Wednesday, 28 October
02:15 pm
Bielefeld University M4-122/126
Effect of Base Extension on Submodule Zeta Functions
Speaker: David Cormican
Oberseminar Gruppen und Geometrie
Let $R$ be a commutative ring and $\mathcal{A} \subseteq \mathrm{End}(R^n)$ a subalgebra of the endomorphisms of a free module over $R$. If $\mathfrak{U}$ is the set of finite index $\mathcal{A}$-invariant submodules of $R^n$, the submodule zeta function for $\mathcal{A}$ is formally defined as:
$$\zeta_{\mathcal{A}, R} (s) = \sum_{M \in \mathfrak{U}} [R^n:M]^{-s}$$
Earlier work has focused on the case where $R = \mathfrak{o}$ is compact discrete valuation ring and $\mathcal{A}$ is generated by a single element of $\mathrm{End}(R^n)$ and this situation is relatively well understood. This talk discusses recent work in which we computed explicit formulae for submodule zeta functions after extending the base ring to $\mathfrak{o}[X]/(X^m)$ for positive integer $m$ and efforts towards developing a general theory for the effect of such base extensions on zeta function.
03:30 pm
Bielefeld University M4-122/126
On the measure of verbal and definable sets in profinite groups
Speaker: Martina Conte
Oberseminar Gruppen und Geometrie
Given a group $G$, any word in $k$ variables gives rise to a word map from $G^k$ to $G$. The study of word maps is an active field of research in group theory, and a natural question to consider is how many elements (in a suitable sense) of a given group can be written as images of a given word map. In this talk I will report on joint work with Matteo Vannacci in which we investigate the (Haar) measure of the images of word maps in profinite groups, especially in free pro-$p$ and free profinite groups. More generally, we also consider the measure of certain existentially definable sets in the same classes of groups.
Tuesday, 3 November
04:00 pm
Bielefeld University U2-205
Heute Mathematik, morgen… Finbridge!
Speaker: Rico Heinemann
Orientierende Praxisstudien
08:00 pm
Bielefeld University Online
You are right, and I apologize
Speaker: Thomas Kahle
TRR 358 Seminar
Doing research changes the researcher. In this talk I will try to document my personal story with AI. I love computers and have been an early adopter of AI with a mostly positive outlook onto the future. Recently the picture has become a lot more grim.\\\\
This has two reasons. The first is that it is becoming clearer every day how we simply cannot extend the trust that we naturally have between mathematicians also to big tech. The second reason is that I observe changes in myself that I don't like.\\\\
I used to say that writing is thinking and I still believe it is true. But I also outsourced a lot of writing to the machine, feeding it notes and unfinished thoughts and then editing the result to sound more like me. For certain texts (like bureaucratic letters) this is certainly an efficient and acceptable way to proceed, but for my core thinking I want to learn to accept that this is a slow and messy human process.
Monday, 16 November
08:00 pm
Bielefeld University Online
AI is a tool: A working mathematician's experience and perspective
Speaker: Martin Raum
TRR 358 Seminar
I trace how AI entered my research workflow and how I refined the tools surrounding it. I focus on two comparatively mature aspects: manuscript review and infrastructure. For review, AI has become a useful component of my toolchain, while mathematical judgment remains with me as the researcher.\\\\
I also describe a workflow for human-guided, AI-generated research, focusing on joint work with Olav Richter and Matt Ortiz. This project served as a case study. Rather than relying on costly, opaque, specialized models, we used standard subscription-based AI tools to develop a workflow that can be adapted to other research projects in mathematics. The case study invites reflection on the need to increase the level of acceptable good to mid-level research and on a potential future for top-level research in mathematics.
Tuesday, 1 December
08:00 pm
Bielefeld University Online
Tba
Speaker: Emily Riehl
TRR 358 Seminar
tba
Tuesday, 15 December
08:00 pm
Bielefeld University online
tba
Speaker: Tony Feng
TRR 358 Seminar
tba
Tuesday, 12 January
08:00 pm
Bielefeld University online
tba
Speaker: Peter Scholze
TRR 358 Seminar
tba
Tuesday, 26 January
08:00 pm
Bielefeld University online
tba
Speaker: Geordie Williamson
TRR 358 Seminar
tba
Tuesday, 9 February
08:00 pm
Bielefeld University online
tba
Speaker: Daniel Litt
TRR 358 Seminar
tba