Mathematical Colloquium
Upcoming talks:
| Tue 2 Jun 2026, 16:30: Yvan Velenik (Université de Genève) TBA |
| TBA |
| Theresienstr. 39, München. Room A 027 |
| Tue 16 Jun 2026, 16:30: Shahar Mendelson (Texas A&M University) Mean estimation and beyond |
| Consider an unknown random vector X, taking values in R^d. Is it possible to "guess" its mean accurately if the only information one is given consists of N independent copies of X? More accurately, given an arbitrary norm on R^d, the goal is to find a mean estimation procedure: upon receiving a wanted confidence parameter \delta and N independent copies X_1,...,X_N of an unknown random vector X - that has a finite mean and covariance -, the procedure returns \hat{\mu} for which the error \| \hat{\mu} - E X\| is as small as possible with probability at least 1-\delta (with respect to the product measure). The mean estimation problem has been studied extensively over the years and I will present some of the ideas that have led to its solution (and to the solution of other questions of a similar flavour that I will outline). Two surprising facts are that in all these problems the obvious choices fail miserably (for mean estimation, that choice is N^{-1}\sum_{i=1}^N X_i); and, that the solution behaves as if the (arbitrary) random vector X were gaussian. ________________________________________ Invited by Prof. Holger Rauhut |
| Theresienstr. 39, München. Room A 027 |
| Thu 23 Jul 2026, 16:30: Kotaro Komatsu (University of Tsukuba) Introducing students to explorative aspects of proving in mathematical activity |
| Proving is a fundamental activity in mathematics, and its teaching has been widely discussed in mathematics education research. A central theme in this body of research concerns the transition from making or evaluating a conjecture to proving it, with proof construction often viewed as the ultimate goal of mathematical activity. However, proving also involves ongoing processes that extend beyond proof construction, including the revision and generalisation of proved statements. In this talk, I discuss these relatively understudied, explorative aspects of proving through two illustrative cases: one relates to Lakatos-style mathematical activity involving proofs and refutations in a secondary school context, and the other focuses on proof by mathematical induction at the undergraduate level. I also discuss implications for task design aimed at introducing explorative proving to students. ____________________ Invited by Prof. Stefan Ufer |
| Theresienstr. 39, München. Room A 027 |
All lectures are on Tuesdays at 4:30 pm in lecture hall A027 unless otherwise noticed.
Looking for past events? You may find them in the Munich Mathematical Calendar.