I first met Toghrul at a Dynaverse Workshop, during his talk on “Decidability of logical theories” that unfolded with an almost deceptive lucidity. He has recently received the Ackermann Award for his doctoral dissertation, and today’s conversation is a chance to see whether my first impression of him holds when the blackboards are gone.
From “probably impossible” to “actually, maybe not”:
What problem did you set out to solve and why does it matter?
“When I first arrived at MPI from Oxford, Joël gave me an overview of roughly a decade of research into verification of linear dynamical systems,” Toghrul says. “And he asked a question that hadn’t been asked in this general form before: is it possible to algorithmically check whether a given linear dynamical system satisfies a given property — expressed, for example, in the language of linear temporal logic?”
“In other words: do there exist algorithms that take a mathematical model of a real-world system and a specification — say, ‘the system always remains in a safe state’ — and decide whether the system meets that specification?”
So the expectation, at least initially, was almost pessimistic.
“Consequently, we expected the problem to be undecidable,” Toghrul says, “provably impossible to solve algorithmically.”
Then comes the twist, told with his characteristic lack of drama.
“However, it turned out that we can, in fact, solve a substantial fragment of the problem,” he says, “through a combined application of ideas from number theory, automata theory, and symbolic dynamics.”
“That discovery opened up many new directions,” he adds, “and those directions became a large part of what we’ve been doing for the last six years.”
How would you describe your doctoral research journey? Was it difficult? Was it enriching? Was it both?
“I view my time as a PhD student as extremely fun, but tiring,” Toghrul says.
“I wouldn’t call it psychologically or technically very difficult,” he says, and then adds after a beat: “But by the time I defended, it had kind of become my whole personality.”
“As a postdoc now, I’ve been recovering back into a more balanced lifestyle,” he adds. Not as a complaint, but more like a small confession that even good phases can take over more of your life than you realise while you’re in them.
Can you recall a moment where an idea almost failed — or suddenly clicked? How did you navigate the uncertainty and setbacks?
Toghrul doesn’t romanticize setbacks, but he also doesn’t pretend they don’t exist.
“My way of dealing with difficulties and setbacks in academia, I think, is a common one. First of all, work on various different things, so that even if one project fails, the others are likely to bear fruit.”
“And then,” he continues, “slowly learn and improve over the long run. And have a thick skin, in general.”
By the end of this chapter (life as a PhD student), what did you learn about yourself as a researcher? What skill or mindset mattered most?
“The most important thing I learned during my PhD is to objectively place myself on the competence ladder of all researchers,” Toghrul says. “In short,” he adds, “I don’t have the impostor syndrome anymore. I am now objective about, and at peace with, the things I can do well and the things at which I am not very good.”
The Ackermann Award and the people who made the work possible
How would you describe your experience with collaborators? How did they shape your work?
“I have been blessed with a large number of collaborators,” Toghrul says, “and they are some of the nicest people around.”
He stresses that collaboration wasn’t just about dividing work. It actively shaped how he thinks.
“In addition to shaping my research ideas, I have often directly learned from them,” he says. He mentions in particular, Joris, Mihir, Mahmoud, Julian, his colleagues from the PhD years, as people he learned a great deal from, simply by working alongside them, day after day.
He also describes a collaboration that broadened the scope of his work beyond the immediate surroundings.
“I was involved in collaborative research with Professor Christel Baier’s group at TU Dresden, and that’s still going on through the large-scale, trans-regional research project called Center for Perspicuous Computing (CPEC).”
He recalls that the joint work felt mostly like taking exploratory baby steps at first.
“But over time, it ended up having a very strong impact on our usual research at MPI.”
He gives a concrete example: their collaboration led to new applications of o-minimality to dynamical systems, ideas that they “discovered together” and then fed back into their broader verification program. Finally, he mentions the work environment.
“I was fortunate to work at MPI-SWS while I was a PhD student at Saarland University. There I found a very stimulating environment.”
“You get to know a lot of people, listen to their talks, and discuss your ideas with them,” he says, “often crossing the boundaries of various disciplines of computer science.”
Congratulations for winning the Ackermann Award! What does it represent to you? Does it change anything?
“Obviously, I am super happy about co-receiving the Ackermann Award,” Toghrul says, grounded in his reaction.
“To me, it means that the larger theoretical computer science community appreciates the work we do at the Foundations of Algorithmic Verification research group at MPI-SWS.”
“It does make me more confident about the quality of my work,” he adds, “it makes me feel more assured about the direction I’m taking and my plans for the future.”
Looking ahead and passing it on
So, what are the big questions you want to tackle next?
“The ideas of my dissertation have now been applied in a couple of other contexts, for example, in showing the decidability of first-order or monadic second-order theories of various classical mathematical structures.”
He makes it sound almost casual, but you can hear the excitement in his voice: taking a toolbox built for one problem and finding where else it can open doors.
“What I want to do next is to apply ergodic theory, which I am learning as a postdoc working with Valérie Berthé, to fundamental problems in computer science, in conjunction with what I learned as a PhD student.”
What advice would you give future doctoral students?
“My advice would be to try to enjoy the PhD phase as much as possible,” he says.
He speaks about the PhD not just as a career step, but as a particular window in life: unusually open, unusually flexible in what you can absorb.
“It is a very distinctive time period when one can learn anything from anyone, and in my opinion, a bit too early to solely worry about publications.”
“I would also recommend trying to be as original as possible. After the PhD, the way one operates can become more restricted and influenced by external factors.”
If the conversation has a takeaway, it’s not “work harder” or “be brilliant.” It’s something simpler: stay curious for long enough that curiosity has time to turn into method. And if you’re lucky, it turns into solid work that other people recognize.
