Deviation after completion of the doctorate

[S.G. Janssens]

At the moment I'm in the final stages of my doctorate in mathematics. (My background is a BS in physics and an MS in mathematics.) My focus and interest have been in applied functional analysis in general and various kinds of abstract and concrete delay equations in particular. These are evolution equations which generate infinite dimensional (semi)dynamical systems. Like all doctorate candidates, I have acquired a certain amount of specialised knowledge and published certain results.

I would very much enjoy continuing doing applied functional analysis and teaching in an academic environment, but sometimes I find the focus on delay equations rather narrow. Recently I have been drawn to the fields of control theory and continuum mechanics, and I would be quite curious to learn more about the functional analytic aspects as well as the physical foundation of at least one of these two. Although these fields may be considered more or less tangent to my own field, on the level of specialisation they are quite different.

My question is: Have any of you, in a similar situation, pursued such a kind of new interest in an academic setting (e.g. as a post-doc) after the completion of your doctorate? How did that work out? Would you advise me to give into my curiosity? Or is current research too specialised for such excursions and am I just wasting my time and past efforts? I thank you for any sensible comments.

 

[micromass]

I think it's normal that during a PhD you will specialize a lot. After your PhD, it is more common to go broader and to perhaps find a new (but somehow related) area of research. Just continuing doing delay equations would probably not be the best for you, you'll need to branch out somehow. It seems you want exactly that, so that's very good.

 

[S.G. Janssens]

Thank you, micromass. I was hoping for some responses from others as well, but I am already happy with your positive reaction.

 

[ZapperZ]

At the moment I'm in the final stages of my doctorate in mathematics. (My background is a BS in physics and an MS in mathematics.) My focus and interest have been in applied functional analysis in general and various kinds of abstract and concrete delay equations in particular. These are evolution equations which generate infinite dimensional (semi)dynamical systems. Like all doctorate candidates, I have acquired a certain amount of specialised knowledge and published certain results.

I would very much enjoy continuing doing applied functional analysis and teaching in an academic environment, but sometimes I find the focus on delay equations rather narrow. Recently I have been drawn to the fields of control theory and continuum mechanics, and I would be quite curious to learn more about the functional analytic aspects as well as the physical foundation of at least one of these two. Although these fields may be considered more or less tangent to my own field, on the level of specialisation they are quite different.

My question is: Have any of you, in a similar situation, pursued such a kind of new interest in an academic setting (e.g. as a post-doc) after the completion of your doctorate? How did that work out? Would you advise me to give into my curiosity? Or is current research too specialised for such excursions and am I just wasting my time and past efforts? I thank you for any sensible comments.

You need to find a niche in the new field in which your background can be a leverage. This will not only make the transition more likely, but also less problematic.

I went from a condensed matter background and into accelerator physics. But I found an area where someone with my background was actually needed. While this often will depend on luck and timing, knowing a lot more about the new field that you want to go into, what direction it is moving in, what big areas in that field that are "hot" or getting funding are important to see if you have a chance and opportunity to be hired with your background.

Zz.

 

[S.G. Janssens]

You need to find a niche in the new field in which your background can be a leverage. This will not only make the transition more likely, but also less problematic.

I went from a condensed matter background and into accelerator physics. But I found an area where someone with my background was actually needed. While this often will depend on luck and timing, knowing a lot more about the new field that you want to go into, what direction it is moving in, what big areas in that field that are "hot" or getting funding are important to see if you have a chance and opportunity to be hired with your background.

Thank you, Zz. I think your advice makes sense and is important.

Certainly in control theory delayed feedback plays an important role, but the perspective of synthesis is different from that of analysis, to which I'm used. More generally, it is my hope (and, a little bit, my expectation) that mathematical knowledge acquired while studying a certain class of infinite dimensional dynamical systems (i.e. delay equations (DE)) is also useful when studying other classes (i.e. certain types of PDE). However, one has to be careful, because although functional analysis and semigroup theory form a commom ground, upon closer inspection, the specific characteristics are usually quite different.

Mathematics aside, since about half a year I have become increasingly eager to turn attention again to applications in (classical) physics, where it once all started for me. I begin to find it important to do more than just writing down the DE / PDE ... and analysing it to bits. The link between the equation and the original physical considerations is, in my opinion, all too often forgotten in abstract analysis. It's not just a necessary evil, but may actually enrich the math.