to hear. You can discuss with them what you plan to talk about and check with them about what background you should assume.
• It is often a good idea to remind the audience briefly about key definitions, even if you think they should know them.
• If possible, your talk should tell a story. Often the genesis of mathematical research is a particular mathematical phenomenon that needs explanation or suggests a general principle. Typically there are interesting examples that display the phenomenon. These examples lead to questions, and the questions lead to research.
• For many interesting mathematical phenomena, there are often natural conjectures that turn out to be false. The examples showing that the natural conjecture is false leads to more subtle conjectures which (hopefully) turn out to be true. If this is the case for your research, then describing the search for the right conjecture and the examples that motivated it can make for an interesting story line.
• Similarly, for many interesting theorems, it is possible to understand the proofs in the following way. There is an obvious way to try to prove the theorem, but the obvious way doesn't work because of certain obstacles. The complications in the proof arise because of the need to overcome these obstacles. In a talk, it is usually very hard to convey the complex deatils of your proof, but it is possible to convey what the obstacles are and to indicate the general idea for overcoming them.
• A typical talk may spend more than half the time setting the stage of your results. In some cases, you may spend less than 1/3 of the time actually discussing your results.
• Generality is important in mathematics, but not in mathematical talks. You should focus on the least general form of your results that are still interesting. You should then indicate briefly the ways in which these results can be generalized.
• Avoid technical definitions. Few listeners can absorb such definitions or remember them during a talk. Instead you want to convey the qualitative meaning of the definition. If there are unavoidable technical conditions, then describe what the conditions are for, why they are important, or why they are natural. It's ok in theorem statements to abbreviate the technical conditions as "under suitable technical conditions". It is important to convey whether the technical conditions really seem to be essential to understanding the phenomena under study, or seem to be needed for your proofs, but may not be needed.
• For a talk at a four-year college, the quality of your presentation and, especially, your giving a talk you may not even get to the statement of your thesis problem. In many cases, the best you can hope for is to convey a flavor for the field that you're working in.