TopMath Award 2026 for Matthias Pfeifer

The TopMath Award is an award for doctoral candidates in the programme who have distinguished themselves through outstanding research achievements. It is awarded once a year. Following a proposal from their mentor or academic advisor, candidates are invited to submit their own application at the beginning of the winter semester. At its final meeting of the year, the TopMath Board selects the winner after extensive consultation. The TopMath Award is endowed with €500 and is presented at the TUM School of CIT's graduation ceremony. 
The winner of the  TopMath Award 2026 is Matthias Pfeifer (research group Algebra). We congratulate the winner and wish him continued success in the pursuit of his mathematical goals!

Text: Matthias Pfeifer

"My research is about deformations of geometric object. I examine special points on such objects, called singularities, and consider if and how the singularities change when the whole object is deformed.

An important class of singularities are so called quotient singularities. They appear when one takes the quotient of a smooth space by the action of a finite group acting on it. These singularities play a central role in the minimal model program and are the topic of the well known McKay correspondence. In 1974, Riemenschneider conjectured that under deformations, cyclic quotient singularities, while they may change slightly, will stay cyclic quotient singularities.

When I started it was already known that the conjecture is true in characteristic 0, as well as over more general fields in dimension 3 and higher. As there is nothing to show in dimensions 0 and 1, this left the case of dimension 2 open. Dimension 2 over fields of positive characteristic turned out to be particularly tricky. I developed new techniques to tackle this problem. Of utmost importance was the new characterization of cyclic quotient singularities I found, which made it possible to show that they can only deform to cyclic quotient singularities. This allowed me to prove Riemenschneiders long-standing conjecture in full generality."

Acknowledgement of the prize winner and his achievements

“The study of singularities is central to algebraic geometry and dates back well into the 19th century. There is a wide variety of theorems and conjectures in this field. One class of singularities is cyclic quotient singularities, which were studied intensively by Oswald Riemenschneider and his school in Hamburg in the 1970s. Matthias Pfeifer generalized one of Riemenschneider’s conjectures to arithmetic settings and proved it there. I was surprised by the very clever and elegant approach he devised for this problem. The academic community has also received this result very positively, and I know of at least one international expert in this field who admitted to me that he had already attempted (unsuccessfully) to prove this conjecture. I am convinced that Matthias Pfeifer is a worthy recipient of the 2026 TopMath Award in every respect.” Prof. Dr. Christian Liedtke, Mentor of Matthias Pfeifer